[Rachmaninoff]

I wanted to share with everyone a new personnel rating system I've developed as part of an ongoing project. I hope it is of interest. Warning: this post is a bit long. I may try to find another format for posting these in the future.

Introduction

In the olden times, I was aware of two personnel rating systems. One of them, designed by Helge "Wesley Crusher" Blohmer, assigned a value to each skill based on the ratio between its "demand" (how many cards call for it) and "supply" (how many personnel have it). Rare skills counted for more, as did skills commonly appearing on dilemmas and missions. There wre other scaling and adjustment factors, but that's the general idea. You can view the most recent update here (from PAQ era): algorithm and results.

Kathy "Major Rakal" McCracken designed an alternate system. The two main changes in her system are (1) only "demand" counts for valuing skills, not supply, and (2) demands are accounted differently by affiliation, since some skills appear more frequently on some affiliations' missions than others. Here is her algorithm and results as of Rules of Acquisition.

When I read about these systems, I couldn't decide which made more sense. The Major's argument was that Christopher Hobson's Computer Skill doesn't make Data's any less valuable, so why should "supply" matter at all? Computer Skill is valuable because of how many cards require it, not because of his rarely it's found. Wesley's system made intuitive sense as well: if there's only one personnel in the game that can provide a needed skill, surely that personnel is more useful than the endless ranks of unremarkable Premiere DipHoLes

(Diplomacy/Honor/Leadership)

personnel.

A few years ago, I reflected back on these questions, with the benefits of a bit more education and mathematical modeling experience. My motivating idea is that not all demands are created equal. Some skill demands you choose yourself; your mission requirements and skills to power your engines are examples of these. Other skill demands are imposed on you by your opponent, through dilemmas and other obstacles they throw in your way. The relative value of these has changed over time. In Premiere days both were important. Premiere dilemmas are generally terrible, as are Premiere personnel, so you very often can get through the dilemmas without having skills to solve the mission. (This still comes up in OTSD tournaments.) In Modern, the second kind of skill is the most important ones. Unless your crew has been massively thinned out, it's rare that you can fight your way through the dilemmas yet not have the skills to solve the mission.

The cause of this change is an interesting evolutionary story. Over time, personnel and dilemmas have gotten significantly stronger, because that's the only way new cards will be sold and used. An expansion with middling cards gets ignored. There is no similar pressure for missions, and indeed harder missions would be ignored and unused. The net result is that mission skills have shrunk to being almost an afterthought today; plan for the dilemmas and the missions will take care of themselves. In Premiere days, by contrast, strategy articles were written with formulas about how many copies of the mission skills you had to include!

I aim for my system to describe the Modern environment, so I will focus exclusively on skills required by dilemmas. (I will separately rate missions, to identify missions that give you the most bang-for-the-buck if you are focused on dilemma skills.) This is one way that not all demands are created equal. Another is that not all dilemmas are created equal. Strong dilemmas should count for more than weak dilemmas when it comes to deciding what skills are important. This means that I will be rating dilemmas alongside personnel.

The strength of dilemmas and personnel are mutually dependent on each other. A dilemma's strength is based both on its consequences (how bad if it hits) and the difficulty of its requirements (the probability that a randomly-selected crew or Away Team can meet them). But crews are not "randomly selected," rather stronger personnel are more likely to appear in your deck and in play. What makes a strong personnel? One who has skills that appear on dilemmas you are likely to face. And again, dilemmas are not "randomly selected," rather your opponent is choosing dilemmas aiming to cause you the maximum amount of pain. Both you and your opponent are acting strategically; the dilemmas you are likely to face affect the personnel you choose, and vice versa. This is the dilemma metagame, and this is what I want to model and solve.

If you're interested in more detail, I can share a longer writeup with equations and definitions. Mathematically, this is what's known as a fixed-point problem; economists would recognize this as a game-theoretic equilibrium. I also wanted to improve my Python skills, so I put together some scripts to do the calculations for me, and I hope to get these in a shareable state before long. Like most projects, this has become a much larger beast than I originally intended. The game has also grown much larger than in its past. To keep things manageable, I will be adding cards in one expansion at a time, so today's update just covers Premiere. I hope to add expansions at a rate of about one a week, but that's probably optimistic.

Without further ado, here are the ratings, again just Premiere for now. Happy to answer any questions or hear any thoughts you may have!

Personnel

Note: You'll find some non-Personnel in this list. I am counting other cards that can help nullify dilemmas as a "generalized Personnel," including equipment and even cards like The Devil (which can nullify Wind Dancer!). Again, this list shows the personnel most helpful in overcoming dilemmas.

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1    Vekor                               [Non]      Premiere                  100
2    Roga Danar                          [Non]      Premiere                  81
3    Dr. Reyga                           [Non]      Premiere                  78
4    Mirok                               [Rom]      Premiere                  76
5    Data                                [Fed]      Premiere                  71
6    Worf                                [Fed]      Premiere                  69
7    Varel                               [Rom]      Premiere                  68
8    Geordi La Forge                     [Fed]      Premiere                  68
9    Jean-Luc Picard                     [Fed]      Premiere                  67
10   Kurak                               [Kli]      Premiere                  66
11   Neela Daren                         [Fed]      Premiere                  65
12   N'Vek                               [Rom]      Premiere                  65
13   Dr. Selar                           [Fed]      Premiere                  64
14   T'Pan                               [Fed]      Premiere                  62
15   Taibak                              [Rom]      Premiere                  62
16   Wesley Crusher                      [Fed]      Premiere                  62
17   Beverly Crusher                     [Fed]      Premiere                  60
18   Sito Jaxa                           [Fed]      Premiere                  56
19   Albert Einstein                     [Fed]      Premiere                  56
20   Hannah Bates                        [Fed]      Premiere                  56
21   Jera                                [Rom]      Premiere                  55
22   Taitt                               [Fed]      Premiere                  55
23   Sir Isaac Newton                    [Fed]      Premiere                  55
24   Soren                               [Fed]      Premiere                  54
25   Etana Jol                           [Non]      Premiere                  54
26   Calloway                            [Fed]      Premiere                  54
27   Tarus                               [Rom]      Premiere                  53
28   Jo'Bril                             [Non]      Premiere                  53
29   Leah Brahms                         [Fed]      Premiere                  53
30   Richard Galen                       [Fed]      Premiere                  53
31   Divok                               [Kli]      Premiere                  53
32   Koroth                              [Kli]      Premiere                  52
33   Torin                               [Kli]      Premiere                  52
34   Dr. Leah Brahms                     [Fed]      Premiere                  52
35   Vekma                               [Kli]      Premiere                  52
36   Dr. La Forge                        [Fed]      Premiere                  52
37   Toby Russell                        [Fed]      Premiere                  52
38   Dukath                              [Kli]      Premiere                  51
39   Alyssa Ogawa                        [Fed]      Premiere                  51
40   Kurn                                [Kli]      Premiere                  51
41   William T. Riker                    [Fed]      Premiere                  51
42   Simon Tarses                        [Fed]      Premiere                  50
43   J'Ddan                              [Kli]      Premiere                  50
44   Mendon                              [Fed]      Premiere                  49
45   Bok                                 [Non]      Premiere                  48
46   Takket                              [Rom]      Premiere                  48
47   Jenna D'Sora                        [Fed]      Premiere                  48
48   Sarek                               [Fed]      Premiere                  47
49   Dr. Farek                           [Non]      Premiere                  47
50   Tasha Yar                           [Fed]      Premiere                  46
51   Palteth                             [Rom]      Premiere                  44
52   Reginald Barclay                    [Fed]      Premiere                  44
53   Medical Tricorder                              Premiere                  43
54   Tebok                               [Rom]      Premiere                  43
55   Pardek                              [Rom]      Premiere                  42
56   Medical Kit                                    Premiere                  42
57   Jaron                               [Rom]      Premiere                  42
58   Narik                               [Non]      Premiere                  42
59   Riva                                [Fed]      Premiere                  41
60   Kareel Odan                         [Fed]      Premiere                  41
61   Linda Larson                        [Fed]      Premiere                  40
62   Sela                                [Rom]      Premiere                  40
63   Taul                                [Rom]      Premiere                  38
64   Alynna Nechayev                     [Fed]      Premiere                  38
65   Satelk                              [Fed]      Premiere                  37
66   Eric Pressman                       [Fed]      Premiere                  37
67   Fleet Admiral Shanthi               [Fed]      Premiere                  37
68   Darian Wallace                      [Fed]      Premiere                  37
69   Gorath                              [Kli]      Premiere                  37
     Kle'eg                              [Kli]      Premiere                  37
71   Taurik                              [Fed]      Premiere                  36
72   Ro Laren                            [Fed]      Premiere                  36
73   McKnight                            [Fed]      Premiere                  35
74   Deanna Troi                         [Fed]      Premiere                  35
75   Exocomp                             [Fed]      Premiere                  35
76   Tomalak                             [Rom]      Premiere                  35
77   Kromm                               [Kli]      Premiere                  34
78   Gowron                              [Kli]      Premiere                  34
79   Tomek                               [Rom]      Premiere                  34
80   Thomas Riker                        [Fed]      Premiere                  34
81   K'Ehleyr                            [Fed]      Premiere                  33
82   Evek                                [Non]      Premiere                  33
83   K'Tesh                              [Kli]      Premiere                  33
84   Gorta                               [Non]      Premiere                  32
85   Toreth                              [Rom]      Premiere                  32
86   Engineering PADD                               Premiere                  31
87   K'mpec                              [Kli]      Premiere                  31
88   Ocett                               [Non]      Premiere                  30
89   Engineering Kit                                Premiere                  30
90   Bochra                              [Rom]      Premiere                  28
91   Devinoni Ral                        [Non]      Premiere                  27
92   Alidar Jarok                        [Rom]      Premiere                  26
93   Vagh                                [Kli]      Premiere                  26
94   Kargan                              [Kli]      Premiere                  26
95   K'Vada                              [Kli]      Premiere                  26
96   K'Tal                               [Kli]      Premiere                  26
97   Interphase Generator                           Premiere                  26
98   Christopher Hobson                  [Fed]      Premiere                  25
99   Baran                               [Non]      Premiere                  25
100  Torak                               [Kli]      Premiere                  25
101  Toq                                 [Kli]      Premiere                  25
102  Konmel                              [Kli]      Premiere                  24
     Nu'Daq                              [Kli]      Premiere                  24
104  Tricorder                                      Premiere                  24
105  Morag                               [Kli]      Premiere                  24
106  Klag                                [Kli]      Premiere                  23
107  B'iJik                              [Kli]      Premiere                  22
108  Giusti                              [Fed]      Premiere                  22
109  Duras                               [Kli]      Premiere                  22
110  Amarie                              [Non]      Premiere                  22
111  Koral                               [Kli]      Premiere                  21
112  B'Etor                              [Kli]      Premiere                  21
113  Shelby                              [Fed]      Premiere                  21
114  L'Kor                               [Kli]      Premiere                  20
115  Varon-T Disruptor                              Premiere                  19
116  Lwaxana Troi                        [Fed]      Premiere                  19
117  Benjamin Maxwell                    [Fed]      Premiere                  19
118  Ishara Yar                          [Non]      Premiere                  18
119  Nikolai Rozhenko                    [Fed]      Premiere                  18
120  Lursa                               [Kli]      Premiere                  18
121  Parem                               [Rom]      Premiere                  18
122  Korris                              [Kli]      Premiere                  17
123  Ba'el                               [Kli]      Premiere                  17
124  Tallus                              [Rom]      Premiere                  17
125  Tokath                              [Rom]      Premiere                  16
126  Norah Satie                         [Fed]      Premiere                  16
127  Morgan Bateson                      [Fed]      Premiere                  16
128  Movar                               [Rom]      Premiere                  16
129  Galathon                            [Rom]      Premiere                  16
130  Fek'lhr                             [Kli]      Premiere                  15
131  Selok                               [Rom]      Premiere                  15
132  Mendak                              [Rom]      Premiere                  15
133  Thei                                [Rom]      Premiere                  15
134  Neral                               [Rom]      Premiere                  15
135  Vash                                [Fed]      Premiere                  14
136  Kahless                             [Kli]      Premiere                  14
137  Batrell                             [Kli]      Premiere                  14
138  Sirna Kolrami                       [Fed]      Premiere                  14
139  Toral                               [Kli]      Premiere                  13
140  Generic PADD                                   Premiere                  12
141  Generic Phaser/Disruptor                       Premiere                  12
142  Alexander Rozhenko                  [Fed]      Premiere                  11
143  Tam Elbrun                          [Fed]      Premiere                  10
144  Mot the Barber                      [Fed]      Premiere                  9
145  Kell                                [Kli]      Premiere                  8
146  Vulcan Mindmeld                                Premiere                  8
147  The Devil                                      Premiere                  4
148  Emergency Transporter Armbands                 Premiere                  2

Dilemmas

Note: You'll find some non-Dilemmas in here as well; I call a "generalized Dilemma" anything that your opponent can choose to make your life more difficult, that can be overcome with skills or other personnel features. I have omitted any dilemma that cannot be overcome with the right skills and features, so you won't see classics like Borg Ship and Cytherians appear. Cytherians is a great dilemma, but doesn't impact the personnel you choose to build a deck.

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1    Shaka, When the Walls Fell               Premiere   100
2    Q-Net                                    Premiere   97
3    Radioactive Garbage Scow                 Premiere   91
4    Alien Parasites                          Premiere   62
5    Ancient Computer                         Premiere   62
6    Hyper-Aging                              Premiere   61
7    Matriarchal Society                      Premiere   61
8    Barclay's Protomorphosis Disease         Premiere   61
9    Nagilum                                  Premiere   57
10   Temporal Causality Loop                  Premiere   53
11   Time Travel Pod                          Premiere   51
12   Hologram Ruse                            Premiere   49
13   Null Space                               Premiere   46
14   Chalnoth                                 Premiere   42
15   Impassable Door                          Premiere   42
16   Microvirus                               Premiere   38
17   Menthar Booby Trap                       Premiere   38
18   Nausicaans                               Premiere   36
19   Microbiotic Colony                       Premiere   34
20   Anaphasic Organism                       Premiere   33
21   Archer                                   Premiere   32
22   Birth of "Junior"                        Premiere   32
23   Gravitic Mine                            Premiere   31
24   Tarellian Plague Ship                    Premiere   30
25   Wind Dancer                              Premiere   29
26   Rebel Encounter                          Premiere   29
27   El-Adrel Creature                        Premiere   28
28   Temporal Rift                            Premiere   26
29   Q                                        Premiere   26
30   Crystalline Entity                       Premiere   24
31   REM Fatigue Hallucinations               Premiere   24
32   Neural Servo Device                      Premiere   23
33   Plasma Fire                              Premiere   22
34   Warp Core Breach                         Premiere   19
35   Firestorm                                Premiere   19
36   Two-Dimensional Creatures                Premiere   15
37   Armus - Skin of Evil                     Premiere   12
38   Tsiolkovsky Infection                    Premiere   12
39   Nitrium Metal Parasites                  Premiere   11
40   Phased Matter                            Premiere   10
41   Male's Love Interest                     Premiere   10
42   Tetryon Field                            Premiere   9
43   Nanites                                  Premiere   9
44   Alien Abduction                          Premiere   9
45   Portal Guard                             Premiere   5
46   Iconian Computer Weapon                  Premiere   5
47   Cosmic String Fragment                   Premiere   3
48   Ktarian Game                             Premiere   1

Skills

Here are the top 10 personnel skills that are most helpful to have to overcome dilemmas, considering the dilemma severity (listed above) and how many dilemmas require them.

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1    SCIENCE                                  0.201
2    MEDICAL                                  0.184
3    SECURITY                                 0.131
4    ENGINEER                                 0.114
5    Diplomacy                                0.078
6    Computer Skill                           0.045
7    Navigation                               0.041
8    Music                                    0.033
9    OFFICER                                  0.021
10   Female                                   0.019

Missions

I rate missions by dividing the number of points possible by the number of personnel you need to have in play before you have a 50% likelihood of meeting the mission requirements, assuming the probability a personnel is in play is proportional to the scores above. Top-rated missions give you a lot of points for their difficulty, assuming you are only selecting personnel based on helpfulness in overcoming dilemmas. Low-rated missions are the opposite; but if you are worried about mission stealing the missions at the bottom of the list are great choices! An opponent is unlikely to be able to solve them without specifically planning to do so.

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1    Pegasus Search                           Premiere                       3.41
2    Investigate Massacre                     Premiere                       3.23
3    Explore Black Cluster                    Premiere                       3.20
4    Explore Typhon Expanse                   Premiere                       3.17
5    Fever Emergency                          Premiere                       3.15
6    Investigate Disturbance                  Premiere                       3.06
7    Investigate Disappearance                Premiere                       3.03
8    Excavation                               Premiere                       3.02
9    Diplomacy Mission                        Premiere                       2.99
10   Study "Hole in Space"                    Premiere                       2.87
11   Covert Rescue                            Premiere                       2.78
12   Relief Mission                           Premiere                       2.70
13   Covert Installation                      Premiere                       2.63
14   Krios Suppression                        Premiere                       2.59
15   Test Mission                             Premiere                       2.48
16   Investigate Raid                         Premiere                       2.40
17   Cloaked Mission                          Premiere                       2.35
18   Wormhole Negotiations                    Premiere                       2.33
19   Seek Life-form                           Premiere                       2.30
20   Investigate Anomaly                      Premiere                       2.29
21   Study Plasma Streamer                    Premiere                       2.21
22   Restore Errant Moon                      Premiere                       2.21
23   Extraction                               Premiere                       2.17
24   Repair Mission                           Premiere                       2.15
25   Investigate Sighting                     Premiere                       2.13
26   Avert Disaster                           Premiere                       2.11
27   Secret Salvage                           Premiere                       2.08
28   Iconia Investigation                     Premiere                       2.08
29   Study Lonka Pulsar                       Premiere                       2.05
30   Survey Mission                           Premiere                       2.01
31   Evaluate Terraforming                    Premiere                       1.97
32   Study Nebula                             Premiere                       1.91
33   Explore Dyson Sphere                     Premiere                       1.90
34   Plunder Site                             Premiere                       1.90
35   Cultural Observation                     Premiere                       1.86
36   Investigate "Shattered Space"            Premiere                       1.85
37   Medical Relief                           Premiere                       1.84
38   Evacuation                               Premiere                       1.81
39   Study Stellar Collision                  Premiere                       1.69
40   Investigate Alien Probe                  Premiere                       1.67
41   Khitomer Research                        Premiere                       1.58
42   Investigate Rogue Comet                  Premiere                       1.52
43   Hunt for DNA Program                     Premiere                       1.51
44   Sarthong Plunder                         Premiere                       1.47
45   Strategic Diversion                      Premiere                       1.24
46   Expose Covert Supply                     Premiere                       1.21
47   New Contact                              Premiere                       0.88
48   First Contact                            Premiere                       0.85
49   Investigate Time Continuum               Premiere                       0.62

Statistics

For each affiliation, I computed the mean and standard deviation of personnel scores. I've counted these two ways -- the affiliation by itself, and the affiliation with non-aligned support. It's very clear that Decipher intended to use non-aligned personnel to even out imbalances among the affiliations, so it's only fair to count them accordingly. I've also computed a weighted mean which I think is more representative than the pure mean. There are a lot of crappy Premiere personnel, but most of them never see play for that reason. The weighted mean is computed as the expected value of the personnel that would appear in play, if the probability of stocking a personnel is proportional to their score. The weighted mean is at least as large as the unweighted mean.

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            Alone                               with Non-Aligned
            n   Mean (Stdev)    WeightedMean    n   Mean (Stdev)    WeightedMean
Federation  57  41.91 (16.95)   48.77           72  42.76 (18.50)   50.76
Klingon     37  29.87 (14.08)   36.51           52  34.51 (18.69)   44.63
Romulan     27  36.08 (18.29)   45.34           42  39.61 (20.72)   50.45

I've also included a histogram showing the distribution of personnel scores by affiliation. Each "bin" corresponds to a range of personnel scores.



Discussion

The really valuable "skills" to have are the big dilemma-busting classifications: ENGINEER, MEDICAL, SCIENCE, and SECURITY, and any personnel that has two of these is going to be really handy to have. Diplomacy is also helpful even though it's demanded on only two generalized dilemmas (Shaka and Q-Net) -- either one of these can wreck your day if you aren't prepared.

You may be surprised that many of the bridge crew don't rank all that high. The highest are Data (5) and Worf (6), with Geordi in 8th and the infamous six-skilled Picard only coming up 9th! Remember, this system is only looking at dilemma requirements, so for the earlier sets it will be less accurate for assessing value. Picard's double Diplomacy is invaluable for Shaka and Q-Net, but he's otherwise unremarkable as a dilemma buster. His six skills certainly help with missions, but we aren't accounting for those in these ratings.

Instead, top billing goes to three non-aligned personnel: Vekor, Roga Danar, and Dr. Reyga, all of them dual-classification (and both classifications critical for dilemmas). Perhaps the infamous early Federation bias wasn't quite as bad as it was made out to be! Conventional wisdom also has that Romulans were terrible, although according to the scores above they're much better at getting through dilemmas than Klingons! Of course, Klingons had battle as an alternate strategy.

The top dilemmas are what you would expect, again keeping in mind that Cytherians are left off, along with anything else without requirements for overcoming. Shaka, Q-Net, Radioactive Garbage Scow, Alien Parasites, and Ancient Computer are exactly what you needed to be prepared for in the Premiere days.

The most point-efficient missions (assuming you're picking personnel only with dilemmas in mind) are Pegasus Search, Investigate Massacre, and Explore Black Cluster; the least are Investigate Time Continuum, First Contact, and New Contact.

Again, happy to hear any thoughts you might have, and to answer any questions! I hope to add in Alternate Universe in another week or so.

[SirDan]

Great read, interesting data, and well presented. I'm looking forward to this being a weekly series as you trek through the past.

[Takket]

I was going to try doing something exactly like this, so, glad I did not since you've already done the work! LOL

Like you my idea was to weigh personnel vs dilemmas. I don't know if you are planning to do this, but my plan was to ask, politely, if CC has dilemma selection data. I know they keep the top 10 on the Affiliation HQ page. So a skill would get weighted more based on the prevalence of the dilemma in the meta.

Rules of Obedience is the #3 dilemma right now. So the skills on that dilemma are slightly more valuable than those on Scientific Method which is #10.

Likewise I would not even assign any value to a skill on dilemmas that are never used. Computer Skill, for example, is getting value because it appears on V'Ger, but it isn't getting any ADDITIONAL value because it appears on Impassible Door, which nobody is using in Modern.

You could probably just take into the account the top 100 dilemmas (ignoring non-skill dilemmas like Cytherians) and have a pretty decent list of personnel.

From there I was going to further break it down by property logo since Lore may be pretty badass but he's going to ruin your deck.

[Taibak]

Can you clarify whether or not your algorithm takes affiliation into account when judging a skill's value? I mean, a dilemma that requires Treachery is going to be quite difficult for a Federation crew, but trivial for Romulans.

[BCSWowbagger]

If you're interested in more detail, I can share a longer writeup with equations and definitions.

As someone who has attempted this in the past (and even created a database with every skill requirement on every dilemma for the purpose at one point), I would be very interested in this, even though I am afraid the math will turn out to be beyond me.

[Rachmaninoff]

Thanks for the repsonses, everyone!

@SirDan: Thanks! This started 4 years ago as a pandemic project that I've worked on in fits and starts (sometimes with breaks of over a year), and I'm hoping making a public post will give me an incentive to keep the momentum going.

@Takket: This is exactly the kind of thing I'm trying to do, except determing dilemma strength endogenously rather than looking to see what's actually being used. If I had that data, it would be very easy to incorporate (and in fact make my job easier since I wouldn't have to estimate dilemma scores). You've hinted at some other ways this kind of analysis can be used, and indeed I've been thinking about them too.

Once the "rating engine" is up and running, I can see it being a component of other tools: optimizing personnel selection (the smallest number of personnel to meet given skill targets); engine-based personnel selection (given a specified number of play engines and corresponding personnel, minimize the number needed to meet skill targets while balancing the number of free-plays evenly among the engines); a dilemma simulator; and a dilemma combo finder (using the simulator to identify tricky combos). I used the code to build a janky alpha-test dilemma simulator to help me with the Gauntlet contest over the summer.

@Taibak: It does not take affiliation into account. The rationale is that when you are building a deck and choosing dilemmas, you don't know the affiliation you will face. (A shame, all those Maman Picards have been sitting in the binder forever!) What you do know is the general metagame in your area, so you have an idea of the probability distribution for what you'll see; and that's represented in my algorithm by assuming that the likelihood each personnel is in a crew/Away Team is proportional to their score. (This does mean that if one affiliation has significantly stronger or weaker personnel than another, they will be correpsondingly more/less likely to appear, which will affect dilemma difficulty anad scores.)

@BCSWowbagger: The general idea is like this. Each personnel is given a score; the scores are normalized so that the most valuable personnel has a score of 100. I assume the probability that any personnel will show up in a crew or Away Team is directly proportional to their score (twice the score, twice as likely to appear). I do the same with dilemmas.

For the moment, assume that the personnel scores are known. From this, I calculate a dilemma score taking into account (1) the consequence of failing the dilemma ("cannot get past unless" counts much more than "stops one personnel (your choice), mission continues") and (2) the probability that a crew/Away Team of an assumed size (6 by default) cannot meet the requirements, assuming that the composition of this crew is random but weighted according to the personnel scores. The dilemma score is just the "consequence" score multiplied by the probability that it hits.

Now assume that we've done this, and we have dilemma scores. From these, we can compute personnel scores. Symmetrically, we assume that the dilemmas you face will be randomly chosen, but weighted according to the dilemma scores. This gives a weighted demand for each skill, and personnel scores are calculated based on how helpful their skills are (given the dilemma scores).

So there's a chicken-and-egg problem; personnel scores affect dilemma scores and vice versa. So we do some iteration to try to find an equilibrium matching "demand" and "supply".

That's the gist, but there are a number of corner cases involving dilemmas that only care about a subset of the team ("one personnel with STRENGTH>9"; "STRENGTH>27 from up to four personnel"), cards that grant skills conditionally (Kits, Tricorders, Vulcan Mindmeld), "wildcards" like K'chiQ, wildcards that depend on what's already there (Lal), downloads, so on, and so forth. I actually got the basic engine written in a few weekends, all the long development gaps were me getting bogged down with deciding how to handle an odd case and then getting sidetracked.

If you really want ALL the details, I've attached a PDF writeup and a ZIP file with the current code. (Edit: forum won't let me upload PDFs, so I put in the ZIP under doc/stccgrates.pdf) I caution that I wasn't planning to share these quite yet, so they're not entirely tidy and polished... in particular the writeup can't decide whether it's a "treatise on personnel scoring" or "development notes for me" or a software user manual, and the code has gotten a bit messy. I'm willing to suppress my inner perfectionist and share it as long as you keep in mind that they're a work in progress!

[BCSWowbagger]

Anything laid out like a white paper in Official White Paper Font is prepared enough for publication in my book.

Thanks for this (and the ELI5 explanation you just gave is more helpful than anything, I'll bet). Will enjoy!

[FranklinKenter]

One minor LaTeX suggestion:

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\newcommand{\card}[1]{\href{https://www.trekcc.org/1e/browsersearch.php?search=#1}{\sffamily{#1}}}

[Taibak]

@Rachmaninoff: Perhaps, but I think you're putting the cart before the horse here. Skills aren't necessarily evenly distributed across every affiliation. Thus, a skill might be more valuable for one affiliation than they would be for another - and it's why I think you need to focus on the personnel more than the dilemmas.

Take Skullduggery as an example. It's not a great card, but if I'm building a Federation deck it's a real threat to my mission attempts. That's because its requirements (Treachery, Greed, Smuggling, or INTEGRITY < 5) are quite rare among Alpha Quadrant Feds. On the other hand, they're quite common among the Ferengi. As such, it stands to reason that a personnel with Treachery might be more valuable to a Federation deck than it would be to a Ferengi deck.

Now this wasn't much of an issue with Premiere because, as you said, dilemmas tended to go back to the five classifications you mentioned, apart from a few oddballs like Shaka, Crystalline Entities in space, and Matriarchal Society, but it becomes more of an issue as you start adding in later sets. Cardassian Trap, for instance, is comparatively easy for the Federation, because they have access to the most Empathy personnel. Skullduggery, on the other hand, is comparatively easy for the Ferengi, who tend to have more Greed, Treachery, and Smuggling. I'm not saying they're necessarily great dilemmas, but they should impact the ratings.

No maybe this becomes less of an issue as the number of Non-Aligned personnel has increased, but if I'm building a deck, I'm absolutely taking into account how rare a dilemma-busting skill is for the affiliations I'm playing.

[FranklinKenter]

This is quite impressive. I developed something similar internally for designers to design dilemmas 10 or so years ago, but it assumed the personnel pool was static, but otherwise estimated the effectiveness of a dilemma based on the probability it would trigger. I used existing widely-played dilemmas to calibrate it.

I have a few substantial comments, and probably more to come.

Then the probability that a feature $f$ appears at some level $i$ is approximately given by a Poisson distribution with mean $n S(f)$, independent of the level of any other feature:\footnote{Technically, I'm assuming that the Away Team consists of a great number of ``infinitesimal'' personnel, and passing to the limit.}
\begin{equation}
\label{eqn:poissonpmf}
\Pr(\mbox{feature $f$ appears $i$ times})=\frac{e^{-nS(f)} (nS(f))^i}{i!}
\,.
\end{equation}

I think it would not be appropriate to model attributes with a Poisson distribution. If X~Poisson$(\lambda)$, then X has mean $\lambda$ and standard deviation $\sqrt{\lambda}$. However, I do not believe that the mean and variance for attributes coincide well enough to do this, especially CUNNING and to a lesser extent STRENGTH. Hence, an extra degree of freedom would be best, and for attributes you should have

\begin{equation}
\Pr(\mbox{feature $f$ appears at least $i$ times}) \approx 1-\Phi^{-1}\left(\frac{i-\mu_f}{\hat \sigma_f}\right)
\,.
\end{equation}
where $\Phi^{-1}$ is the inverse normal CDF, $\hat mu_f$ is the sample mean of feature $f$ among 6 personnel and $\hat \sigma_f$ is the sample standard deviation for feature $f$, both as measured by $\vec x$

Assume that the dilemma scores $y_d$ are known.
The demand functions are given by this formula, which uses the normalized dilemma scores:
\begin{equation}
\label{eqn:demandfunction}
...
D(f,i) = \sum_{d : i_d(f) > 0} \hat{y}_d \min \left\{\frac{i}{i_d(f)}, 1 \right\}
\end{equation}
where $i_d(f)$ is the level of feature $f$ required on dilemma $d$.

I am very skeptical of your choice for the demand function. Namely, the mere existence of a dilemma will necessarily increase the demand for those skills even if that dilemma is exactly the same. The runs counter to the premise that the score vector is supposedly a mixed-strategy vector for the personnel and dilemma "players'' In fact, I changed the data files to duplicate the Shaka, When the Walls Fell aptly named "Shaka, When the Walls Fell 2" and again with "Shaka, When the Walls Fell 3" and from 2 to 3 it only reduced from 100 to 91, implying that "Shaka, X" should be played 35% more (200 to 273) just because there are now more versions of it.

With that, I guess one of the main criticisms is that it is not clear what, if anything, is your objective function or even what the model is that necessitates a fixed-point algorithm. Without that, it is hard to determine how to interpret the output. The algorithm appears to converge to two mixed-strategies, but those strategies don't seem to coincide with optimal strategic choices. For an extreme example, I added a WALLx20 dilemma that required Barbering. While Mot the Barber and the "Shorten the Hair" dilemma scored 100, there relative probabilities do not indicate an optimal strategy: "Shorten the Hair" would almost always be played (next was Shaka at 3) whereas Vekor was still at 25, indicating that Mot was still showing up less then he should in order to overcome all of those copes of "Shorten the Hair".

I believe the main culprit here is that the implied objective functions for personnel and dilemmas are different. Dilemmas are trying to maximize the expected score. On the other hand, personnel are trying to optimize some sort of linearized variation of the expected score. For instance in an extreme scenario, if there the only a dilemmas that require [skill] requires [skill] x3 but yet all personnel with that skill have [skill] x2, all of those personnel get 2/3 of the credit. However, this scenario is functionally the same as though all of the dilemmas require [skill] x2 and personnel have [skill], but the current demand function only grants 1/2 of the credit. Hence, the full benefit of adding more of a skill (e.g. "the demand") is not accurately captured by $D$. In another extreme example, if every dilemma required [skill] (in addition to other skills) but yet most all personnel had [skill], the probability that that dilemma would have it effects as a result of lacking [skill] is small. Yet, because of the quasi linearization, everyone with that skill gets the same benefit never mind the fact that that skill is not actually needed anymore.

There are probably many solutions to this.

Probably the most mathematically sound way is to back up and explicitly define the objective functions for the "dilemma" and "personnel" players. The most canonical example would be to maximize (resp. minimize) the expected score of encountering a dilemma. You are already do this for dilemmas, though for personnel it will be slightly more complicated. But in any case, this results is in a zero-sum two player game that should be fairly straightforward to solve. The arguments of the optimal solution give you your scores. For better or for worse, this method will score any card that is strictly worse than another card as 0. The main advantage here is that any additional constraint you want to add can simply be placed as a constraint within this zero-sum game. For instance, you can require that the "personnel" player only use personnel of one affiliation (save non-aligned); or looking forward, that no more than one third of the personnel play for free to a particular; or that at least 25\% of the personnel have command stars, etc. etc. The downside is that you may have to resort to "black boxes" (e.g. Gurobi, etc.) to numerically solve these.

Another way is to weight the demand by the estimated gradient for each skill. Namely, for each feature $i$, define
\[ \delta_i = \frac{ \mathbb{E} \mathcal{S}_{+1 i} (\vec x, \vec y) - \mathbb{E} \mathcal{S}_{-1 i} (\vec x, \vec y)}{2} \]
where $\mathbb{E} \mathcal{S}_{+1 i} (\vec x, \vec y)$ is the expected score with one "free" instance of feature $i$ and $\mathbb{E} \mathcal{S}_{-1 i} (\vec x, \vec y)$ is the expected score with one instance of feature $i$ removed. This estimates the net benefit of one additional/net penalty of one less instance of that feature. If this estimated slope is practically zero, that feature will have no consideration on how to adjust the personnel population. Even if this is not 100% mathematically consistent, it solve the issue with the later example above: If a skill is oversubscribed, it's marginal demand is very small.

[jadziadax8]

Hawt.

[Rachmaninoff]

Thanks for the continued feedback! I appreciate the suggestions.

@Taibak and @FranklinKenter's feedback both get at a fundamental difficulty I've been struggling to resolve. In particular, I share Franklin's skepticism about my demand function, and have tried a few other candidates in the past that I found even more unsatisfactory. The root issue is that scoring an individual dilemma is much easier than scoring an individual personnel.

Scoring an individual dilemma is fairly straightforward: given a distribution of personnel, estimate the probability that they meet the requirements and go from there. By contrast, an individual personnel is much harder to evaluate in isolation from the larger pool. Most dilemmas require a team of several personnel to overcome; so how do we gauge the helpfulness of a single personnel card without considering all the others as well (or the pool available to that affiliation, or with a given engine.)

The most consistent way to address this is to score personnel simultaneously as a group, together with optimizing the personnel in a deck, rather than independently as I've done. As I understand Taibak and FranklinKenter's posts (and please let me know if I've misunderstood), both of you are proposing distinct approaches to doing so.

Taibak's idea is to identify how helpful a given personel is relative to their affiliation, given a known set of dilemma requirements. This would presumably need to be paired with an "affiliation choice" model so that when we return to the dilemma scoring, we can compute the probability that, say, Picard appears as Pr(Picard | playing ) * Pr(playing ). I'm a bit hesitant to do this, for two reasons: (1) the number of possible personnel pools will start to get out of hand once we start considering Treaties, different play engines, and so forth and (2) properly computing the probability of playing an affiliation/faction in a game-theoretic way is not obvious, especially given correlations among different subfactions/engines within the same affiliation. I'll admit to having thought about this only superficially, but one approach might involve a discrete choice model that can handle correlations among alternatives, e.g. a nested logit or some such. I'd be interested to hear any thoughts on paths forward with this approach.

Franklin's idea is to simultaneously score personnel by computing a mixed strategy to optimize an explicit objective. (In my system there is an implicit mapping from the score I compute to probabilities that cards appear, but without grounding on fundamental principles.) Again, I've not thought deeply about how to do this, but it seems computationally daunting. The similar problem to "identify the smallest group of personnel that meets a skill matrix" is NP-hard

(the set covering problem is a special case)

. There are probably some good heuristics out there; I did something very simple along these lines for the Gauntlet contest and there are surely much more clever approaches.

All this is to say that I could not think of an easy way to score personnel as a group, so I took a different tack akin to Wesley and the Major: compute the value of individual features in some way, and then construct a personnel score by summing the scores of the features they posseess. Franklin's suggestion at the end is alternative, better-grounded way to do this, and I will think on it some more.

For an extreme example, I added a WALLx20 dilemma that required Barbering. While Mot the Barber and the "Shorten the Hair" dilemma scored 100, there relative probabilities do not indicate an optimal strategy: "Shorten the Hair" would almost always be played (next was Shaka at 3) whereas Vekor was still at 25, indicating that Mot was still showing up less then he should in order to overcome all of those copes of "Shorten the Hair".]

...

For better or for worse, this method will score any card that is strictly worse than another card as 0.

I would argue that "strict dominance" should not result in 0 scores, either for dilemmas or personnel. The 2-copy dilemma rule in Modern means that you'll still want some Vekors even in a Shorten the Hair environment, and (at least for unique personnel) there's still room for Riker because you won't stock Picard x10 in a deck. This is not a strong argument in favor of my system

(reality has feature X, therefore models with feature X are ipso facto preferable is a frustratingly common fallacy)

, but rather a critique of models where strict dominance reflects in arbitrarily large score differences. The "proper" way to account for this might be to add constraints in the strategy set in the game, but I don't know what the algorithmic implications are.

An alternative is to distinguish more clearly between the *scores* (which should exhibit a range of values to provide meaningful comparisons at all points on the spectrum) and the mapping between scores and the probability distributions used for a mixed-strategy equilibrium (which need not). Strict dominance may be less of an issue in the strategy than in the scoring.

(The 2-dilemma limit also makes me less concerned about the Shaka X counterexamples. If there are multiple Shaka clones out there, then I really do need to be prepared to stock double Diplomacy rather than go after a different mission. Whereas in a "one-shot" attempt Franklin is absolutely right that dilemma clones should not affect the optimal strategy.)

Again, I greatly appreciate the feedback and this has given me a lot to mull over. To avoid losing momentum, for the time being I will continue adding expansions and tweaking the existing code to handle them, or else I fear I'll never get out of the gate. (The fastest way to distract an academic is to dangle a shiny, fancier model in front of them!) But I will keep thinking over these alternatives. Would be very interested if Taibak, Franklin, or anyone else wants to implement a demonstration or prototype of an alternative system and see how the results compare.

[Taibak]

To be honest, I don't think taking affiliation into account will be prohibitively difficult.

For instance, you mention play engines, but I really don't think that's an issue. I mean, Tasha Yar isn't going to suddenly gain skills just because you're using Continuing Mission. What the engines will do is let you break down the data set into smaller pieces. Instead of running one big sample with every personnel in an expansion, you can run each affiliation separately. For instance, you've done Premiere, so instead of one big sample you could do three smaller samples for and , and , and and . That shouldn't be that hard.

As you add more sets in, you can break it down even further. You could (and probably should) do a sample that covers all personnel, but you could also do smaller data sets for and , and , and so forth.

And here's why I think this is critical. Let's assume that there's a dilemma that kills all my personnel unless I have 2 Greed present. For most affiliations that's not really a problem because there are plenty of options out there. On the other hand, let's say I'm running a deck based on Battle Stations: Sovereign Class. Suddenly, I have to run Lisa Azar and Nicky the Nose because they're quite literally the only personnel available with Greed. Every other viable affiliation, sub-affiliation, and faction has more Greed personnel available to them, so the skill is less valuable, but for it would be critical for my hypothetical Federation deck.

Granted, that's an extreme case, but hopefully it gets the point across.

As for cards that let you mix affiliations, that's still just plugging in another chunk of data into the module. It will take time, yes, but I don't think it should be all that difficult. Honestly, I don't even know if Treaties are played enough to make that worth while, but I'd at least run it for and cards because of Here By Invitation. It's just a question of how much work you want to put in to make the model viable.

[Rachmaninoff]

@Taibak

I agree that certain skills are scarcer for some affiliations than others, and that this is a consideration when picking personnel for a deck. But I don't think it's as easy an adjustment as you make it sound.

It is straightforward to repeat the analysis with smaller pools of personnel, say, one for each affiliation. The hard part is reconciling the dilemma scores, which will be different each time. Your hypothetical dilemma would have a high score when doing the analysis with the Federation pool, and a lower score when run with the Klingon and Romulan pools. The dilemma score is a critical element of the personnel rating (higher-rated dilemmas count more than lower-rated ones when determining the value of a feature), and it needs to be the same across all three pools of personnel (because when choosing dilemmas, you don't know the affiliation you will face). So how can we come up with a single dilemma score from the three different runs?

The naive approach would be to average the scores across the three pools. Even doing this means a nontrivial change to the codebase -- we need to add in an additional level of nesting to identify subpools from the larger one, score them separately, average dilemma scores and iterate; and it's not immediately obvious whether this nesting should happen outside or inside the current iterative scheme. I call this approach naive because it neglects the fact that stronger affiliations are more likely to be chosen, so the weighting of dilemma scores should take the personnel scores into account somehow. (The dynamic of "Romulans die to Firestorm" -> "Firestorm is a strong dilemma" -> "Actually nobody plays Romulans so Firestorm isn't that good after all".) I have some fuzzy ideas about how to do this properly, using game theory, or discrete choice, or some such, but this also does not appear trivial, especially because there are correlations between the strength of the factions (nonaligned personnel common to the pools, or Treaties, etc.)

For the moment, I'm sidestepping these difficulties by computing scores in a way that lets me calculate a personnel's score independent of the larger pool from which they're drawn, based only on the dilemma scores. The upside is computational; one downside (among others) is that you can't directly use the scores to decide, say, which 15 personnel you should include in your deck to maximize your chance of getting through dilemmas, or the smallest group of personnel you need to hit a skill matrix. Both of those problems are computationally daunting (the latter is NP-hard), and I'm not ready to tackle them (yet). I suspect my scoring system can be used to build some good heuristics for those problems, but that's a task for future work.

By the way, I very possibly could be wrong about the difficulty of doing this. I would be thrilled if you can find a good way, and I'm happy to give you some pointers on working with the code if you want to try it out yourself. I would be very interested to see the differences in the scores generated by my method so far, and an alternative method that you propose.

[Rachmaninoff]

Here's the update for Alternate Universe!

Before diving into the analysis, I want to thank those who have given me feedback. I've been taking notes and at some point in the future may revisit some things in the engine, but none of my thoughts are fully-developed enough yet to write out (let alone implement). So for now, the calculations are proceeding as before.

Tables first, analysis below. (PS: Does anybody know a way to put formatted tables into a forum post? Right now I'm putting plain text in code blocks, but if I could do an HTML table it would be a whole lot more readable.)

Personnel

Code: Select all

1    Vekor                               Premiere                  [Non]       100  100 +0
2    Data                                Premiere                  [Fed]        71   94 +23
3    Roga Danar                          Premiere                  [Non]        81   92 +12
4    Dr. Reyga                           Premiere                  [Non]        78   80 +2
5    Geordi La Forge                     Premiere                  [Fed]        68   79 +12
6    Mirok                               Premiere                  [Rom]        76   78 +2
7    Beverly Crusher                     Premiere                  [Fed]        60   78 +18
8    Wesley Crusher                      Premiere                  [Fed]        62   76 +14
9    Beverly Picard                      Alternate Universe        [Fed]             71 (new)
10   Worf                                Premiere                  [Fed]        69   71 +2
11   Tasha Yar - Alternate               Alternate Universe        [Fed]             70 (new)
12   Dr. Selar                           Premiere                  [Fed]        64   70 +6
13   Governor Worf                       Alternate Universe        [Kli]             69 (new)
14   Takket                              Premiere                  [Rom]        48   66 +17
15   Rachel Garrett                      Alternate Universe        [Fed]             65 (new)
16   Varel                               Premiere                  [Rom]        68   64 -3
17   Sito Jaxa                           Premiere                  [Fed]        56   63 +7
18   Jera                                Premiere                  [Rom]        55   63 +8
19   Richard Galen                       Premiere                  [Fed]        53   63 +10
20   Taibak                              Premiere                  [Rom]        62   62 +0
21   Leah Brahms                         Premiere                  [Fed]        53   62 +9
22   J'Ddan                              Premiere                  [Kli]        50   62 +12
23   Kurak                               Premiere                  [Kli]        66   61 -5
24   Divok                               Premiere                  [Kli]        53   61 +8
25   N'Vek                               Premiere                  [Rom]        65   61 -4
26   Calloway                            Premiere                  [Fed]        54   61 +7
27   Neela Daren                         Premiere                  [Fed]        65   61 -5
28   Dr. Leah Brahms                     Premiere                  [Fed]        52   61 +8
29   Dr. La Forge                        Premiere                  [Fed]        52   60 +9
30   T'Pan                               Premiere                  [Fed]        62   60 -2
31   Bok                                 Premiere                  [Non]        48   60 +11
32   Jean-Luc Picard                     Premiere                  [Fed]        67   59 -8
33   Alyssa Ogawa                        Premiere                  [Fed]        51   58 +7
34   Simon Tarses                        Premiere                  [Fed]        50   58 +7
35   Montgomery Scott                    Alternate Universe        [Fed]             58 (new)
36   Lt. (j.g.) Picard                   Alternate Universe        [Fed]             57 (new)
37   Toby Russell                        Premiere                  [Fed]        52   57 +5
38   Vekma                               Premiere                  [Kli]        52   57 +5
39   Jo'Bril                             Premiere                  [Non]        53   56 +3
40   Etana Jol                           Premiere                  [Non]        54   55 +1
41   Dathon                              Alternate Universe        [Non]             55 (new)
42   Medical Tricorder                   Premiere                               43   55 +12
43   Dr. Farek                           Premiere                  [Non]        47   55 +8
44   Jenna D'Sora                        Premiere                  [Fed]        48   53 +6
45   Albert Einstein                     Premiere                  [Fed]        56   53 -3
46   Tasha Yar                           Premiere                  [Fed]        46   52 +6
47   Koroth                              Premiere                  [Kli]        52   52 -0
48   Sir Isaac Newton                    Premiere                  [Fed]        55   52 -3
49   Hannah Bates                        Premiere                  [Fed]        56   52 -4
50   Taitt                               Premiere                  [Fed]        55   51 -4
51   Soren                               Premiere                  [Fed]        54   50 -4
52   Jaron                               Premiere                  [Rom]        42   50 +8
53   Reginald Barclay                    Premiere                  [Fed]        44   50 +6
54   Tarus                               Premiere                  [Rom]        53   49 -4
55   Palteth                             Premiere                  [Rom]        44   49 +5
56   Torin                               Premiere                  [Kli]        52   49 -3
57   Taul                                Premiere                  [Rom]        38   49 +11
58   Dukath                              Premiere                  [Kli]        51   48 -4
59   Linda Larson                        Premiere                  [Fed]        40   48 +8
60   Eric Pressman                       Premiere                  [Fed]        37   47 +10
61   Narik                               Premiere                  [Non]        42   47 +5
62   Ian Andrew Troi                     Alternate Universe        [Fed]             47 (new)
63   Medical Kit                         Premiere                               42   47 +5
64   Mendon                              Premiere                  [Fed]        49   46 -3
65   Kurn                                Premiere                  [Kli]        51   46 -5
66   William T. Riker                    Premiere                  [Fed]        51   46 -5
67   Darian Wallace                      Premiere                  [Fed]        37   45 +8
68   Ajur                                Alternate Universe        [Non]             45 (new)
69   Taurik                              Premiere                  [Fed]        36   44 +8
70   Sarek                               Premiere                  [Fed]        47   43 -4
71   Gorath                              Premiere                  [Kli]        37   43 +6
     Kle'eg                              Premiere                  [Kli]        37   43 +6
73   Exocomp                             Premiere                  [Fed]        35   42 +7
74   Sela                                Premiere                  [Rom]        40   42 +2
75   Gorta                               Premiere                  [Non]        32   41 +9
76   Pardek                              Premiere                  [Rom]        42   41 -2
77   Kromm                               Premiere                  [Kli]        34   41 +6
78   Boratus                             Alternate Universe        [Non]             40 (new)
79   Tomek                               Premiere                  [Rom]        34   40 +6
80   K'Tesh                              Premiere                  [Kli]        33   39 +6
81   Deanna Troi                         Premiere                  [Fed]        35   39 +3
82   Tebok                               Premiere                  [Rom]        43   38 -4
83   Baran                               Premiere                  [Non]        25   38 +13
84   Kareel Odan                         Premiere                  [Fed]        41   37 -3
85   Ro Laren                            Premiere                  [Fed]        36   37 +2
86   Engineering Kit                     Premiere                               30   36 +7
87   Riva                                Premiere                  [Fed]        41   36 -5
88   Nu'Daq                              Premiere                  [Kli]        24   35 +11
89   Satelk                              Premiere                  [Fed]        37   35 -2
90   Major Rakal [Fed]                   Alternate Universe        [Rom][Fed]        35 (new)
91   Jack Crusher                        Alternate Universe        [Fed]             35 (new)
92   McKnight                            Premiere                  [Fed]        35   35 -1
93   Devinoni Ral                        Premiere                  [Non]        27   35 +8
94   Alynna Nechayev                     Premiere                  [Fed]        38   34 -4
95   Fleet Admiral Shanthi               Premiere                  [Fed]        37   34 -3
96   Engineering PADD                    Premiere                               31   33 +2
97   Maques                              Alternate Universe        [Non]             32 (new)
98   Commander Tomalak                   Alternate Universe        [Rom]             32 (new)
99   Thomas Riker                        Premiere                  [Fed]        34   32 -2
100  Shelby                              Premiere                  [Fed]        21   31 +11
101  Tomalak                             Premiere                  [Rom]        35   31 -4
102  Evek                                Premiere                  [Non]        33   31 -2
103  Gowron                              Premiere                  [Kli]        34   31 -3
104  Mendak                              Premiere                  [Rom]        15   31 +16
105  Tricorder                           Premiere                               24   30 +6
106  K'Ehleyr                            Premiere                  [Fed]        33   30 -3
107  K'mtar                              Alternate Universe        [Kli]             30 (new)
108  Toreth                              Premiere                  [Rom]        32   30 -2
109  Bochra                              Premiere                  [Rom]        28   29 +1
110  Ocett                               Premiere                  [Non]        30   28 -2
111  B'Etor                              Premiere                  [Kli]        21   28 +7
112  K'mpec                              Premiere                  [Kli]        31   28 -3
113  Duras                               Premiere                  [Kli]        22   27 +6
114  Richard Castillo                    Alternate Universe        [Fed]             26 (new)
115  Paul Rice                           Alternate Universe        [Fed]             26 (new)
116  Lwaxana Troi                        Premiere                  [Fed]        19   26 +7
117  Morag                               Premiere                  [Kli]        24   26 +2
118  Toq                                 Premiere                  [Kli]        25   26 +1
119  Major Rakal [Rom]                   Alternate Universe        [Rom][Fed]        25 (new)
120  Vagh                                Premiere                  [Kli]        26   25 -1
121  K'Vada                              Premiere                  [Kli]        26   25 -1
122  Kargan                              Premiere                  [Kli]        26   25 -1
123  Alidar Jarok                        Premiere                  [Rom]        26   24 -2
124  Christopher Hobson                  Premiere                  [Fed]        25   24 -1
125  Ishara Yar                          Premiere                  [Non]        18   24 +5
126  Konmel                              Premiere                  [Kli]        24   24 -1
127  Nikolai Rozhenko                    Premiere                  [Fed]        18   23 +5
128  K'Tal                               Premiere                  [Kli]        26   23 -2
129  Lursa                               Premiere                  [Kli]        18   23 +6
130  Giusti                              Premiere                  [Fed]        22   23 +1
131  Torak                               Premiere                  [Kli]        25   22 -3
132  Klag                                Premiere                  [Kli]        23   22 -1
133  Galathon                            Premiere                  [Rom]        16   22 +6
134  Parem                               Premiere                  [Rom]        18   21 +4
135  Movar                               Premiere                  [Rom]        16   21 +6
136  Interphase Generator                Premiere                               26   21 -4
137  B'iJik                              Premiere                  [Kli]        22   21 -1
138  Amarie                              Premiere                  [Non]        22   21 -1
139  Neral                               Premiere                  [Rom]        15   21 +6
140  Ba'el                               Premiere                  [Kli]        17   20 +3
141  Koral                               Premiere                  [Kli]        21   20 -1
142  L'Kor                               Premiere                  [Kli]        20   20 -0
143  Berlingoff Rasmussen                Alternate Universe        [Non]             20 (new)
144  Vash                                Premiere                  [Fed]        14   20 +5
145  Stefan DeSeve [Fed]                 Alternate Universe        [Rom][Fed]        20 (new)
146  Selok                               Premiere                  [Rom]        15   19 +4
147  Fek'lhr                             Premiere                  [Kli]        15   19 +4
148  Stefan DeSeve [Rom]                 Alternate Universe        [Rom][Fed]        19 (new)
149  Benjamin Maxwell                    Premiere                  [Fed]        19   19 +0
150  Howard Heirloom Candle              Alternate Universe                          18 (new)
151  Generic Phaser/Disruptor            Premiere                               12   18 +7
152  Tokath                              Premiere                  [Rom]        16   18 +1
153  Tam Elbrun                          Premiere                  [Fed]        10   18 +8
154  Korris                              Premiere                  [Kli]        17   17 -0
155  Varon-T Disruptor                   Premiere                               19   17 -3
156  Lakanta                             Alternate Universe        [Non]             17 (new)
157  Data's Head                         Alternate Universe                          17 (new)
158  D'Tan                               Alternate Universe        [Rom]             16 (new)
159  Norah Satie                         Premiere                  [Fed]        16   16 +0
160  Tallus                              Premiere                  [Rom]        17   16 -1
161  Morgan Bateson                      Premiere                  [Fed]        16   16 -0
162  Toral                               Premiere                  [Kli]        13   16 +2
163  Kahless                             Premiere                  [Kli]        14   15 +1
164  Sirna Kolrami                       Premiere                  [Fed]        14   15 +0
165  Thei                                Premiere                  [Rom]        15   15 -0
166  Batrell                             Premiere                  [Kli]        14   14 -0
167  Alexander Rozhenko                  Premiere                  [Fed]        11   13 +2
168  Kell                                Premiere                  [Kli]         8   13 +4
169  Alternate Universe Door             Alternate Universe                          12 (new)
170  Mickey D.                           Alternate Universe        [Non]             12 (new)
171  Generic PADD                        Premiere                               12   11 -1
172  Devidian Foragers                   Alternate Universe                           9 (new)
173  Destroy Radioactive Garbage Scow    Alternate Universe                           9 (new)
174  Mot the Barber                      Premiere                  [Fed]         9    9 +1
175  Vulcan Mindmeld                     Premiere                                8    7 -1
176  Thermal Deflectors                  Alternate Universe                           7 (new)
177  Eyes in the Dark                    Alternate Universe                           7 (new)
178  Targ                                Alternate Universe        [Kli]              6 (new)
179  I.P. Scanner                        Alternate Universe                           5 (new)
180  Humuhumunukunukuapua'a              Alternate Universe                           4 (new)
181  Yellow Alert                        Alternate Universe                           4 (new)
182  The Devil                           Premiere                                4    3 -0
183  Emergency Transporter Armbands      Premiere                                2    2 +0
184  Jamaharon                           Alternate Universe                           2 (new)
185  Edo Vessel                          Alternate Universe                           1 (new)

The biggest winners and losers (tables show old score, new score, and difference). Note that all scores in this system are relative and scaled from 0-100; an increase or decrease is relative to the rest of the pool, not about absolute strength.

Code: Select all

1    Data                                Premiere                  [Fed]        71   94 +23
2    Beverly Crusher                     Premiere                  [Fed]        60   78 +18
3    Takket                              Premiere                  [Rom]        48   66 +17
4    Mendak                              Premiere                  [Rom]        15   31 +16
5    Wesley Crusher                      Premiere                  [Fed]        62   76 +14
6    Baran                               Premiere                  [Non]        25   38 +13
7    J'Ddan                              Premiere                  [Kli]        50   62 +12
8    Geordi La Forge                     Premiere                  [Fed]        68   79 +12
9    Medical Tricorder                   Premiere                               43   55 +12
10   Roga Danar                          Premiere                  [Non]        81   92 +12

Code: Select all

176  Hannah Bates                        Premiere                  [Fed]        56   52 -4
177  Sarek                               Premiere                  [Fed]        47   43 -4
178  Interphase Generator                Premiere                               26   21 -4
179  Tebok                               Premiere                  [Rom]        43   38 -4
180  Neela Daren                         Premiere                  [Fed]        65   61 -5
181  Kurn                                Premiere                  [Kli]        51   46 -5
182  William T. Riker                    Premiere                  [Fed]        51   46 -5
183  Kurak                               Premiere                  [Kli]        66   61 -5
184  Riva                                Premiere                  [Fed]        41   36 -5
185  Jean-Luc Picard                     Premiere                  [Fed]        67   59 -8

Dilemmas

Code: Select all

1    Empathic Echo                       Alternate Universe                         100 (new)
2    Q-Net                               Premiere                               97   81 -17
3    Shaka, When the Walls Fell          Premiere                              100   80 -20
4    Radioactive Garbage Scow            Premiere                               91   76 -16
5    Alien Labyrinth                     Alternate Universe                          71 (new)
6    Zaldan                              Alternate Universe                          69 (new)
7    Ancient Computer                    Premiere                               62   60 -3
8    Malfunctioning Door                 Alternate Universe                          59 (new)
9    Conundrum                           Alternate Universe                          57 (new)
10   Matriarchal Society                 Premiere                               61   54 -7
11   Hyper-Aging                         Premiere                               61   53 -8
12   Temporal Causality Loop             Premiere                               53   53 -0
13   Alien Parasites                     Premiere                               62   52 -10
14   Barclay's Protomorphosis Disease    Premiere                               61   50 -10
15   Nagilum                             Premiere                               57   48 -9
16   Time Travel Pod                     Premiere                               51   43 -8
17   Null Space                          Premiere                               46   41 -5
18   Hologram Ruse                       Premiere                               49   40 -8
19   Impassable Door                     Premiere                               42   38 -4
20   Hidden Entrance                     Alternate Universe                          38 (new)
21   Chalnoth                            Premiere                               42   35 -6
22   Menthar Booby Trap                  Premiere                               38   31 -6
23   Nausicaans                          Premiere                               36   31 -5
24   Microbiotic Colony                  Premiere                               34   30 -4
25   Microvirus                          Premiere                               38   30 -8
26   Gravitic Mine                       Premiere                               31   30 -1
27   Birth of "Junior"                   Premiere                               32   27 -5
28   Wind Dancer                         Premiere                               29   27 -2
29   Coalescent Organism                 Alternate Universe                          26 (new)
30   Anaphasic Organism                  Premiere                               33   26 -7
31   Archer                              Premiere                               32   26 -6
32   Cardassian Trap                     Alternate Universe                          26 (new)
33   Thought Fire                        Alternate Universe                          25 (new)
34   Tarellian Plague Ship               Premiere                               30   25 -5
35   Rebel Encounter                     Premiere                               29   24 -5
36   Crystalline Entity                  Premiere                               24   23 -2
37   El-Adrel Creature                   Premiere                               28   22 -6
38   Q                                   Premiere                               26   22 -4
39   Temporal Rift                       Premiere                               26   22 -4
40   REM Fatigue Hallucinations          Premiere                               24   20 -4
41   Neural Servo Device                 Premiere                               23   19 -4
42   Outpost Raid                        Alternate Universe                          17 (new)
43   Plasma Fire                         Premiere                               22   16 -6
44   Parallel Romance                    Alternate Universe                          16 (new)
45   Firestorm                           Premiere                               19   16 -3
46   Isabella                            Alternate Universe                          16 (new)
47   Warp Core Breach                    Premiere                               19   16 -3
48   The Gatherers                       Alternate Universe                          14 (new)
49   Two-Dimensional Creatures           Premiere                               15   14 -1
50   Worshiper                           Alternate Universe                          12 (new)
51   Nitrium Metal Parasites             Premiere                               11   12 +0
52   Frame of Mind                       Alternate Universe                          11 (new)
53   Armus - Skin of Evil                Premiere                               12   11 -2
54   Interphasic Plasma Creatures        Alternate Universe                          11 (new)
55   Tsiolkovsky Infection               Premiere                               12   10 -2
56   Rascals                             Alternate Universe                          10 (new)
57   Phased Matter                       Premiere                               10    9 -0
58   Nanites                             Premiere                                9    9 -0
59   Tetryon Field                       Premiere                                9    8 -1
60   Male's Love Interest                Premiere                               10    8 -1
61   Ferengi Attack                      Alternate Universe                           8 (new)
62   Alien Abduction                     Premiere                                9    7 -2
63   Iconian Computer Weapon             Premiere                                5    6 +1
64   Portal Guard                        Premiere                                5    4 -2
65   Quantum Singularity Lifeforms       Alternate Universe                           3 (new)
66   Cosmic String Fragment              Premiere                                3    3 -0
67   Ktarian Game                        Premiere                                1    1 -0

The biggest winners and losers. Again note that all scores in this system are relative and scaled from 0-100; an increase or decrease is relative to the rest of the pool, not about absolute strength.

Code: Select all

1    Iconian Computer Weapon             Premiere                                5    6 +1
2    Nitrium Metal Parasites             Premiere                               11   12 +0
3    Nanites                             Premiere                                9    9 -0
     Ktarian Game                        Premiere                                1    1 -0
     Temporal Causality Loop             Premiere                               53   53 -0
     Phased Matter                       Premiere                               10    9 -0
     Cosmic String Fragment              Premiere                                3    3 -0     

Code: Select all

63   Barclay's Protomorphosis Disease    Premiere                               61   50 -10
64   Alien Parasites                     Premiere                               62   52 -10
65   Radioactive Garbage Scow            Premiere                               91   76 -16
66   Q-Net                               Premiere                               97   81 -17
67   Shaka, When the Walls Fell          Premiere                              100   80 -20

Skills

Here are the top 10 personnel skills that are most helpful to have to overcome dilemmas, considering the dilemma severity (listed above) and how many dilemmas require them.

Code: Select all

1	MEDICAL	        0.177
2	SCIENCE	        0.153
3	SECURITY	    0.135
4	ENGINEER	    0.121
5	Diplomacy	    0.053
6	Exobiology	    0.048
7	any Tricorder	0.036
8	disruptor	    0.035
9	Computer Skill	0.035
10	Navigation	    0.031

Missions

Code: Select all

1    Pegasus Search                      Premiere                             3.41 3.50 +0.08
2    Investigate Disturbance             Premiere                             3.06 3.27 +0.21
3    Investigate Massacre                Premiere                             3.23 3.25 +0.01
4    Explore Black Cluster               Premiere                             3.20 3.18 -0.02
5    Fever Emergency                     Premiere                             3.15 3.17 +0.03
6    Explore Typhon Expanse              Premiere                             3.17 3.15 -0.02
7    Excavation                          Premiere                             3.02 3.01 -0.00
8    Diplomacy Mission                   Premiere                             2.99 3.01 +0.01
9    Study "Hole in Space"               Premiere                             2.87 2.94 +0.07
10   Covert Rescue                       Premiere                             2.78 2.89 +0.11
11   Investigate Disappearance           Premiere                             3.03 2.86 -0.17
12   Warped Space                        Alternate Universe                        2.83 (new)
13   Covert Installation                 Premiere                             2.63 2.80 +0.18
14   Krios Suppression                   Premiere                             2.59 2.66 +0.07
15   Wormhole Negotiations               Premiere                             2.33 2.52 +0.18
16   Investigate Raid                    Premiere                             2.40 2.48 +0.08
17   Relief Mission                      Premiere                             2.70 2.43 -0.27
18   Cloaked Mission                     Premiere                             2.35 2.42 +0.07
19   Test Mission                        Premiere                             2.48 2.38 -0.11
20   Seek Life-form                      Premiere                             2.30 2.36 +0.07
21   Investigate Anomaly                 Premiere                             2.29 2.35 +0.06
22   Restore Errant Moon                 Premiere                             2.21 2.34 +0.13
23   Investigate Sighting                Premiere                             2.13 2.23 +0.10
24   Extraction                          Premiere                             2.17 2.19 +0.03
25   Study Plasma Streamer               Premiere                             2.21 2.17 -0.05
26   Repair Mission                      Premiere                             2.15 2.16 +0.01
27   Compromised Mission                 Alternate Universe                        2.06 (new)
28   Iconia Investigation                Premiere                             2.08 2.05 -0.04
29   Secret Salvage                      Premiere                             2.08 2.01 -0.08
30   Evaluate Terraforming               Premiere                             1.97 1.99 +0.02
31   Plunder Site                        Premiere                             1.90 1.93 +0.03
32   Avert Disaster                      Premiere                             2.11 1.90 -0.21
33   Medical Relief                      Premiere                             1.84 1.87 +0.03
34   Evacuation                          Premiere                             1.81 1.85 +0.04
35   Study Lonka Pulsar                  Premiere                             2.05 1.84 -0.21
36   Explore Dyson Sphere                Premiere                             1.90 1.83 -0.07
37   Khitomer Research                   Premiere                             1.58 1.78 +0.20
38   Diplomatic Conference               Alternate Universe                        1.77 (new)
39   Investigate "Shattered Space"       Premiere                             1.85 1.75 -0.10
40   Cultural Observation                Premiere                             1.86 1.73 -0.12
41   Study Nebula                        Premiere                             1.91 1.70 -0.20
42   Qualor II Rendezvous                Alternate Universe                        1.69 (new)
43   Survey Mission                      Premiere                             2.01 1.68 -0.33
44   FGC-47 Research                     Alternate Universe                        1.64 (new)
45   Investigate Rogue Comet             Premiere                             1.52 1.55 +0.02
46   Investigate Alien Probe             Premiere                             1.67 1.53 -0.13
47   Hunt for DNA Program                Premiere                             1.51 1.52 +0.01
48   Sarthong Plunder                    Premiere                             1.47 1.48 +0.01
49   Study Stellar Collision             Premiere                             1.69 1.42 -0.27
50   First Contact                       Premiere                             0.85 1.42 +0.56
51   Strategic Diversion                 Premiere                             1.24 1.29 +0.05
52   Expose Covert Supply                Premiere                             1.21 1.25 +0.04
53   Fissure Research                    Alternate Universe                        1.14 (new)
54   New Contact                         Premiere                             0.88 1.14 +0.26
55   Risa Shore Leave                    Alternate Universe                        0.67 (new)
56   Investigate Time Continuum          Premiere                             0.62 0.64 +0.02
57   Brute Force                         Alternate Universe                        0.46 (new)
58   Quash Conspiracy                    Alternate Universe                        0.21 (new)
59   Reunion                             Alternate Universe                        0.17 (new)

The biggest winners and losers:

Code: Select all

1    First Contact                       Premiere                             0.85 1.42 +0.56
2    New Contact                         Premiere                             0.88 1.14 +0.26
3    Investigate Disturbance             Premiere                             3.06 3.27 +0.21
4    Khitomer Research                   Premiere                             1.58 1.78 +0.20
5    Wormhole Negotiations               Premiere                             2.33 2.52 +0.18

Code: Select all

55   Study Lonka Pulsar                  Premiere                             2.05 1.84 -0.21
56   Avert Disaster                      Premiere                             2.11 1.90 -0.21
57   Study Stellar Collision             Premiere                             1.69 1.42 -0.27
58   Relief Mission                      Premiere                             2.70 2.43 -0.27
59   Survey Mission                      Premiere                             2.01 1.68 -0.33

Statistics

For each affiliation, I computed the mean and standard deviation of personnel scores. I've counted these two ways -- the affiliation by itself, and the affiliation with non-aligned support. It's very clear that Decipher intended to use non-aligned personnel to even out imbalances among the affiliations, so it's only fair to count them accordingly. I've also computed a weighted mean which I think is more representative than the pure mean. There are a lot of crappy personnel, but most of them never see play for that reason. The weighted mean is computed as the expected value of the personnel that would appear in play, if the probability of stocking a personnel is proportional to their score. The weighted mean is at least as large as the unweighted mean.

Note the values in parentheses now show the change from before, rather than the standard deviation.


By affiliation:

Code: Select all

	        Alone					            with non-Aligned				
	        n	Mean (diff)	    WeightedMean	n	Mean (diff)	    WeightedMean	
Federation	70	44.63 (2.72)	52.52 (+3.75)	92	44.6 (+1.84)	53.46	(+2.70)
Klingon	    40	36.38 (6.51)	39.41 (+2.90)	62	31.79 (-2.72)	46.83	(+2.20)
Romulan	    33	39.67 (3.59)	44.67 (-0.67)	55	44.72 (+5.11)	49.97	(-0.48)

By set:

Code: Select all

PERSONNEL           n   Mean (stdev)    WeightedMean
Premiere            136 40.78 (19.26)   49.88
Alternate Universe  25  37.21 (19.21)   47.13

DILEMMAS            n   Mean (stdev)    WeightedMean
Premiere            48  28.30 (20.16)   42.67
Alternate Universe  19  29.47 (26.60)   53.48

MISSIONS (0-100)    n   Mean (stdev)    WeightedMean
Premiere            49  62.42 (18.57)   67.94
Alternate Universe  10  36.15 (23.92)   51.98

Here is an updated histogram showing the distribution of scores by affiliation.



Discussion

So, what's new with Alternate Universe? The big change is the introduction of a new king dilemma. Shaka and Q-Net have been bumped down a bit, both because of a number of new Diplomats (including Dathon, who can pass Shaka by himself), but also because Empathic Echo proves a stronger wall! Surprised? You're in good company; you would have had that in common with most of the field at '97 Worlds. This was shortly after Decipher clarified the dilemma resolution rules, so that the lack of "Discard dilemma" at the end meant Empathic Echo was a *wall* requiring SECURITY and MEDICAL. (It's also the first kill-wall of the game!) A lot of players didn't realize it, but Dave Bowling and Todd Soper (#1 and #2) both stocked multiples of Empathic Echo to counter the redshirting that was rampant at the time, alongside the standard Shakas. If a redshirting deck faced Shaka, it was usually just a one-turn delay Tent-ing for Dathon; Empathic Echo posed a bigger challenge, since no one personnel could pass it at the time. (Todd did stock a Plexing in his Tent, though!)

AU introduced a number of other strong new dilemmas: Alien Labyrinth, Zaldan (another kill-wall!), Malfunctioning Door, and Conundrum all hit the top 10. The presence of these dilemmas significantly boosted Data into the #2 personnel position; he has ENGINEER for Alien Labyrinth, Exobiology for Zaldan, and a Soong-type android for Malfunctioning Door. Roga Danar was also a big winner (SECURITY for Empathic Echo, ENGINEER for Alien Labyrinth, high STRENGTH for Malfunctioning Door), as were Beverly Crusher and Takket (MEDICAL for Empathic Echo, Exobiology for Zaldan). DipHoLes tended to drop a bit in score; Shaka/Q-Net were still strong dilemmas, but nowhere near as dominant as in Premiere.

While AU did bring a number of strong dilemmas, on the whole the personnel were actually slightly weaker than in Premiere. You had some strong new dilemma-busters like Beverly Picard, Montgomery Scott, Rachel Garrett, and Dathon; but a number of personnel with specialized uses but not great for dilemmas -- Targ, Mickey D., Stefan DeSeve, Lakanta, Ajur and Boratus. The missions were *substantially* weaker the standpoint of a point-to-ease ratio. A lot of "cool", weird missions -- Reunion, Quash Conspiracy, Brute Force, Risa Shore Leave, Fissure Research -- but not easy for the average deck to do if you're picking your personnel just to overcome dilemmas. (Side note: these were all great choices if you were concerned about mission stealing!).

No change in terms of relative affiliation strength. Federation still has the easiest time getting through dilemmas, followed by Romulans and Klingons in that order.

What will Q-Continuum bring? Find out next week!