Neil Armstrong
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Back in December 2010,
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wrote up an excellent series of posts which analyzed the results of the PBFs to date. You can find the historical analog to this post here.

Since Billytea's previous analysis pre-dates the Exodus expansion, I wanted to see how things had changed with Exodus. I only analysed Exodus games because I was particularly interested in the new characters and the interaction between the Exodus modules. Since I’m interested in "out of the box" game balance, I didn’t include any games with significant house rules: I allowed up to two character nerfs, usually Cain and Kat/Tory, but nothing else. So, for example, games with Selwyth’s modified agendas and Vollick’s Treachery 2.0 aren’t included.

I haven’t updated the base game or pegasus statistics, so any comparisons to those will unfortunately be flawed unless someone brings them up to date.

Win Statistics
Exodus

Sixty Exodus games that meet my criteria were completed as of mid-July 2012.


That’s a significant advantage to the cylons. I see two possible hypotheses: PBFers are becoming better cylons over time, or Exodus has been more difficult for humans than pegasus or the base game. In any case, cylons are heavily favoured to win in any Exodus game.

Cylon wins are listed by cause as follows:


Damage accounted for the majority of Cylon wins in Exodus, followed very closely by morale and population. Centurion, Fuel and Food wins remain rare.

The difference in the cylon win percentage between 5- and 6- player games has disappeared:


Although 7-player games appear difficult for humans to win, a change in a single game’s result would swing the win percentage back to even with 5 and 6 players due to the small sample.

Cylon Leaders

I was particularly interested in the effect of a Cylon Leader. In Billytea’s analysis, games with a Cylon Leader were more likely to see the Cylons win. Exodus appears to continue this trend:


The presence of a Cylon Leader also appeared to change the manner of cylon victory:


Games without a cylon leader were more combat-oriented, with damage, population and centurions combining to account for 70% of human demise. With a cylon leader the emphasis shifted towards crises, with morale victories taking the lead.

Considering that most games with a cylon leader are 6-player, and that 2/3 of the sympathetic agendas require the human team to win, I hypothesized that the higher cylon win percentage has made winning an Exodus game as a cylon leader more difficult than pegasus. Examining Cylon Leader win percentages, I found that this was not really the case. Sympathetic cylon leader have a fair chance of winning, while hostile cylon leaders have an uphill climb, although their odds are still better than a player that stays human in a 7-player game.


Although sample sizes are small, cylon leaders seem to be having trouble winning with "their" team, meaning one of the humans win agendas in a 6-player game and one of the cylons win agendas in 7-player game (there weren’t any 5-player games with a cylon leader). Conversely, when they join the "wrong" side they’ve enjoyed far greater success. This could be because a cylons win agenda in a 6-player game is essentially 3v3, and a humans win agenda in a 7-player game is 2v5, neither of which are balanced scenarios.


Interestingly, the agenda distributions are spot on (33% the "wrong" team, 67% the "right" team). Whaddya know, sometimes statistics are right One noteworthy anecdote, although statistically insignificant due to sample size: the two agendas involving food (Genocide and Convert the Infidels) remain winless, which was also true in the Pegasus analysis. I expected this result, since the addition of Exodus crises further diluted the Food/Water shortages.

Finally, I wanted to examine the effect of a cylon leader on the team they support, regardless of whether the cylon leader won.


For sympathetic games, having a cylon leader support the humans slightly improves their chances compared to the baseline of 72% cylon wins for 6-player games with a cylon leader. Having a sympathetic cylon leader support the cylons significantly increases their win rate. The combination of a very high cylon leader win rate and a very high cylon team win rate could indicate that the Sympathetic-Cylons Win agendas are too easy to accomplish and too pro-cylon with Exodus, although with only six games completed under those conditions it could still be random chance.

For hostile games, humans have never won if the cylon leader doesn’t support them. Combined with a very low cylon leader win rate, my conclusion here is that cylon leaders may be playing too pro-cylon, and need to take more steps help the humans. This should draw out the game and give them more time to fulfill their objective. If the leader supports the humans, they may have a good shot - although those results are statistically insignificant due to a sample of only three games.

Exodus Modules

I also wanted to see how the different modules of Exodus interact. 56 of 60 games included Conflicted Loyalties, so there’s no good way to isolate its effect. Ignoring Conflicted Loyalties, we can aggregate games based on whether they include the Cylon Fleet, the Ionian Nebula, neither, or both.



Since a large majority of games use all of the Exodus modules, the sample sizes make it difficult to draw many firm conclusions within any specific subset other than "Both", where cylons overperform compared to the baseline of 70% cylon victory.

One interesting observation is that without the Ionian Nebula, cylons fared quite poorly, with a 42% win rate over a sample size of 12 games. I’m at a bit of a loss to explain this - it could be that the addition of stronger characters, Mk7s/the CAG title, 6-strength skill cards and the predictability of the pursuit track are enough to tip the balance unless trauma and the Battle of the Ionian Nebula are around to throw a wrench into the mix.
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Hmmm, I'd say update your spellcheck to include "cylon" in its dictionary, but I gotta admit, it is a nice visual aid having the word "cylon" stand out.
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Just to note that the probability of getting 18 or fewer human wins out of 60 assuming an equally balanced game is 0.00134 (so a 0.134% chance of it happening if it is equally balanced). So this suggests statistical significance.

It would be interesting to update the original stats, if anyone wants to do the work involved in that.
 
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Stefan Lopuszanski
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Has anyone taken a crack at updating these statistics? I'm curious on the statistics when looking at Treachery cards being included and some other stuff. I'm working on a game that utilizes some mechanisms from BSG and any data for balancing and design would be useful. Thanks.
 
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