We played a couple, then moved onto a week-long game of Global. I like “Revised” quite a bit, but my usual opponent is none-too-happy with the ability of transports to shoot back.
; )
Predicting Victory or Defeat - How do you know you are ahead or behind?
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So using logistic regression and more data, my model is predicting 87% of game outcomes (using all the data from round 1 to the end of rounds), and 100% of games starting on round 5 (eg once the game has progressed for a couple rounds - this model is very accurately predicting the winner!).
Now my problem is I’m not quite sure how to give a simple explanation of how logistic regression works. In fact I’m somewhat confused myself.
Variables
Both measured at the end of Russian turnUnitDif: AXIS IPC Units - Ally IPC units
IPCDif: AXIS IPC Territory - Ally IPC territory
The Model
116 rounds of data - roughly 15 games              Predicted
             Allied Win   Axis Win  Percent Correct
Observed Allied Win 28        10       73.7
       Axis Win  5        73       93.6Overall Percent Correct - 87.1
(It isn’t predicting Allied wins as well, because 2/3 of my data was axis wins)       B     SE      Sig      Exp(B)
UnitDif  .038   .011    .000      1.039
IPCDif   .110    .035    .002      1.116
Constant 6.644  1.501   .000    768.146Cox and Snell R Squared: .520
Nagelkerke R Squared:  .724I think this means that if UnitDIF changes by 1, your chances of winning change by 3.9%. If IPCDif changes by 1, your chances of winning change by 11.6%. But both of those values seem kind of high. So is that right?
Also if the IPCDif is zero then it means for the game to be even the UnitDif should be 177 (6.644/.038) - is that right?The logistic model is complex because it has something to do with a ratio of two exponents (e to the power of something).
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“I think this means that if UnitDIF changes by 1, your chances of winning change by 3.9%. If IPCDif changes by 1, your chances of winning change by 11.6%. But both of those values seem kind of high. So is that right?
Also if the IPCDif is zero then it means for the game to be even the UnitDif should be 177 (6.644/.038) - is that right?”Yay, numbers.
Give me more things to throw at my opponents to confuse them.
More numbers!
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So I did a prediction for my
current game with DJensenMy (very tentative) prediction model, assisted by my math skills (also tentative in this area), predicts that (as of the end of R9) you have a 1 in 250 chance of winning (though the 95% confidence interval is that your odds of winning range from 1 in 12.5 to 1 in 5000).
Hmm, the 95% confidence interval might even be bigger than that.
B SE Sig Exp(B)
UnitDif .038 .011 .000 1.039
IPCDif .110 .035 .002 1.116
Constant 6.644 1.501 .000 768.146At R9 our situation:
IPCDif: -6
UnitDif: -12y=-6* 0.111 –12*.038+6.644
y=5.522e^5.522=250.13
However since it could be plus or minus 2 confidence intervals, your chance of winning could be as high as
e^2.522=12.45
or as low as
e^8.522=5000 or so -
I should note that the confidence interval is inflated because UnitDif and IPCDif are correlated (0.560). If I only use UnitDif the confidence interval is only half the size.
I’m not sure if this means that the confidence interval measurement is inflated due to the correlation and that the true interval is smaller, or if the actual interval increases too. Tentatively I’d suspect the first is true.
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This math is seriously fracking insane.
The way I predict Victory or Defeat is that I look at the board and use my intellectual knowledge of A&A to determine if I’m doing good or not!
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Here is a good rule of thumb…
If you are playing against Ankmcfly, you are behind.
/WOOT!
//Thank you, thank you very much.
:wink: -
Some additional findings…
1) The balance of power (Axis Naval IPC - Allied Naval IPC) for navy has the same impact as it does for land (Axis Land IPC - Allied Land IPC). The coefficients are currently 0.041 and 0.045 (no statistical difference).
2). The amount of territory occupied by Japan or Germany has the same impact. Eg. it is just as useful for Japan to go up several IPCs of territory as it is for Germany. On the Allies side, UK and Russian territory is equally valuable (US territory is less valuable, possibly not valuable at all but that might be due to colinearity).
- A small bribe, ideally by paypal, to the other player can increase your chances of winning by 73.2% normally, but only by 37.9% in tournament games. Ok, late April fools =)
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Oops. Battlemap doesn’t include ICs in your land unit count (or anywhere else). This is particularly bad for Japan (eg. exclusion of IC values, downgrades the effectiveness of the model - and it’s especially bad because a 15 IPC difference in the model is like a 60% difference in your odds), but also matters if the UK or US were to build an IC.
I’m not sure what will happen if you included other ICs - like say SEU IC was a battleground (eg nobody could produce in it because they’re fighting over it - then its effective value is more like 0).
So I think I might work on including ICs…
Weird that BattleMap counts AA guns, but not ICs.
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AA’s are movable units, IC’s are not.
IC’s help supply lines and production capability, but aren’t really units and I think it is probably better that they aren’t included.
If you want to take production capability into account that might be a good idea, but the IPC value itself shouldn’t count in the units.
Just as an extreme example to show a possible skew, you could have Japan with 5 IC’s worth 75 IPC and Russia with 5 armor worth 25 IPC. Even though Russia is negative -50 IPC, they are still in a much better position to win.
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The alternative of not including ICs, is should you penalize Japan (in the model) for building an IC instead of two transports? Most players build at least one IC for Japan, and generally two if they are doing ok. Also, I think if Japan conquers an IC in India (from the UK) it should count as some kind of IPC gain. Maybe 30 IPCs is too high if the UK is wasting their money on armor and fighters to defend it.
I also think that invading CAU should be worth more than the 4 IPCs of territory (adding the IC’s impact would have roughly doubled the importance in the model of taking CAU).
I included ICs in the model and it didn’t make a difference. Their impact is too small to measure. Maybe the fact that serveral Allied games had US ICs on Japanese islands, or SIN made the variable less effective - as those ICs tend to be not so valuable.
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I also think that invading CAU should be worth more than the 4 IPCs of territory (adding the IC’s impact would have roughly doubled the importance in the model of taking CAU).
Definitely adjusting territory value depending on the owning country is a good idea. Strategic positioning is by far the most important variable but is also the hardest to measure.
In this case, Cauc is definitely worth more than it’s IPC value but it should also be higher for Germany controlling it than Japan. Germany owning Cauc usually means that both Axis powers are strong but Japan owning it is usually how the game plays out. Russia collapses to Japan while Germany collapses to the other allies.
Persia, Kazakh, and Novosibirsk also should have a much higher value if controlled by Japan because that is the ideal Russian defensive line. If one of those territories is being traded every turn, or worse, solidly under Axis control the others will quickly fall. Having your model run after the Russian turn is the best place to do it since Japan controlling one of those territories after the US and Russians have moved means that Japan holds them strongly as opposed to just trading them.
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I wonder if the Triple A developers have a set of strategic values that I could test?
They’re developing an AI - so they should have something of that nature.
My guess is that the effects are going to be pretty subtle. Also, I’m more in need of early game factors - affecting the first 4 rounds. Unlike the previous version of the game, this one seems to have less bottlenecks and thus less points of strategic importance (eg. Kareila used to be very important).
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I do not think there has been any work done on the TripleA AI in a long time.
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The formula gives you rough estimate. Here are some cases where it can be biased.
Imagine that according to this formula you are behind.
If you got behind by being unlucky, then this formula will predict a lower chance of your victory than what is actually true (Ex. my game against ncscswitch where I recovered from what I thought were long odds of around 1 in 20 - the long odds weren’t as low as I thought they were.)
If you got behind by bad strategy, then this formula will predict perhaps a roughly equal chance to that which is actually true (this is my guess - I’m not entirely sure about this).
If you got behind despite being lucky, then this formula will predict a higher chance of your victory than what is actually true.
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If you take over a game that is behind, the average player (taking over a losing side) will have a higher chance of victory than what this formula predicts (since players who get behind in the game aren’t as good, unless they got behind due to bad luck).
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Akreider2 - great ideas ! I’m also a fan of statistics.
I can send you >50 games in TripleA 0.902 and some in 0.821. A lot are also in the archives of Tripleawarclub.org
Obviously, the predicted probability of victory should either assume equal skill, or include the difference in skill (assuming previous experience is relevant). Look about the theory behind ELO and like ratings in chess. It’s quite likely that a poor player may ruin an ‘equal’ position, or need more real luck to win.
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One day I might write a triple A file parser. Then I could automatically collect the data (manually input is a bit of a pain). Well that’s if Triple A stores summaries on a by round basis - which I doubt. Does it? I need unit-IPC totals at the end of the Russian turn, for every round of the game (starting R1).
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One TripleA TSVG comprises all the history so far up to a position. The format is compressed or coded somehow, unparseable as text anyway. One may understand the format from the Open source.
Loading the TSVG into TripleA, it can reconstitute the position at any moment between actions - including at end of R1 of any turn. TripleA also does some good summaries inside, including IPC incomes and total unit values by countries and Axis/Allies.
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