You need to add up the total Unit IPC value for each side (land and naval, not including ICs). If it’s a tie at the end of the Russian turn (or if the Axis is ahead), then the Axis is very likely to win the game. You can do this automatically if you are using a program like aBattleMap.
I developed a statistical model for predicting game outcomes which is pretty accurate (100% accuracy on my small sample of games, starting on round 5):
http://www.campusactivism.org/blog/node/189
I got a notification - maybe they are just being delayed up to 7 days. I received a couple emails recently that looked like they were delayed 7 days.
They used to work fine. So this changed sometime in the past 1-3 months.
I have axisandallies.org on my whitelist for spam, but haven’t been getting notifications of new messages on the topics that I’ve subscribed to. Are notifications working? Do I need to whitelist another domain (eg do the emails get sent from somewhere else)?
In Russia 1, assuming the standard opening of attacking BEL (3 inf, 2 fig) and WRU (with everything else or almost everything else), should you
The larger question is whether it makes sense to sacrifice an armor to gain a 2 IPC value country? I think it makes sense for a 3 IPC value country in almost all cases (because you get the 3 IPCs, and at least 1 more IPC of damage to attacking infantry, as well as causing your opponent to divert resources to the attack), but for 2 IPCs it might not.
And then what should Germany do? Should it blitz into an empty ARC only to get destroyed by a Russian attack on R2 (without much chances of a German counter-attack).
I think the way you play this only makes 1-2 IPC difference, so it’s total micro-management =)
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).
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.
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.
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).
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.
So I did a prediction for my
current game with DJensen
My (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 .000 768.146
At R9 our situation:
IPCDif: -6
UnitDif: -12
y=-6* 0.111 –12*.038+6.644
y=5.522
e^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
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 turn
UnitDif: 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       93.6
Overall 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    768.146
Cox and Snell R Squared: .520
Nagelkerke R Squared:Â Â .724
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?
The logistic model is complex because it has something to do with a ratio of two exponents (e to the power of something).
I wonder if you could also try to calculate a confidence level? Eg. Game 1 was in round 30, and based on the independent >variables the axis should win with a confidence level of 90%. Game 2 was only in round 6, and it was calculated that the axis >should win but with a confidence level only of 55%.
The model with you give a predicted outcome and a standard deviation for that (For instance it might give you a 0.9 with a 0.2 standard deviation). So you could get a confidence level from that. Maybe a logit model will do a better job of this (as it will tell you chance of getting exactly 0 or 1, whereas the linear regression says you can get 0.9 which is an outome (a near win) that doesn’t exist as it represents an uncompleted game). I’ll see if I can get SPSS to upgrade.
Hopefully we won’t bore everyone else (people I still need data files - send me your aBattlemaps!!!) on the thread.
Maybe it would be helpful to clarify that there is are two Ys. The observed outcome and the predicted outcome. The predicted outcome will vary a lot (in the 0 to 1 range, but it could go as far as -1 or +2). The observed outcome is currently 0 or 1.
Weighing records might be a good idea. I suspect excluding them might work even better. Eg. if I can collect enough data for the last 1-3 rounds of a game that would be the best.
Weighting - I tried it out, using the Round as the weight, and it boosted R^2 from 0.35 to 0.55. However i can get better results by excluding the early rounds.
–
Hmm, logistic regression is meant to deal with 1/0 outcomes. However I don’t see how to do it with my SPSS version (11), so I’m going to try and get a new version.
BTW - do you have any aBattlemaps you can send my way? (Ideally with bid data).
Hmm, I think what you are describing is covered by linear regression process. I’m using OLS (ordinary least squares) regression and SPSS (software which does most of the work for me). Are you familiar with OLS?
I’m fuzzy on some of the exact details as to how OLS works because it’s been 5+ years since I was doing major statistics work.
Here is the wikipedia entry:
http://en.wikipedia.org/wiki/Least_squares
Rclayton - interesting idea, but wouldn’t you run into a problem because the value that you’d have for Y would have to be created by the exact same factors that you had as x1, x2, and x3?
For instance, you wouldn’t want to use the IPC income as Y (because my regression analysis has shown that is a good measure of the “outcome”, but that there are other factors that affect it as well - such as total unit value).
If you are regressing IPC income on IPC income, of course your model will be very good at predicting because they are the same thing! A similar problem exists if instead of IPC income you define victory as a continuum from 0 to 1 based on multiple factors. Your dependent variable (your ‘y’) needs to be different from your independent variables - and theoretically caused by them.
…
My latest finding is that the model gets better and predicting if I remove the early rounds. Thus the R^2 (percent of variance predicted) can increase from 45% to as much as 85% (or possibly even more, though I don’t have enough last round data), if I only look at the latter rounds. This makes a lot of sense, because in the early part of the game you don’t know who is going to win (for that matter, the 45% of variance predicted was probably coming from the latter round records and very little to none of it from the first couple rounds).
To increase prediction power in the earlier rounds where the game is nearly even, you’d have to be able to predict luck (impossible) or measure skill (possibly using league rankings).
To do a regression you need an outcome – or a “Y”.
The basic model is a rather simple
y=mx+b (standard linear equation)
Except that it is more like
y=m1x1+m2x2+…+ b
(a linear equation with several factors)
So my data needs a Y. Which is currently 1 if the Axis wins, and 0 if the Allies win. You cannot use a “probability of winning” unless there is a way of scientifically measuring it.
Is anyone an expert on different types of regressions? I’m wondering how much a problem using a linear regression is for a variable that only has a 1 or 0 outcome?
The problem is that the difference between winning by a slim margin, and totally devasting someone can be big. For instance, you can win a narrow victory with the Axis and Allies unit IPCs being equal, or have a big victory with a 200+ IPC difference. Ideally you’d have a win that was a “1” and a larger win that was a “1.5” or “2”. Any idea of how to measure this based on an Axis and Allies board? You could use victory cities, but I tend to think that they are a joke.
Is there any way to parse a map file? I’d like to convert it into an array of number of units per country, so I could write a computer program to generate a data file for analysis.
With the latest model, 1) AXIS IPC territory held (J+G territory) and 2) total unit IPC value difference are the two significant factors (p=0.001).
As an example of early results, I first excluded the round 1 data (I’m taking data after the Russian turn) because there is a series of slaughter moves that typically happen in the first round. Eg. the fact that the UK has a battleship in the Mediterranean is worth a fraction of its 24 IPCs. Results are improved by excluding round 1 data.
My main variable is the total value of Axis units in IPC minus that of the Allied units.
Just to show that you can find out stuff with very little data, with a lousy 30 data points, this one variable explains 43% of the outcomes.
Adj R^2 = 0.433
Constant=.793
AxTotDif (the difference in IPCs)
B= 0.0034
T=4.89 (significant level is better than 0.001, or there is a greater than 99.9% chance that this variable is statiscally significant)
Thus, if you have zero IPC difference, the Axis has a 79.3% chance of winning (this makes a lot of sense - the Axis has better supply lines). For each IPC difference, the probability of winning increases by .34%. Note: these numbers are going to change a LOT, once I add some more data points.
In other news, this is pretty crazy, the difference in IPC value for land units has no significant impact, all of the difference comes from the naval IPC difference. That’s what happens when you only use 30 data points =)
- Win / Lose is not a simple binary measure. You need to include the offset caused by a bid. I can guarantee that the Axis will >always win with a 100 IPC bid. I can also guarantee that the Axis will loss if the Allies get a 100 IPC bid.
Interesting. I’m thinking of using a standardized 9 VCs or concession for victory. Hopefully the League and Tournaments will provide a good set of people playing standardized games.
Bid is a variable. So far most of my data set has very similar bids (one 5 and a bunch of 7s), so it isn’t a measurable factor in those cases.
- Not all victory cities are created equal, nor are all victory conditions. In an 8 VC game, Leningrad and Calcutta dominate the Axis >strategies. 9 VC adds Moscow or occasionally London to the list for the Axis. Allied strategies often start with “Stop Axis” before >they move on to identifying VC targets for 8 or 9 or more VC. Strategies will change based on the required VC count and on any >time limits imposed.
Yes.
- IPC production rates have a long term effect. You can expect that there is a lagging phase relationship between IPC totals and >winning. Another way to think about it is with everything else being equal, larger IPC production will win out over time.
You’re on to something… So far (in very early results) the most powerful factor in the difference in Axis vs Allies units, because it is the best measure of the impact of the player’s strategy, and how much territory they’ve controlled in the past and present. By contrast, the current IPC value of territory isn’t so important.
- Unit type and location is a short term effect. Since victory conditions are tied to physical control of certain territories, measuring >unit counts is not sufficient. They should be measured in terms of combat value and distance from victory cities.
Which is why my model will probably never predict more than 70-80% of the outcome. Counting the balance of units around Russia and Germany so as to determine whether either capital is about to fall, would be helpful, but darn hard.
I am interested in your results. Currently, I watch VC count, and IPC count as rough indicators. I also look at unit combat totals >and time/distances from VCs that are in contention that is much more subjective at this point. Schemes for valuation of units >become technically complex, mathematically messy and time consuming so I have not pursued them.
By this - Were you thinking of giving units different valuations from their IPC cost? Ex. if Japan has a stack of armor next to Russia, and a lack of infantry, they aren’t worth 5 each (more like 4 to 4.5). Too complex to do a good job of though.
If you do become successful at identifying what leads toward victory, it will be a valuable input towards building a smarter AI for >the game.
I like this. Maybe I should work on the AI. I’ve always wondered why AIs were so stupid. I used to play a lot of Civilization 2 and 3, and that AI was very stupid (the Civ 4 one is much better). I programmed an AI for Connect 4 once (using Turbo Pascal 7).