Predicting Victory or Defeat - How do you know you are ahead or behind?

I’m interested in doing a scientific analysis to determine how factors that you can observe during the game predict whether the Axis or Allies will win.

By using statistics (eg linear regression or one of the non-linear variants since we’re actually dealing with a yes/no outcome - so it isn’t linear), with a good bit of data, regression analysis should provide us with some answers.

What factors can you use to predict victory?

1. Round - what round you are on is key.  At least for the first five or so rounds where the Axis is behind in IPCs.  I think round is a good proxy for position.  The problem isn’t so much what round you are on, but how well the Allies have their convoys setup.  (Turn would matter too, but I assume that the data collection will hold the turn constant.  Eg. you’d take measurements before the turn of the same country every round.)

2. IPC income - you could either use IPC income, or you could analyze the map on a common turn (ex. before the Russian turn, starting round 2) and use the IPC value of the territory everyone holds.

IPC income could be analyzed on a country basis, or by summing the Axis powers vs the sum of the Allies powers.  You can try several things and see what works the best with regression.

3)  Total unit values in IPC by class.  Break down units by land, air, and sea - either for each country, or for the Axis vs the Allies.  (Ex axis has 200 IPC of air, vs Allies having 225 IPC)

I think these three factors are key.  Other factors could be added like whether the Russian or German capital is captured, but generally the game is decided by that point - and I’d like to be able to predict what will happen before that.

Can you think of any other factors that would be easy to measure and possibly good predictors?

I’d be very happy to do all the data analysis (using SPSS, I’m a former sociology grad student). The problem is that I need the data.  I probably need at least 100 data points.  200+ would be better (eg 20 games that last 11 turns).

Does any such data set exist?  Or is there anything that I could use?

One idea is to use the IPC summaries that people provide in “play-by-forum” games on this board, as I think just using this one factor could provide a good predictor of game outcome.  There are some people who like to provide summaries of how much IPCs of territory each country has, and how much they have in the bank.  However, I’ve noticed that they do it sporadically.  Are they any forum members who do this consistently?

Alternatively I could analyze the maps - this is a lot of work. Is there any way to get ABattlemap to count the number of IPCs worth of territory each player has?  Or the IPC value of the units?

What format does ABattleMap use to store info?  I could possibly write a script to gather this type of info from AAM files.

Someone should make abattlemap available via this site (unless there is a copyright restriction on that).  Having to login to get it is annoying.

Great I see the info view now!  I’d wondered if people were such perfectionists as to manually track that data!

I wish they had planes in a seperate category.  Planes can be used as land or navy.

Other Factors
The Bid - seems obvious, but once you take into account the unit IPC values does the bid really matter?  I guess it might be a small improvement on IPC values because you get to place the units where you want to.  By the third or fourth round, the bid’s factor is likely absorbed into other factors.

I’m Looking for Data

If anyone has a collection of ABattlemap files, please PM me or reply here or by email or something.  I’m collecting as many AAM files as I can.  I want them to include the results of the Russian turn (so that things are standardized). So Russia would be the last country to have moved.  I’d like files starting on R1 (eg after R1 is completed).

Ideally I’d like to know
-who was playing the game  (to avoid collecting duplicate data)
-what round it is on (hopefully you have included this in the filename -  eg tcnance_akreider_J1.aam)
-the bid (though this isn’t necessary)

I’d like to collect several hundred of them.  You could zip them up and send them to me by email.  Thanks!

Meanwhile, I’ll check the forums.  But the moderator might have deleted old ones, and sometimes people only post them sporadically, so you might have a better collection that you could email to me.

email - aaron@campusactivism.org

• 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).

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 =)

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).