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XVM win chance prediction algorithm

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The XVM win chance prediction algorithm seems to be something that is still mysterious to a large number of players, so I thought it would be good if I shed some light on it. Plus, I'd like to get some discussion started on how to improve it.
 
I've broken it down into multiple formulas.
 
 
1. Win Chance formula
 
Chance_Eqn.png
 
This formula calculates the win chance of your team from the calculated weight of each team. The win chance cannot be higher than 95% or lower than 5%.
 
 
2. Team Weight formula
 
Team_Eqn.png
 
Here we can see that the Team weight is just the summed weight of each individual player on the team. Nothing very interesting here.
 
 
3. Player Weight formula
 
Player_Eqn.png
 
Now we are getting closer to the meat of the win rate prediction calculation. The thing to note in this formula is that weight of the tier is either 1, 0, or -1. Therefore, the tier of the tank a player is driving can add or remove 25% of the weight.
 
 
4. XWN Weight Formula
 
XWNEqn.png
 
The A stands for account stats. As you can see, the average tier of tanks played on the account plays a role in this calculation, but it's rather small and really doesn't shift things more and 15% either way unless a tanker is sealclubbing or has sealclubbed for a large number of battles.
 
The xwn stat is a number between 0 and 100 that is calculated by this formula
 
XWNCalculation.png
 
I didn't really look into how this formula works, so I have no idea if it's good or bad. However, this is how XVM calculates it if you wanted to know.
 
 
5. Win Rate Weight formula

 

WREqn.png

Nothing really too interesting to say about this one other than if a tanker's account win rate is above 48.5% the weight will be greater than 1, and it will be less than 1 if below.
 
 
6. Battles Weight formula

 

Battles_Eqn.png
 
The x in the conditional should be A_{battles}. Basically the more battles a tanker has played, the closer to 1 this weight will be.
 
 
7. Tier Weight formula

 

Tier_Eqn.png
 
This formula leads to some weird things for tanks that have different match making. Light tanks end up being weighted the same as tanks that are a tier higher. Also, the sealclubbing Pz. B2 ends up being weighted like a tier 3 tank rather than a tier 4.
 
 
Well, that's how XVM predicts win chance. I'm really interested to see what the mathematicians of WoTLabs think about it.
 
I think that the weakest part is the tier weight. I have some ideas about how to improve this with per tank weighting, but I have to set up a testing method first. So, let me ask a question. How would you test the validity of a win rate prediction algorithm? My thought is to compile about 1000 random replays, and retrieve all the necessary data to do the predictions. Then, compare the average prediction to the real win rate average as well as comparing the error rates. I'll be interested to hear your comments.

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I feel stupid and don't understand it, therefore it can't be true.*pubbie mentality activated*

But seriously, do you think the probability of winning is close enough to be relevant? Most of the time I didn't find it accurate, so I turned it off. 

A 35% chance team can actually put a fight against their enemies, and maybe even win, most games that are supposed to be steamrolls isn't, and steamrolls usually happen randomly anyway, or beyond a certain point where the player skill gap becomes so obvious the team with odds with it will just take advantage of it. So a study is very much needed to actually test this, I won't do it though because I tend to get influenced by writing the future in stone.

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I deconstructed that thing on the EU forums a while back:

http://forum.worldoftanks.eu/index.php?/topic/412074-win-chance-xvm/page__st__20__pid__8607174#entry8607174

 

It's an awful predictor, and only appears to work because it's been statistically fitted for mid tiers. It most likely overestimates the swing at low tiers and underestimates it at high tiers, and is highly inaccurate for individual matches.

 

It's possible to create a much better predictor by taking advantage of the fact that damage, frags and probably the invisible contribution factors have a near-linear relationship with winrate. If you wanted to make an accurate predictor, you'd do something like this:

  1. Create a contribution-linear tank-adjusted skill metric (fixed version of WN8 or whatever).
  2. Rate each tank using the parts you removed from the skill metric.
  3. Map the difference of teamsum(skill*tank) to a gaussian based on the variance not accounted for.

Part 3 can either be handled statistically, or based on the known total variance minus an estimate of the skill & tank variance.

 

None of this is particularly difficult. However, I don't believe there's any merit to predicting matches. The current win chance is widely misunderstood and misused, and improving it as a predictor is only likely to make that worse.

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Well have you ever thought about creating a genetics algorithm to determine the right formula? I guess that this would be ideal scenario for it - you got very limited amount of input variable, very well measurable (and scalable) output and huge data set for training the algorithm.

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I noticed as the battle tier goes up, the XVM chance to win prediction is less reliable in terms of how often you will win a 40% or 45% chance to win battle. If you are in a tier 9 or tier 10 battle and XVM says you have a 45% chance to win, you are often screwed unless you have a more favorable tank composition for the map.  Also the XVM chance to win formula is way off.

I collected data from 2,115 solo pub battles and did a bit of analysis on it. It was collected during two separate time periods. Once when I was a 1,000 WN8 player and once when I was a ~1250-1300 WN8 player. It was about 1,000 battles each time. I've mentioned it before in other posts and posted the info here before in threads about matchmaker.  XVM chance to win is way off in reality for most players of average or below average skill.  In reality a large part of your battles are predetermined by the disparity of skill in the teams if you are an average player.  

 

Also, overall the chance to win is pretty close to 50% with the chance to win average increasing slightly as your skill level increases.  Lets face it, if you are a 400 WN8 44%er, your team's chance to win is lowered every time you are on the team.  Same as your team's chance to win is increased when you are a 2,000 WN8 56%er

 

I wonder if a simpler formula that takes into account WN8, win rate, and tank win rate would give more accurate results.

Here are my results:

Average predicted win rate: 50.82%

Actual win rate: 51.77%

Standard Deviation: 11.15%

 

XVM Win Chance % of wins % of Battles
Greater than 65% 98.72% 7.94%
Greater than 60% 96.50% 16.83%
Greater than 55% 90.64% 32.06%
Less than 45% 8.09% 27.23%
Less than 40% 3.40% 15.22%
Less than 35% 1.51% 7.04%

 

Since this forum doesn't seem to allow tables to be posted, here is the data in an image:

XVM%20chance%20to%20win%20analysis.jpg

 

50% chance to win battles were 3.83% of all battles.

 

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None of this is particularly difficult. However, I don't believe there's any merit to predicting matches. The current win chance is widely misunderstood and misused, and improving it as a predictor is only likely to make that worse.

 

 

Well if the current w/r predictor is bad, and it could be improved, then it should either be improved or removed. Misinformation is worse than no information in the vast majority of cases. If the predictor is misunderstood and misused, that is the fault of the user. There is no reason to inflict the misinformation on everyone because of some.

 

I noticed mine was not working last night. Not sure why. I never take it as engraved in stone, but I do change my strategy accordingly at times, in order to have as much effect as I know how to, and to at least perform as well as I can, in order to mitigate a loss as much as possible.

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The most obvious failing of the XVM win chance is that it relies on account overall stats, where as tank-specific and/or recent stats would be much more relevant.

 

For example, a player may have a 57% win-rate in a specific tank but a 49% overall win-rate, and so their contribution to the battle is much greater than expected by the prediction.

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