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How team balance (win chance) affects your battles

XVM SBMM blowout roflstomp

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NeatoMan #1 Posted Jun 02 2019 - 18:40

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* disclaimer - win chance is not a single game predictor!   It can never tell you if you will win or lose any particular game.   It is a long term indicator based on many combinations of players, tanks, maps, etc.  Any one specific combination of those can deviate from that average. If you think win chance can tell you if you will win or lose then you are a complete idiot and you should stop reading right now, crawl back under the rock you came out of, and please don’t ever look at win chances ever again.

 

...on to the data.

 

I’ve been collecting and analyzing XVM win chance data for years, and since XVM stopped reporting win chance over a year ago, I haven’t seen any replacement that has been tested.  So I came up with one.

 

Inspired by WoTnumbers data posted by Mfezi, I developed a new win chance formula based on PR ratings.   With his help I’ve gathered over 8.5k battles worth of data from 5 different players, along with player PRs for every player in those battles.  Many thanks go to him for getting this going. I’ve posted this data piecemeal in other threads, but will summarize it all here.

  

The win chance formula

My win chance formula is based on total team PR ratings.  Any rating will probably do, but this is what we got to work with.

   

Win Chance = 50% + [ (team1PR - team2PR) / (avgPRteam1and2) ] * 140%

 

Most of the tweaking of the formula involves that last number (140%).  I’d need data from more players before settling on that as a final value.

 

*edit - revised formula now includes battle tier:

           Win Chance = 50% + [(team1PR - team2PR) / (avg team1&2 PRs) ] * [1.0 + (tier^2)/160]

 

that last part replaces the  *140% in the previous formula.  It makes the skill difference have a greater impact on the win chances as you move to higher tier.  It may still need some tweaking.

 

Here is how it holds up.  Win chances are gathered into 5% brackets (e.g. 50% includes all games from 48% to 52% win chance) , as I gather more data I should be able to narrow that range.  The maximum it can predict seems to be 90/10. Anything above/below that is treated as 90% or 10%, i.e. it appears you always have a chance.

 

 

An ideal formula would display  y = 1.000x + 0.000, with R2 = 1.000.  I’m at y = 1.019x + 0.0045, with R2 = 0.9974, which is pretty damn good, I must say.

 

People have said with regard to XVM’s win chance  “you need to account for tier of tank, seal clubbing, stock tank, blah, blah, blah”.   XVM did take this into account to some extent, but apparently you don’t need all of that.  Players seem to generally behave like their overall rating. Those specifics may allow this to become accurate using smaller sample sizes, but overall it seems to do the trick just fine without it.

 

Distribution of win chances

The matchup of two randomly selected 15-man teams should follow a normal distribution pattern, i.e. most games will fall in the middle, with fewer at the extremes, like this:

 

 

Over time, and over a variety of conditions you should expect to win in each bracket according to the win chance, i.e. you will expect to win 50% of the 50% win chance games, 60% of the 60% games, etc.  These expected results are based on your PR rating, which is an overall rating. Specific instances may vary, such as playing only one tank, or platooning with the same people for an extended period.  

 

The shape of the curve is determined by the random MM.  It is based on the 29 other players in battle. The shape will be pretty much the same for everyone. The position (or shift) of the curve along the x-axis is based on the individual's own rating (PR). The peak will fall somewhere near your own win rate, unless you platoon a lot with really good or really bad players, or have a "unique" play style.

 

You can see just how much your own PR shifts the curve here. Same team mates and opponents, the only difference is you.

https://docs.google....dit?usp=sharing

 

If you platoon with the same people a lot, your curve will be a little narrower, since you remove some of the randomness in the MM.  If we base this off per tank ratings, or combine results from different players (as I did with all the data posted here), the curve will spread out, since you are now adding more variety to the ratings.

 

Margin of victory vs win chance

We can see the effect of any imbalance with this win chance measurement, particularly how imbalance affects the degree of victory (margin of victory).  This data seems to fit with what I gathered using the old XVM win chance.

 

Margin of victory is the difference in the number of surviving tanks at the end of battle; 0-3 is a close game, 10+ is generally regarded as a blowout.  It is shown as % of games within a particular bracket (e.g. of the 636 games in the 35% win chance bracket, 17.6% of them were close, and 25.2% were blowouts).

 

 

Margins don’t appear to be largely affected until you get beyond 2:1 odds, or 33% / 67% win chance (highlighted green rows).   Approximately 2/3rds of games fall within that range. I wouldn’t consider anything lopsided until at least 33/67 based on these results.   Exact proportions may vary depending on how much your own PR shifts the win chance curve, but the random part of the MM gives you ~2/3rd in that range.  It’s up to you to make it better/worse.

 

If you wonder what balanced teams (SBMM) would be like compared to random MM just look at the green rows and compare them to the “Grand Total” row at the bottom.  That’s the level of change you can expect.

 

I also grouped margins into high/low ranges at the end of the chart (0-6 = low, 7-15 = high).  It gives a pretty good indication of how games change beyond 2:1 odds. It stays fairly consistent within the 33/67 range, but changes beyond that.  Also, it’s not a huge change either. You still get a decent number of close games even with lopsided teams.

 

Blowouts also increase as you move to higher tiers, so if you feel you are seeing more blowouts, perhaps it's because you are playing higher tiers

 

 

Another thing I keep hearing is: “Gaah, I am seeing way more blowouts this patch”  yet these values have remained fairly constant in my data going all the way back to patch 8.0.  So when people complain about how many blowouts, lopsided teams, or what not is going on in the MM these are some baseline numbers to go by. It is tier dependent, so you will see more blowouts in the upper tiers than lower tiers.

 

Game durations from the old XVM data also followed the same trend; becoming faster beyond 2:1 odds.  The battle duration data from WoTNumbers needs some adjustment atm, so I don’t have it available for comparison.

 

*edit* finally got battle duration data to work.  Seems like average battle times aren't as bad as many have claimed.

 

First table shows average battle time by battle tier

Second table (and graph) shows the distribution of battle times (grouped by minute)

 

 

and now by win chance.  On average games don't get much faster until the extreme win chances

 

 

 

If you don’t believe any of this I am always looking for new data to add, so if you run WoTNumbers, you can contribute to this, verify it,  and be assured I am not making any of this up.


Edited by NeatoMan, Aug 26 2019 - 04:13.


Isola_di_Fano #2 Posted Jun 02 2019 - 18:48

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I feel people either get discouraged by a low win chance or over confident if it is too high ... both affecting negatively players, imo.



NeatoMan #3 Posted Jun 02 2019 - 18:50

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View PostIsola_di_Fano, on Jun 02 2019 - 12:48, said:

I feel people either get discouraged by a low win chance or over confident if it is too high ... both affecting negatively players, imo.

So I shouldn't report facts because some people are stupid?



Exiledcrow #4 Posted Jun 02 2019 - 18:51

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Great data.

 

Will have no effect on the tin-foil hat brigade.



Exiledcrow #5 Posted Jun 02 2019 - 18:51

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View PostNeatoMan, on Jun 02 2019 - 18:50, said:

So I shouldn't report facts because some people are stupid?

 

Nope. Just have realistic expectations of how much reality stupid people can handle. 

NeatoMan #6 Posted Jun 02 2019 - 18:54

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View PostExiledcrow, on Jun 02 2019 - 12:51, said:

Nope. Just have realistic expectations of how much reality stupid people can handle. 

hence the disclaimer right at the beginning.



PotatoLegend99 #7 Posted Jun 02 2019 - 19:12

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I don't put much stock in PR these days...lots of people that have climbed their way up to "good" PR numbers just through playing tens of thousands of battles...like me! I sometimes divide a person's PR number by their total battles played for funsies and sometimes take an extra step and multiply the resulting ratio by their win rate at low, mid, or high tiers.

NeatoMan #8 Posted Jun 02 2019 - 19:15

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View PostPotatoLegend99, on Jun 02 2019 - 13:12, said:

I don't put much stock in PR these days...lots of people that have climbed their way up to "good" PR numbers just through playing tens of thousands of battles...like me! I sometimes divide a person's PR number by their total battles played for funsies and sometimes take an extra step and multiply the resulting ratio by their win rate at low, mid, or high tiers.

and yet it still appears good enough for all this; at least, as good as when you account for all that stuff like WN8 and XVM'x xte did.   btw, win rate is factored into PR ratings.



SimplyPzB2 #9 Posted Jun 02 2019 - 19:50

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First off it's important to acknowledge when someone puts the effort in, and Neato has done that, no 'gut feeling' ramblings here.

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Second, I would encourage Neato to reach out to XVM and see if they'd be interested in testing/using his formula so that XVM can offer Win Chance again.  (Otherwise, this w/c calculator becomes useless - no one is going to manually do this for every battle...)

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Neato's information builds the perfect case for Skill BALANCED match maker.  See his chart below:

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View PostNeatoMan, on Jun 02 2019 - 18:40, said:


 

Distribution of win chances

As with all random systems, the distribution should follow a normal distribution pattern, i.e. most games will fall in the middle, with fewer at the extremes, like this:

 

 

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It's important to note the PURPOSE of sBmm.  And that is to promote fair, competitive, fun, and engaging gameplay.  So let's see what the table above, based on random mm, can tell us about what sBmm will do for gameplay.

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Let's start with the 10% column.  92 battles were played in total.  8 were won.  If I asked you to play a game where you KNEW you were only going to win 8 out of 92 battles - how 'excited' would you be to actually play that game?  If we are all being honest, no one wants to play a game with that much BUILT IN LOSS. 

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If you look at the 15, 20, and 25 columns, same argument.  You losing is BUILT IN.  Not fun, not challenging, not fair, crapfests of battles. 

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When we look at the 30 and 35 columns, you could start to say these might be challenging, as you can start to win enough that if you like being the underdog these games might have some appeal, because there is ALMOST a reasonable chance to win. 

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If you look at just the 35,40,45,50, 55, 60, and 65 columns - THIS IS SBMM.  The teams are roughly balanced based on team skill.  You have a REASONABLE CHANCE to WIN EVERY BATTLE.  There are no guaranteed wins/losses in these columns.  Which is the definition of FAIR.  And because BOTH teams have a chance to win, that makes 100% of these battles competitive, which is more fun and more engaging.

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When we look at the 60 and 65 columns, reverse argument for the unfavorable columns.  You could say these two columns might still be challenging, as the underdog enemy ALMOST has a reasonable chance to win.

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When we get to the 70, 75, 80, 85, and 90 columns - we have the exact opposite argument from the lower columns.  I.e. these games are very boring.  Look at the 90 column.  There were 92 battles played in total.  74 were won.  If I ask you to play a game where you KNEW you were going to win 74 out of 92 battles - how excited would you be to actually play that game?  If we are being honest, no one wants to play a game with that much win BUILT IN.

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What skill Balanced match maker would to, and all it would do, is eliminate the outlier crap battles.  I.e. it would eliminate the 10, 15, 20, 25, 30 and 70, 75, 80, 85, 90.  Which would be great.  No more frustrating guaranteed losses, and no more boring guaranteed wins. 

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It's also important to note the frequency of just how often you get these battles.  Neato's data shows that the 10, 15, 20, 25, 30, 70, 75, 80, 85, and 90 columns ARE ABOUT 1/3 of all your battles.  I'll let you do the math on 1/3 of your total battle count.  I'm guessing it's a pretty big number.  Now multiply that number by 6 minutes (the average battle duration).  How MANY DAYS have you spent playing battles where you had ZERO impact on the outcome because random mm predetermined the winner. 

-

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Skill BALANCED match maker for all, fair battles for all, every battle should be a fair fight (at least from the start).

 

 

 



Nixeldon #10 Posted Jun 02 2019 - 20:34

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View PostSimplyPzB2, on Jun 02 2019 - 13:50, said:

First off it's important to acknowledge when someone puts the effort in, and Neato has done that, no 'gut feeling' ramblings here.

-

Second, I would encourage Neato to reach out to XVM and see if they'd be interested in testing/using his formula so that XVM can offer Win Chance again.  (Otherwise, this w/c calculator becomes useless - no one is going to manually do this for every battle...)

-

Neato's information builds the perfect case for Skill BALANCED match maker.  See his chart below:

..and you still have no idea what he posted, what win chances represent, or how they came to be.


Edited by Nixeldon, Jun 02 2019 - 20:48.


NeatoMan #11 Posted Jun 02 2019 - 20:39

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View PostSimplyPzB2, on Jun 02 2019 - 13:50, said:

Let's start with the 10% column.  92 battles were played in total.  8 were won.  If I asked you to play a game where you KNEW you were only going to win 8 out of 92 battles - how 'excited' would you be to actually play that game?  If we are all being honest, no one wants to play a game with that much BUILT IN LOSS.
So let's see the difference between this scenario and SBMM:  

 

random MM:  you get a rare 10:90 battle, you likely lose.   you are just as likely to get a rare 90:10 battle, you likely win   Played out a bunch of times they even out, so you split wins and losses.   You are far more likely to get a 50:50 battle, which according to the odds you are likely to split too.   From a game play perspective a 10:90 loss isn't much different than a 50:50 loss.

 

SBMM:  you get put on 50:50 teams, or close to it, which according to the odds you should split roughly 50:50.  They play out much the same as the random battles.

 

the difference.  In a random MM if you are a good player you will shift the odds in your favor giving you fewer 10:90 games vs 90:10 games, and you win more games.  In SBMM you will always be balanced and if working properly will keep splitting your games.  

 

bottom line is in SBMM wins and losses get shifted, while game play doesn't improve noticeably.  If I don't know the odds all I notice is the shift in wins/losses.

 

Block Quote

When we get to the 70, 75, 80, 85, and 90 columns - we have the exact opposite argument from the lower columns.  I.e. these games are very boring.I.e. these games are very boring

 If they play out much like the other battles, why would they be any more or less boring?

 

Your obsession with the odds, without taking into account any of the background is what is causing all your distress.  You are a perfect example of why I put the disclaimer in the beginning.  It applies to people like you.  You DO NOT get any of this, and your misuse of these stats is self-inflicted pain and distress.

 

Block Quote

Second, I would encourage Neato to reach out to XVM and see if they'd be interested in testing/using his formula so that XVM can offer Win Chance again. 

I won't, specifically because of you.  People with OCD don't need any more "encouragement"



spud_tuber #12 Posted Jun 02 2019 - 20:40

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View PostNixeldon, on Jun 02 2019 - 13:34, said:

..and you still have idea what he posted, what win chances represent, or how they came to be.

And ends his post like a political speach with an emotional appeal slogan.



Kliphie #13 Posted Jun 02 2019 - 20:44

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I know it's just an arithmetic error, but it's hard to take numbers seriously from someone who can't do simple math.  Eighty-two games in the 10% column, not 92.  

Rides_with_Death #14 Posted Jun 02 2019 - 21:06

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Xvm should just programed in 60% chance  at the start of ever game and not used the real chance values.. and not told anyone just so people would stop [edited] 

Nixeldon #15 Posted Jun 02 2019 - 21:06

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I like what you have done with the game data so far. The win chances seem close enough for comparative use. Even though we have easily verifiable information, it won't stop da_Rock002 and his 50% blowout rate posts. 

 

If you can, could you overlay the win chance distributions of the players? I ask this because of the denial of the probability shifts.


Edited by Nixeldon, Jun 02 2019 - 21:07.


Copacetic #16 Posted Jun 02 2019 - 21:37

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View PostKliphie, on Jun 02 2019 - 20:44, said:

I know it's just an arithmetic error, but it's hard to take numbers seriously from someone who can't do simple math.  Eighty-two games in the 10% column, not 92. 

 

he prob don't give a damn if you take them or not

NeatoMan #17 Posted Jun 02 2019 - 21:43

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View PostNixeldon, on Jun 02 2019 - 15:06, said:

If you can, could you overlay the win chance distributions of the players? I ask this because of the denial of the probability shifts.

 

Here are two, a 3005 PR vs 6696 PR player

 

You can also see how much your PR shifts the curve below.  Though it doesn't account for tier, so if you have a 6k PR and play low tiers it will have a greater impact than if you play tier 10,  The setup below is for mainly a tier 7-10 population

https://docs.google....dit?usp=sharing



Nixeldon #18 Posted Jun 02 2019 - 21:45

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View PostNeatoMan, on Jun 02 2019 - 15:43, said:

 

Here are two, a 3005 PR vs 6696 PR player

 

You can also see how much your PR shifts the curve below.  Though it doesn't account for tier, so if you have a 6k PR and play low tiers it will have a greater impact than if you play tier 10,  The setup below is for mainly a tier 7-10 population

https://docs.google....dit?usp=sharing

 

Thanks.

 



Copacetic #19 Posted Jun 02 2019 - 21:46

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seems sbmm would have a minimum effect if any

Nixeldon #20 Posted Jun 02 2019 - 21:51

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View PostCopacetic, on Jun 02 2019 - 15:46, said:

seems sbmm would have a minimum effect if any

It would start squeezing win rates and that is about it.







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