# “One-sided battles are extremely rare”… Or are they?

Hello,

**Shade1982**, who’s given me permission to use his material, has **made a graph** **from his last 100 battles to verify if WG’s statement that one-sided battles are extremely rare is indeed true**, the results…although I never believed in WG’s statement, it still surprised me, will quote it:

**PS:** Let me know in the comment section your opinion.

“Hey all,

yes, just to bore you out of your mind, I am going to create another topic about the matchmaker. But with a bit of a twist. This is about WG’s statement saying one-sided battles are extremely rare and they don’t feel the need to do anything about it. Well, we already know about the new matchmaker which is going to fix the team’s tier and class composition, but that still doesn’t fix the one-sided battle issue.

As to the “it’s rare” statement. As with a lot of things, that tends to be subjective. What threshold constitutes ‘one-sided’ battle? Well, for WG apparently, that is only true with 15-0 or 15-1 battles. But is that correct? In my personal opinion, battles ending with 15-5 are also extremely one-sided. If you count everything up to that score, the ‘rare’ part in that statement suddenly changes to ‘just uncommon’.

So, I decided to do a little fact-finding. Now, there is no clear line in the scientific method as to what percentage constitutes a fair representative number, but I decided to use my last 100 battles. I did no cutting or leaving out, as to not skew the results. Those are my last 100 random battles, not CW or SH and I played mostly from tier VII up to tier X, so it might be different at other tiers. I use vbAddict’s ADU tool to upload all my battles to make it easier for me to get the statistics. After that, I put all the results in an Excel file and counted the difference (or delta if you will) between kills and put it in a chart.

**This was the result:**

[Clarification: the bar for ’10’ means the difference in kills was 10. This was usually a 15-5 battle, but could also be a 14-4 battle.]

As you can see here, over 100 battles, the difference in kills being 10 was actually *the* most common result. Now that is hardly rare, is it? In a good team distribution system, you would expect this chart to go from high to low, from left to the right. Funnily enough, during these 100 battles, I suddenly had no more 15-0 battles, even though I used to have those all the time…

Now, I hope someone at WG reads this and thinks “hmm, maybe the variables for our analysis are wrong”, but somehow I highly doubt that.

What is your opinion on the matter?

(For full disclosure, I have added the Excel sheet. If you think I did something wrong, let me know.) ”

**RG: **The spreadsheet wasnt downloadable over the forum so** Shade1982** emailed it to me: Here’s the link.

I would say that games where players skills are more or less balanced and still there is such unbalanced outcome are ok and nothing to be done, except full change of mechanics or some unfair balancing.

But why the hell WG does not implement skill based MM when this is clearly what is missing? 15:1 game where from start is 70+% chance to win is no fun to either side. Ding Ding WG, wake up finally!

I think one of the problems is that it is not realy clear what one means with a skill based MM.

I vote against a MM where you meet only players of your same skill level. I suppose that this is the kind wargaming is so deadly against.

But I strongly vote for a balanced MM where not all foul eggs are in one basket. This could be easily achieved by implementing a kind of post processor to the MM: after the MM has done it’s work this routine could just swap equivalent tanks between the teams to provide both teams with similar skilled players.

An easy addition to the MM with a lot of impact on gameplay.

Unfortunately it requires a treat which seems to be on short supply: the ability to admit that it is not working as intended. So expect more stats and statements showing that everything is fine.

Master of Arrogance, isn’t this one of their next titles???

Interestingly, this parallels my own project. I’m also looking into the frequency of one-sided battles (although I would define them as any battle where the losing team eliminates less than half of the winning team).

I’m also recording map, battle mode, map side, battle tier, and duration of the battle.

15-5 is not a problem of MM but a snowball effect.

Mr DRC you are wrong, WG has a skill-based MM, otherwise they couldnt form such battles with 70% winchance … wake up sir, WG is a profit-oriented company. Victor Kislyi has become billionair with the money of people, who believe WoT is free to play.

He sold them the best thing: the dream of beeing a good tanker and as a graduated mathematiker he delivers the stats for their dream. This 15-5-thing is very ugly for dreamers…and Victor.

You know that if you want to implement skill based MM that the MM will have even more problems than now.

So i don´t think that the few % of the games it would affect positive are worth the effort/risk.

Also Snowball xP

I have to agree with the snowball theory. Once things start to fall apart for one team, they weill continue to fall apart exponentially. a skills based method would make battles last longer but, as in actual battle, once a weakness has been discovered and exploited, it’s over. eventually a 15/5 battle will be 10 v. 1 the odds of overcoming that can be calculated but they’re astronomical.

Before that it might have been 11 v 2, still not good. It could even have been 12 v 7 before it got to 10 v 1 but it was still over.

Those “one sided battles” are only natural. Once team A has say 1-3 tanks less than team B the gap widens as the remaining few tanks of team A have it harder and harder to hold their ground against the relatively higher number of enemy tanks in team B. This has only little to do with the actual skill gap between the teams. Just watch some top clan cw battles or pro team ESL/Faceit battles. Even though both teams are highly skilled once a team falls behind by a couple of tanks it’s over soon.

Shade & Rita,

Firstly, props for measuring real data rather than speculating.

Your results are roughly what one would expect, actually, because of what others above have referred to as “snowball effect.” The basic idea is that once your team has more tanks, it can more quickly eliminate enemy tanks by focusing fire. But why would you get anywhere near 10? Let’s do a little math (eek!).

This very problem was studied during WW1 by a brilliant British engineer Frederic Lanchester. He was interested in predicting the outcome of ranged (in his case, aerial) battles, and derived equations known as Lanchester’s Power Laws (which you can Google). The relevant law here is Lanchester’s Square Law, which says that the number of casualties your tanks (or whatever) will inflict on the enemy over time is proportional to the *square* of the number of tanks you have [1].

What is the intuition for squaring the tank count? One factor is obvious: if you have twice as many tanks as the enemy, then you can inflict roughly twice as much damage. The less obvious factor is that you also have roughly twice the HP, so your tanks can survive about twice as long. In the end, if you are doing twice the damage for twice as long, then you are doing four times as much damage.

Let’s set up a simple stochastic process to see what margin of victory you would expect from WoT battles. Here are the rules:

1. calculate the relative chances of each team killing an enemy tank as the square of the number of tanks it has;

2. consult RNG gods to see who loses a tank;

3. repeat until one team loses.

Now let’s run this experiment lots of times (say 1,000,000), and count up how many times each margin of victory shows up. When I did this, I found that the median margin of victory was with 11 tanks surviving (see http://imgur.com/a/ro2gR). You can reproduce this yourself (see [2] below for code).

I don’t, of course, have WG’s data on this, but my guess is that the real distribution is to the left of what this model predicts (i.e., the median margin is fewer tanks, perhaps the 10 you saw). Lanchester’s Square Law essentially assumes that all friendly tanks fight in one group and shoot at all enemy tanks in one group, but during a WoT match there are two or more such “fights” going on most of the time; this will effectively make Lanchester’s exponent lower than 2. There are other factors, such as unequal tank firepower, HP, and mobility among tanks in a single battle, victory via base capture, platoons, spotting mechanics, and so on. I suspect the effect of these is so small that it can be ignored in practice, but I’ll leave working out the details as an exercise to the motivated reader 🙂

[1] Lanchester, F. W. (1956). Mathematics in warfare. The World of Mathematics, 4, 2138–2157.

[2] source below:

import random

def sample():

greens, reds = 15, 15 # start w/ 15 tanks each

while greens > 0 and reds > 0:

green_power, red_power = greens**2, reds**2 # Lanchester’s Square Law

prob_red_loses_tank = green_power / (green_power + red_power)

rand = random.random()

if rand < prob_red_loses_tank:

reds -= 1

else:

greens -= 1

return reds – greens

histogram = [0] * 16

for sample_count in range(0,1000000):

victory_margin = abs(sample())

histogram[victory_margin] += 1

print(histogram[1:])

In tears of joy I read this comment as this is the way one should address the matter in hand. No feelings attached, only educated reasoning. I think the Lanchester’s square law fits nicely to the conditions on the WoT match apart from the mentioned winning by base capture and fighting in smaller unequal (also more or less isolated) groups as these most certainly drives the distribution to the smaller difference the most.

One way to improve this calculation would be to take into account the length of the battle and the average effective dpm caused by each team in percentage of team health. It would take some rather extensive research for sure.

Slight problem applying the Lancaster Square Law here…

It applies to real-world situations. Where tanks don’t have health-bars, or instant-repair kits, or any of the other things that a tank in WoT has. In reality, particularly in the reality where Lancaster worked, with aircraft? You’re fine, or you’re dead, either from being shot or from making a hole in the ground. You don’t get to have a third of your health shot off and still be able to do things. So, then you can ‘snowball’ in an entirely different manner, because the person that didn’t get killed skews the balance in applicable power. In WoT that doesn’t happen, because putting a round into someones tank doesn’t kill them, in many cases, allowing them to shoot back, run away, what have you.

The Square Law does not, and can not, apply to the situation at hand, since the situation is a game.

You also missed the fact that I did not blindly apply Lanchester’s differential equations, which are continuous and would predict a draw every time; I created a simple discrete stochastic model. See my response to an anonymous comment below for more details.

My aim was to illustrate how a “skewed” result can arise naturally using very simple mechanics, not to argue that the most common margin is 10, 11, or something else. The two relevant factors here are (a) you have a small number of units on each side, so taking one out is a big deal, and (b) focused fire amplifies small, possibly random, advantages. My guess is that healthbars are an insignificant detail, but I encourage you to modify the model to cover them and tell us whether (and how) this makes a difference to the margin of victory distribution. But be a good scientist and publish your methods and data like both Shade and I did.

As a side note, a good model does not have to account for everything you can think of (and I pointed out some things that mine does not cover). Newton assumed that space is Euclidean, which Einstein later showed is not the case. But despite this omission, Newton’s Laws have been good enough to get spacecraft accurately around the vastness of our solar system.

An insightful analysis, though not necessarily totally applicable. As you note, there are several confounding factors which cause WoT to deviate from Lanchesterian statistics. This can also be seen from the fact that Lanchester predicts very few “close” results in comparison to “snowballed” results, whereas we all know that one or two good players can carry the game from a severely disadvantaged position.

Lanchester designed his formula around large numbers (thousands) of infantry. In general, an infantryman can reasonably be assumed to either be active or incapacitated, and there’s a difference of one bullet between one state and the other. The fighting effectiveness of the aggregate force is a smoothly changing function, amenable to bulk statistical analysis of this sort, but only due to the large numbers of individual troops involved.

The formula was also applied to warships. The number of warships in a given battle is generally small (dozens at most on each side), but the fighting effectiveness of any given warship tends to diminish in relatively small steps with the damage it takes – turrets and directors knocked out, engine rooms flooded, rudders jammed, key officers incapacitated and replaced by their juniors – long before the ship is actually sunk. The Battle of the River Plate is instructive here. In this context, Lanchester’s formula remains valid in principle.

World of Tanks doesn’t really behave like that. The number of tanks on each side is small (exactly fifteen each), and each can take a large proportion of its maximum sustainable damage while retaining near 100% fighting effectiveness. Okay, you can sustain damage to various subsystems and crewmen which does have an effect, but you often end up with a team full of tanks with very little health but little or no functional damage, and thus retaining full fighting effectiveness except for being on “sudden death”.

I think this “sudden death” business is potentially very important for analysis, as it greatly increases the chance that a full-health enemy tank can kill you, rather than you killing him. The simple code listing above does not model that factor, nor is it obviously captured by Lanchester’s formula which it relies on. It should however be straightforward to construct such a model, though it may take a little longer to evaluate than the simple one.

The tactical performance and balanced makeup of the teams is also a major factor, but we have already made the simplifying assumption that they are equal for the purpose of analysis. Also, while capping is a *possible* winning condition in WoT, it is not especially common in practice, so we can discount it when considering a basic fairness analysis.

As a starting point, though, we can simply evaluate different Lanchester exponents, for example for values between 0.0 and 3.0 inclusive, to see whether they fit the data better. We can also produce the CDF plots, and thus determine the median and percentiles rather than just the mode.

When we do that, we find that the standard exponent of 2.0 predicts that as many as 10% of games will end in 15:2 or worse results, while the median battle has a 15:6 result. This agrees fairly well with the small empirical data set provided, although that is very noisy data due to its small size. (Maybe a larger data set can be found somewhere.)

But looking at the opposite end of the CDF, Lanchester predicts that only 4.3% of games should have results of 15:11 or more even, while the empirical data shows fully 25% of games in that category – a discrepancy that can’t be ignored. We have to reduce the Lanchester exponent to about 0.75 to reach 25% at this point, which spoils the previously close agreement at the snowballed end of the scale.

In short, the Lanchester statistics are not a close fit to the data before us. This, to me, is a strong suggestion that individual strong players – who both survive longer and do more damage per minute on average – have a disproportionate effect on battle results. Which is what we suspected in the first place.

Very good point, Taihennami (and should’t it be taihen-na-nami anyway?), a good player will disproportionally affect the battle outcome. But even a good solo player won’t overcome overwhelming numerical superiority most of the time — what are good solo winrates, 60%ish? Feel free to change the code to model unbalanced teams (which is the real effect you’re after, because if you have unicums on both sides then it’s all back to RNG), fighting in multiple groups, and anything else. Find out which factors are most important, and show us your model and the data it produces.

The main problem with “fitting the data” here is is that there are no good real statistics to calibrate against (perhaps someone can figure out if it’s possible to get this data via the WG API or in some other way?) Despite Shade’s valiant efforts, 100 samples is much too small, so it’s pointless to argue how exactly the model fits. I think it does explain how a very skewed result can arise naturally in a fair system, which was my objective.

Dammit, I wanted you to be wrong when I heard about you in that Jingles vid so I could b*tch on WG some more but I did it myself and got the same result (and surprisingly produced a very similar code to yours). So yea, here you go confirmation of the results in R software.

Scores <- c()

for (i in 1:100000){

a <- 15

b <- 15

death <- a == 0 || b == 0

while (death == F){

p <- runif(1,0,1)

q <- runif(1,0,1)

a.balance <- (a/(a+b))^2

b.balance <- (b/(a+b))^2

a.test <- isTRUE(p <= a.balance)

b.test <- isTRUE(q <= b.balance)

if ( a.test == T & b.test == T){

a <- a-1

b <- b-1

}else if(a.test == F & b.test == T){

a <- a-1

}else if(a.test == T & b.test == F){

b <- b-1

}

death <- a == 0 || b == 0

}

Scores[i] <- abs(b-a)

}

hist(Scores)

Ladies and gentlemen, this is how great science is done: question results that don’t make sense to you and see if you can reproduce them independently.

Well done, Airborne.

the snowball-theory is based on a tactical manover called rush. the americans call it Blitz. But even such a manover cant cause so much 15-5 outcomes.

The ammount of the snowball is a combination of bad MM and bad RNG for the loosers and good MM combined with good RNG for the winners.

a MM should try to reach 15-10 or better 15-14. a good MM should proof his results and if neccessary correct them. If u wanna make money with MM u need 15-5 or lower. lower would be more money, but u could run out of the -5 side.

No; as I explained above, in an absolutely fair and unbiased system you would expect games to end somewhere around 15–5 or worse. So you could argue that on average games in WoT are more, not less, close than expected.

Moreover, there is no reason why WG would need 15–5 to make money. In fact, I would expect close matches to be more exciting, likely to keep players engaged longer, and more likely over time to get them to pay. (A conjecture on my part, but I think not an unreasonable one.)

Blitz is called by the Germans and by such tactical manoeuvre you can achieve a 15-0 victory, IF!!! executed correctly and with a high degree of coordination. Consult the history books for real- life examples of this, most recently in the Gulf War. What I understand from your comment is that your ability to think logically, read simple graphs and derive informed decisions is the same as Harabme’s. If you want to provide a constructive argument, be ready to back it up with clear data as SillyFox did.

Be well!

Blitz is called by the Germans, it has nothing to do with the snowball effect, where the first is a tactical strategy and the second is a number’s advantage. And yes, by such tactical manoeuvre you can achieve a 15-0 victory, IF!!! executed correctly and with a high degree of coordination. Consult the history books for real- life examples of this, most recently in the Gulf War, or if real- life is boring for you go and watch CW battles of the better clans in WoT, there you can clearly see what blitz is and how it works. What I understand from your comment is that your ability to think logically, read simple graphs and derive informed decisions is the same as Harabme’s. If you want to provide a constructive argument, be ready to back it up with clear data as SillyFox did.

Be well!

WoT: 75% f2p vs. 25%p2w

http://www.spiegel.de/netzwelt/games/victor-kislyi-im-interview-zum-computerspiel-world-of-tanks-a-837782.html

What a crap. This link is 4 years old, I wish the game would still be like 4 years ago.

Leaving all snowballs aside (I agree with this theory btw) we didn’t have this kind of games 4 years ago. I remember having one game which ended 15:1 and telling my new clanmates about it, that these kind of outcomes only happen every 500-800 games you played (na-server).

Wargaming introduced many dozens of tanks and nations since then. Powerfull tanks with good guns compared to what was before. So the ability to take hitpoints from the board was widely increased. But not once were the hitpoints themselves increased; the average hitpoints per games and per battletier is almost the same as years before.

So if a team makes a mistake by e.g. leaving a flank open the game is quickly over, your influence on the outcome is minimal. Unlike in WoWS, where there is way more often time to manouver and correct a teams mistakes by supporting a flank.

Crapgaming obviously realized this. Wasn’t it early this year where this (fake) conference took play in the NA headquarters, even with Victor?

And what happend so far?

A lot imho. Almost every patch one or two of the most popular mods got included in the game, it’s getting more and more comfortable to play, most matches last 10 minutes or longer, in most matches I have the satisfiying feeling to have contributet; well, I’m talking about World of Warships 😉

And World of Tanks?

Each and every patch they add more pixels to existing tanks, they spend time for changing existing minimaps, they introduce more tanks again.

It feels like sprinkling sugar on that bull and call it candy.

And what about the promised fixes of the infamous matchmaker? the gameplay? the above mentioned problems? In half a year they produced ONE sandbox iteration without any improvements of the game itself. And lot’s of denials and excuses and modified statistics to prove that there are no problems.

Which begs the question:

Was Victor Kislyi just lying to animate us to still spend more money on this game?

Or are his leadership skills only little better than those of a floating plastic bag?

Either way, how do they expect us to be interested in new products of Crapgaming?

Action stations !

Lanchester’s laws dont count here. Bing Lanchester’s laws. We ve to use here the Salvo combat model …

but lets think about Mr Lanchester. his outgoings are always 0,all loosers dead .

best case: only 4 dead winners, btw the winner had 1.4 times more tanks. but same firepower.

worst case: 50% of the winners are dead, the winner had double firepower, but was outnumbered by 1.3 : 1

if u re outnumbered by 2:1 u need 4 times more firepower to gain a draw.

……..UPS……….

Mr. Frederick W. Lanchester says:

if u have a spread at10, than u was outnumbered by ca.1,5 : 1

if u have a spread by 7 or 8, u had double firepower, but was outnumbered by 1.3 : 1

…….We have to use the salvo combat model which includes a simulation for the RNG………..

I think you missed the fact that I did not blindly apply Lanchester’s differential equations (which are continuous and would predict a draw every time), but formulated a simple stochastic model. I only used Lanchester’s law to roughly estimate the fighting effectiveness of N tanks as N². See my response to Wanka’s comment below to see how this follows from the diff eqs, and why you were drawing the wrong conclusions by directly consulting the Lanchester’s model plots on the Wikipedia page.

But you brought up the salvo combat model, which is an interesting point, so let’s discuss that. That model is actually very similar to Lanchester’s model: the only real difference is that it also models a defensive capability that can be concentrated — things like AA or CAP.

You might think that armour is like this, but this is not so, because armour cannot be concentrated defensively. Think about it like this: a single plane is more likely to be defeated by 100 AA guns shooting back than by 2, but if you fire one shell at a bunch of equally armoured and positioned tanks, you have the same chances of the shell bouncing whether there are 2 enemy tanks or 100. In other words, the effect of adding armour is the same as reducing the alpha of the opposing guns.

And, if you remove the concentrated-defence component from the salvo model, you are back to Lanchester’s equations.

In any case, I was not claiming that my model reflects the exact nature of WoT battles, or that you should expect a specific margin; in fact, I pointed out several factors that I did not model, and hypothesized that in real WoT battles the median margin of victory is probably smaller. What I did demonstrate is that a seemingly skewed result falls out naturally from a very simple (and, I think you would agree, 100% balanced) battle model. I’m sure WG has much more sophisticated and accurate models, and of course you are welcome (and encouraged) to use the code I posted to develop (and test!) better models yourself.

I extended your code to cover not only different Lanchester exponents, but the effects of needing multiple shots to knock out a tank. It now takes a lot longer to produce a complete set of results, but they are as fascinating as the scores of a QI show. When I’ve got the complete set, I’ll follow up with an assessment of which parameters correspond closest to the empirical data.

Since the blog comment format loses the indentation (which is a bit crucial for Python), I’ve pastebinned it: http://pastebin.com/Bjr6NYpD

Contrary to my expectations, tanks each having a health pool makes complete team wipes *more* likely. I’m not entirely certain why. The effect persists even with an exponent of 0, which is equivalent to having just one gun active at a time on each team.

Excellent, Taihennami, props for actually experimenting with better models rather than making emotionally-based arguments. I’ll be very interested to see how the various factors you affect match stats. And, now that you’ve taken up the gauntlet, I can happily retire 🙂

I would like a sample size of 1k battles, although this is about what i expected.

I think less brawling, and making combat ranges longer would work against the snowball effect. In a close range brawles with a high number of tanks on each side, losing a single tank (over extends or whatever) is immediatly impactful on that area,because of the disadvantage loses more. Then you end up with a snowball. If you spread tanks out more, losing a small area with few tanks wont be as crippling.

Don’t you think players would just concentrate in one or two groups anyway to get a local numerical advantage? They certainly should if they want to win.

WoT players certainly do concentrate their forces. But we call it “camping in the base” or “lemming train” because it is a tactical *disadvantage*, leaving the flanks open.

http://imgur.com/a/ro2gR) dont know what this should say or which WG-Troll loaded it up.

Maybe its a Lanchester’s Square Law model for 10 vs 14.

My Lanchester’s Square Law looks like this https://en.wikipedia.org/wiki/Lanchester%27s_laws#/media/File:Damagerace.JPG

You are missing the fact that Lanchester’s differential equations that you plotted,

dA/dt = -B

dB/dt = -A

are *continuous*. This means that half a tank (i.e., a tank w/ half of its HP) is considered to have half the firepower of one tank (i.e., w/ full HP). But in WoT, a tank w/ 1 HP can cause just as much damage as a tank w/ full HP (which is, of course, why you should prioritize killing high-firepower tanks w/ low HP).

Non-continuity actually matters a great deal, because w/ 15-vs-15, taking out one enemy tank removes a substantial portion of the total enemy firepower. You can see this by yourself: set the initial tank counts in the code I posted to something much bigger (like 1,000 or 1,000,000) and check that the median margin of victory gets smaller relative to the total tank count. In fact, as tank counts tend to infinity, the margin of victory will tend to 0, which is exactly what you will get by solving Lancaster’s equations above.

This is also scientifically interesting, because it means that the bistability in this system (green or red victories by a substantial margin) is caused by low unit counts, and is very different from what the continuous equations above would predict (draws) or what you would see for large numbers of units (much closer matches). The same effect turns up a lot in microbiology, for example in biochemical signalling cascades like those involved in your adaptive immune response. Pretty cool, no?

Finally, I estimated the fighting power of a given number of tanks as the square of the tank count. This actually follows from the equations above: use the chain rule to get an expression for dA/dB, solve the resulting differential equation, and you will see that difference in fighting power is related to the difference of squares of the unit counts.

Shade1982 analysis has too few data points, but there is a hint for a 2 maximum curve one around 5 and one around 10 difference in kills. So most common battle results are 15-5 and 15-10. If saying that 15-5 is unbalanced i would not blame the MM but the player base.

It’s a real difference if the tomatoes in your team are in low tier or top tier tanks. Is your scout sucking or not etc. You could skill/tank wise balance the game perfectly, but if the “Red Baron” is top tier vs enemy “unicorn”, the other side has greater change to win. Ask yourself, with what tank are the good players playing with? Not with the Sturer Emil, but with tanks that outperform or at least out rank others. So this is one thing WG should consider and make MM in that case more unbalanced with bias towards team that has less skilled players at top level!?! – Would this be fair to good players?

WOWS does ranked battles with has a skilled or rank based MM and i would say it’s a small difference. If your team looses and other wins – no stats, skills, tank balance does not matter. By the fact that our team lost, only means that we got the worse part of “good” players and you are back to square one.

Yes, Shade has far too few data points. I wonder if WG’s API can be used to obtain margins of victory; does anyone know? It would be interesting to see what the statistics are with a very large sample count.

I suspect the high peaks at 4 and 10 are outliers; with so few data points, the confidence intervals are probably be very wide. (In general, stochastic processes are more likely to be skewed in the short term than people expect; this is called Gambler’s Fallacy). But it would be very interesting if one also saw two peaks for a very large number of battles, because it would mean that there are at least two very different strategies to win battles.

In any case, if you are proposing changes to the MM, it might be a good idea to model them and run enough experiments to see the effects. I would expect that this is exactly what WG does when they consider changing things like the MM.

I have a similar impression with games often descided with 10 or more kills for one side.

Perhaps another important fact is:

Most games do not go longer than 4min. Slower tanks, artillery or tank destroyers, are not able to play it’s typical game. You have either to play your tank unorthodox or to use fast tank destroyers (currently german scorpion or grille) or mobile artilleries (M53, Lorraine) to keep up and have a chance to make some damage.

My personal impression – I like mostly the games which are balanced from the players and which tend to endure 8min or longer. The feeling of a real battle and playing the tanks to its purpose is much more generated. Perhaps WG should consider to offer different “winning” methods to make games again longer and to give therefore each existing tank again a purpose on the map. My opinion.

Just introduce little gifts/bonuses that you have to click somewhere “on” the minimap and gone are the empty flanks!!! (The minimap is not used enough and that make all the difference)

Just my 5 cents

The engish word Blitz was invented by the people of london during the german airraid against their city. Some years later the american analysts tried to find a word for the new german (tank)-tactics at the beginning of the war. The germans at that time didnt have a word for what the developed since 1918 with the cableconnected Sturmtruppen, they called it sometimes combined wappons, because infantry was now able to call in artystrikes. During the Versailles treaty tanks were added to the Sturmtruppen-idea and radio killed the cableconnected phone. the translation for blitz is lightning. After the war the word blitz came back to germany as blitzkrieg, describing the early wartime. i m not a american, but i know what a lightning is. it comes suddenly out of nothing and its very fast. b.e. a very long pass over the flank during a ballgame, or some radioconnected Pz3 attacking unexepted in your not-radiooperated flank. (BTW: if u re fast and wanna have fun with the grandfather of MBT, go warthunder and drive pz. 3l or pz. 3m)

The blitz is in random rare, it needs good players who understand eachother without TS3, at e-sports its a common tactics and at real combat is that what every commander wants, because its adrenalin pur.

here at this topic i d say the spread of 10 dont has to do anything with a blitz. tankers can blitz and be blitzed, even in a wot-random

The Lanchest square law predicts 10 surviving tanks after a match 14 vs 10. enemy extinguished no rush or blitz involved. no bulletinterception by RNG.

if Mr Shade1982 says: 10, Mr Lanchester would answer: you have fought a battle 14 vs 10.

As I explained in my response to your other comment, a margin of victory of 10 does not mean you started with a ratio of 1.4:1 unless you have an astronomical number of tanks in every battle.

FWIW, I think in esports one would see margins closer to what my model predicts, because teams tend to play as a single concentrated group.

here again the link for my lanchester-interpretation. he named the top graf Win by outnumber. red line starts with 1,4 units , blue line 1,0 units https://en.wikipedia.org/wiki/Lanchester%27s_laws#/media/File:Damagerace.JPG

the two grafs below show conditions under other beginning-scenarios.

teams playing as a single concentrated group dont leave the lancaster-law, because its made for pretty equal developed forces like ger vs uk … or any esport-liga ….and tactics have lower influence, cause all teams would adept a new standart imedeatly ….

https://en.wikipedia.org/wiki/Lanchester%27s_laws#/media/File:Damagerace.JPG

I think you’re worried that I’m having trouble understanding these graphs; I’m not. Given the fact that I showed you how to derive the square law from the equations you plotted, it’s a good bet that I understand the math, don’t you think?

But I don’t think you understood my explanation why having a 15-vs-15 match is very different from the large numbers the differential equations model as continuous, and how if you have lots and lots of tanks then you get closer to your plots. Without this effect, the world would not exist as we know it (and you and I would not exist to wonder about WoT matches), so it’s a worthwhile principle to understand.

@Sillyfox you forgot to take into account T110E5 platoons, if one team has two or more E5’s with half a brain, they automatically win because the E5 is definitely not overpowered and totally has frontal weakspots. As you can tell I’m clearly kidding, really interesting to see you do all the math.

margins of victory are visible at ADU under Replays, chance tab Summary to Teams and u find the deads and the survivors.

here again the link https://en.wikipedia.org/wiki/Lanchester%27s_laws#/media/File:Damagerace.JPG

the top graph is named Win By Outnumber. red starts with 1,4 units and blue with 1,0. somewhere in the net u find a original frederick lanchester book where he calculates a war for 1000 units facing 1400 units.

the other two graphs below show war where one side has the advantage of superior firepower (here at wot: unbalanced RNG).

The lanchester-law is made for dealing big data (astonomical numbers)

The lanchester-law doesnt work facing a tactical genius in one single battle.

The lanchester-law does work with the standart tactic against a genius.

let me quote Napoleon: if u have superior tactics, dont fight too often cause every victory u show the enemy one part of your art

…

Napoleon was beaten at Leipzig with the standart tactics against a genius: engage every unit of the genius with one of your own units till the genius has no unit to envold his superiority.

The lanchester-law works better at esport as at random.

teams playing as a single concentrated group dont leave the lanchest-model.

the influence of tactics is at esport lower as at random, good new Genius-tactics are adepted immideatly by all other esport teams. At random it takes time till the last tanker got it.

HP dont play any role, as long as HP is equal on both sides. unbalanced HP appear in a lanchester-surrounding as superior firepower (advantage).

even halfdead-lanchester-tanks or vessels can fire back and are still part of the Lanchester-model.

The Lanchest-law is a good mean for calculating backwards a mesured spread.

here the example for our situation: if spread is 10, the beginnig situation (MM) was as unbalanced as a battle 21:15. it is mathematicly not correct, but it gives roughly a orientation for how unbalanced the MM works

For this case a salvo combat model is not needed:

if WG has made a un-balanced MM, they wouldnt engage a un-balanced RNG to compensate it and if they do so, the spread would be lower and we would have a balanced battle.

if wot is p2w: RNG and MM would work together forming the spread.

the 2 lower pictures in my damagerace-link show situation with a unbalanced RNG as win by advantage and draw.

Math is gr8…

Put 1 top tier idiot/bot in 1 team… or put platoon of brainless idiots in 1 team…

Now do math again…

We are back at start: INTRODUCE SKILL MM

(whatever they take as SKILL variable will be better than as is now)

Is that so hard? For a month? For a seven days? For one fuckin weekend to play normal ?!

agree, my feeling told me MM is working with a 15-3 result and i didnt need any math to tell u:

15-14 or better 14-15 wold deliever better battles

…

install xvm and forget their winchanceformula, but watch the distribution of the bluenicums, than bluenicums and greens together, forget lanchester, ready!

maybe u will see as funny things as i see:

Shade1982 measured pretty close to my feeling.

Congratulation Shade1982 to your good shot.

This is really interesting…

So I’ve only looked at the ideal probably of a 15:0 result … Partly because of laziness partly because that’s what Wargaming is interested in.

So the exponent in Lancaster’s model is supposed to basically represent skill and the ability to kill vs defend oneself.

So with an exponent of 1 the probably of a 15:0 result is 0.22% … With an exponent of 2 the chance sky rockets to 2.68% … Modern combat is apparently an exponent of 1.5 … Correlating to a 1.27% chance of a 15:0 result.

But what if there is an unequal exponent?

So if you have a team that has a slight discrepancy of skill (exponent of 1.5 against 1.55, remembering this is an exponent so it’s a pretty significant skill gap of a small number of players across a team … Which in my experience is about 10/100 battles on the Asia server) the chance of a 15:0 result in favor of the higher skilled team is 1.07% and in favor of the lessor skilled team 0.40% giving a total of 1.47% chance of a 15:0 win (agnostic of which team is better)

So using Wargaming’s metric of a 15:0 or 14:0 result being the one sided result isn’t sensitive enough to account for unbalanced matchmaking …

I’m working on developing a full probably analysis on this so I can see the full spectrum and if there are other noteworthy differences in the results when you start playing around with the relative exponents.

My experience varies greatly depending on what time/day I’m playing … I also imagine that experiences will vary dramatically based on the server you play on too.

Great — I’d be curious to see your analysis, and what factors you discover end up affecting the results.

One correction before you start. The exponent represents the ability to concentrate firepower, not skill; skill can be modelled as a linear factor that modifies firepower. Mathematically speaking, if you look at the original differential equations

dA/dt = −βB

dB/dt = −αA

then skill is a part of the α and β factors. So, with an exponent of 2, to defeat a 2× numerical superiority, you need 4× the skill. (I discussed some factors that can reduce the ability to concentrate firepower, and therefore the exponent, in my original comment.)

An example where the exponent is much closer to 1 is hand-to-hand combat where the tight formations don’t leave enough space for more than one soldier to fight a specific enemy, as commonly occurred in the ancient world.

Consider the battle of Cannæ — widely considered one of the most brilliant tactical feats in history — where Hannibal decisively defeated a (very) numerically superior Roman force under Varro. Hannibal knew his troops were veterans and better on a per-soldier basis, but he also knew that they were not 4× better (assuming here for the sake of example that the Romans had 2× the soldiers), so he had to find a way to limit the ability of the Romans to concentrate striking power. His encircling manœuvre did exactly this: most Roman soldiers were stuck inside the circle behind their comrades, while the actual fighting was only going on at the circle periphery. In effect he lowered the Lanchester exponent to 1; in this situation, the α and β factors became dominant, and the Carthaginians’ superior skill resulted in a crushing defeat for the Romans.

In individual battles, your experience will of course vary greatly, but statistics are about long-term trends. The most common margin of victory probably also depends on various factors, including time of day, how tired you are, and so on. I think to take these into account, you would want to model (a) a range of skill in each team, and (b) a difference in skill between two teams; the range of skill in each battle you can estimate by looking at the average queue length and the overall player rating distribution. I did not model either effect, but it would be very interesting if someone did.

Let us know how your probabilistic model turns out.

I uninstalled WoT for good about 2 weeks ago.

Reason: 12 games where my team had no chance to win the match.

Strangely, these games were not noobs vs unicums but rather a poor distribution of tanks that left our team no chance to win.

Eg: in the last game where I was in my T110E5, the enemy team had the following tanks (That I can recall):

2 E5s, 1 – obj 260 (reward mission tank), 1 Type 5 Heavy, 2 T110E3s, 1 Jpz E100 among others.

The big tanks in my team were:

2 E5s, 1 – IS-7, 1- T57, 1 platoon (3) of russian meds + 1 bat and others were tier 9s and 8s.

Yes the number of tier 10s were equal in both teams but look at the ability to slug it out.

Most maps don’t provide enough freedom to the meds to flank + in this match I think the only way we could’ve won its if everyone of us was firing gold ammo.

FWIW, it’s also normal that this happens with an appreciable frequency, even in a system where over the long term the odds are perfectly even (such as flipping a fair coin). The phenomenon that this is at odds with human intuition is called Gambler’s Fallacy (which you can Google).

The main problem I see is when one side has four or five more top tier heavies. The difference having much more armor and HP is critical, especially early game.

I analyzed my replays using the https://github.com/Phalynx/WoT-Replay-To-JSON code and some python code.

I included only battles that did not end in a draw or base capture.

You can see the results here: https://plot.ly/~pjhdekoning/28/score-difference-795-battles/

Oh good, some more data to chew on.

Your results fairly closely match a stochastic-Lanchester distribution with an exponent of 1.0 – not 2.0, as is standard for massed infantry, nor 1.5 as is apparently now used for modern combat.

just a info: my feeling told me, same years ago, when i tried to find out how wot works: the MM comes into heavy trouble, if serverpopulation is 3500 or lower, first effects may appear at 5000 … but real life … so i stoped playing at low-frequence-server-times.

Well I’ll say that the complete bullshit of war gaming’s coding has caused me and a few of my friends to stop spending any money on this trash heap ever again.

The one sided crap is consistent and clearly evident. Player skill has no role in outcome. Rather I’ve seen consistent evidence that one sided battles are pretty much every battle.

It’s as if there is a system in place that determines who should win before the match even takes place.

We’ve all seen evidence of the absolute bullshit RNG system in play. Bouncing shots or missing shots repeatedly with no viable explanation given aside from the bullshit wargaming excuses that it’s internet latency or server and network speeds effecting game play. So all 15 of us are experiencing this simultaneously? Why is the red team so fortunate? Oh must be coincidence. A coincidence that is repeated over 51% of the time is not a coincidence… it’s a design intended to happen.

Examples are, Players that receive bonuses that are obvious in battles from the start. Teams that make every shot and miracle shot’s while the other side is low rolled and screwed over by an obvious RNG system is not fun. Nothing can be done to defeat it… not even better internet. Because the outcome was already favored to one side before the match started.

I don’t pay for one side bullshit like that and think wargaming is making a huge mistake coding it that way. I have my theories why they do it. And they can deny it even exists till the cows come home.

Fact is they currently have a fucked over RNG system and matchmaking that I’m of the opinion, that it’s meant to favor new players and bad players with poor outcomes to have a sudden increase in RNG rolls so as to encourage these new and numerous players to continue paying and spending money.

Why that is a mistake on war gaming’s part is because your community of Veterans players and skilled tankers are getting shafted by your matchmaking and very biased RNG system… and we are stopping our paying for this type of gaming model.

They don’t think the revenue is worth trying to maintain so from a business perspective they will give advantages to a much larger group of potential income. Can you blame them?

That is why I no longer support their company with another cent. Hell, I rarely play anymore because the one sided outcomes are becoming more and more consistent. Even matches my team rolls through the other team like shit through a goose I’m left thinking how badly they got shafted on rng and matchmaking.