After seeing this article, I decided to publish my own, but this time about World of Tanks (WoT). To understand what twists or spins are, you need to explain the basic mechanics of the game. Before each battle, two teams of 15 players are randomly formed, depending on the type of vehicle they have chosen, and then the battle itself starts. In battle, each vehicle has a certain number of hit points, armor penetration and onetime damage that is inflicted upon penetration, a vehicle is considered destroyed if its number of hit points is 0. And the distinguishing feature of WoT is that armor penetration and damage are normally distributed random variables. And that’s where twists or spins come in. For example, players believe that armor penetration and damage are not truly random, but are determined by some tricky algorithm to prevent strong players from winning a lot (spins) and vice versa to help weak players make at least some results so that they do not lose interest in the game (twists).
Research Object and Data Source
First, I tried to make a list of mechanisms through which the twist can be implemented and got the following:

Damage Per Shot: Data Collection Is Simple and Therefore Analyzed

Penetration on shooting: there is no way to collect data here, as this information is not displayed anywhere

Accuracy: The projectile can be deflected from the ideal trajectory randomly

Matchmaker: Situations where a stronger player is more likely to be placed on teams that are known to be weak, and vice versa

Denying an Opponent: An opponent who is one shot away outlasts him
To check for the presence or absence of twists, I collected data from the streams of two strong players (KorbenDallas is a witness of the twist sect and the_barbarian does not really believe in them), who played the same tank (T95E6) for quite a long time. This made it possible to collect fairly large samples for analysis. In this article, I will discuss points 1, 4, and 5.
Damage Per Shot
For this section, data was collected from several streams and the sample size was approximately 500 values for each of the players.
As you can see in the image above, the histograms for shot damage fit pretty well into the normal distribution curve, suggesting that shot damage is likely to be distributed normally. Also, based on these samples, the mean, the standard deviation, was calculated. They were 400.3 and 32.39 for the_barbarian and 399.38 and 33.3 for KorbenDallas, which corresponds well to the passport damage of 400. Using this data, I estimated confidence intervals of “Three Sigma” and got the following: 400.3±4.1 for the_barbarian and 399.38±4.9 for KorbenDallas. These intervals overlap well and there is no reason to say that one player has an advantage over another. Thus, the average values are most likely not subject to twists, and this is to be expected, since such deviations are quite easy to notice.
Now let’s deal with the following kind of twists: if you knock out high damage per shot many times in a row, then the player will get into a spin (i.e. subsequent shots will have much lower than average damage) or vice versa. To check for this kind of tweaking, you will have to refer to the analysis of the time series.
For time series, you need to build an autocorrelation function. If there are values that are very different from the neighboring ones, then subruttas exist. However, autocorrelation can only detect the presence of a linear relationship, which may not be true for the analyzed samples. So I calculated the “autoreciprocal information,” i.e., the reciprocal information between the original time series and its shifted copy. And I got the following:
As you can see, when the shift is small, the value of mutual information is small, but not zero. This is due to the finite sample sizes. And as the shift increases, the sample sizes decrease (because the shift is not cyclical) and the mutual information grows due to the smallness of the samples. But these results again suggest that there are most likely no twists.
Readers may wonder how sensitive “automutual information” is to the presence of twists. To do this, an unfair time series was generated according to the following principle: if two times in a row the damage is less than (greater) than the average, then the next shot will have damage greater than (less) than the average. As you can see from the figure below, even such a small interference with the generation of random variables can be noticed. To be fair, it’s worth noting that the dishonest series has a value that stands out noticeably at the beginning of the graph about 1 in 6 cases.
Balancer
As I mentioned earlier, another way to implement tweaks is the load balancer, i.e. the algorithm responsible for creating commands. The main thesis here is that weak players are thrown into a deliberately stronger team, and strong players into a weaker one. Part of the reason for this is the fact that player win rates are somewhere between 43% and 70%. Lower win rates can only be achieved by engaging in outright sabotage, and larger ones can only be achieved by playing in a platoon (i.e., always together and with voice communication) of three strong players. However, the reason lies rather in something else.
It’s not that the matchmaker keeps track of the player’s win rate and tries to push it up or down, but that the entire tank community is a huge interacting and selfconsistent system. This will manifest itself, for example, in the fact that everyone cannot lose at the same time, because if there are losers, then there will be winners (draws can be neglected, because there are very few of them). Yes, there are very bad players who will always drag the team to the bottom. But, first of all, tanks are played 15 vs 15 and their contribution can be compensated by other players. Secondly, they may come across equally bad players, and one of them will have to win, which will increase their win rate. And here a vicious circle appears: the more bad players there are (the percentage of victories is less than 43%), the more often they will meet against each other in battles, then their chances of winning will already be 50/50, and this will inevitably lead to an increase in their percentage of victories, since before that it was generally 43%.
To test my reasoning, I used the following model. I took 1000 players (you can take another number, it doesn’t matter). For each player, I assigned a random evenly distributed number from 0 to 1 (although you can take another distribution), which can be called a skill. 0 means that the player doesn’t understand anything at all and will always lose, and 1 means that the player will always win. Then, I conducted battles for these players according to the following principle. First, I created a team of random players and calculated the average skill of the team. Well, whoever had more skill won. And such battles were held many times so that each player played about a hundred battles. And after that, I built the following graphs of the player’s win rate depending on his skill. As seen for 15v15 fights, an individual player’s skill has little effect and a very bad player can have the same win rate as a good player. In the case of 3v3 fights, a strong player can draw out a team, while a weak player can sink it.
I also tried to explain the asymmetry between the lower and upper bound by the win rate (43% is much closer to 50% than 70%). To do this, let’s assume that each tank has 2000 hit points. Then to have 50% wins overDeal an average of 2000 damage. If the player is very bad, then his minimum contribution will be 0 damage (and it cannot be lower, because otherwise it is already purposeful sabotage). A good player, on the other hand, has no such limits and can deal 5000 damage on average, thereby covering the contribution of 2.5 players and gaining a win rate much farther from 50% than the win rate of a bad player.
Denying
The last point I would like to discuss is finishing off the opponent. It often happens that the enemy has 350 hit points, the average damage at penetration is 400, but due to the fact that the damage is distributed randomly, the damage passes less than 350.
And while I was looking at the streams for the dataset, I sometimes paid attention to how the streamer reacted to whether he finished off the opponent or not. And I made this table.

finished off 
didn’t finish it off 
altogether 
Noticed 
2 
6 
8 
Didn’t pay attention 
3 
2 
5 

5 
8 
13 
I then applied Fisher’s precise test to determine whether there was a relationship between these events and the response to them. According to the Fisher test, the probability of obtaining such results is 20%. This suggests a certain bias (the player is more likely to notice that he doesn’t finish off the opponent because of the spin than that he finishes them off), but the confidence probability of this is quite small, so it is impossible to say for sure here.
And a little bit about psychology
It seems to me that spins and tweaks were invented due to the fact that random variables do not behave the way the player wants. For example, it is very common to hear complaints that the damage three/four/five times in a row is (above) below average and this is due to (under)spinning. The probability of these events alone is not that small (1 in 8/16/32). The following example illustrates this perfectly. If you compare the sequence of 0 and 1 with equal probability created by a computer and a human, you can notice the difference: in a human sequence, 0 and 1 alternate much more often, while in a computer sequence you can find five 0s in a row.
In this example, try to guess where the sequence is:
011000110100111010000111000110101001011010101111010
11011111111110110000111101110000000011110111101000
Hidden text
Correct Answer: The First Line Is Human
The second line for the player, if 1 is counted as aboveaverage damage, and 0 below average, will feel like this: 110111111111101 (wow) 1000011110111 (so far everything is fine, but should be unscrewed) 00000000 (ahh, unscrewed) 11110111101000 (everything is fine again).
Another mental distortion is that negative experiences are remembered much better than positive ones. Therefore, the player may not remember how he had aboveaverage damage many times in a row yesterday (or he got into strong teams), but it is great to remember how yesterday he was unable to finish off someone due to damage much lower than average and lost the fight.
In fact, twists and turns are invented by the subconscious to justify successes and failures in the game.
In lieu of conclusion
In this article, I checked for the presence of only some unscrewing mechanisms and came to the conclusion that there is no reason to believe that they exist (at least in the mechanisms that I was able to test). One could argue that there are very clever tweaks that cannot be noticed by these tests. But this analogy comes to mind. Someone in his garage makes burnt Mercedes, and once this person sold a Mercedes, but the buyer noticed that it was burnt. Of course, they were beaten for this, and in order not to burn in this place next time, this part is either replaced with the original, or made completely identical to the original. At the next sale, they notice problems with another part and it also has to be replaced, and so on until this someone starts producing a complete analogue of the Mercedes. And the question arises, why torture yourself so much and make a Mercedes in the garage, if you can go to work at a Mercedes factory and get the same money? And the same question arises with twists. Why bother with it when an honest random gives similar results?
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