Mere_Anarchy
#1
Posted 24 November 2014 - 03:38 PM

First Sergeant

Players

37233battles

1,118

Member since: 07-07-2014

The following table is my attempt to model the percentile breakdown of World Tanks Blitz player stats similar to that used for World of Tanks (see WoTLabs). Summary statistics were calculated for the variables that are largely comparable irrespective of number of games played or type of vehicle. These include Win Rate (WR), Hit Rate (HR), Damage Ratio (DaR), and Destruction Ratio (DeR) This data is based on a sample of 491 players randomly collected over the past 10 days.

Win Rate

Hit Rate

Destruction

Ratio

Damage

Ratio

Category

Percentile

Under 40.7%

Under 49.9%

Under .43

Under .51

Beginner

0.00%

40.7-44.6%

50-60.3%

.43-.65

.51-.67

Basic

6.00%

44.7-47.7%

60.4-68.6%

.65-.84

.68-.83

Below Average

20.00%

47.8-50.2%

68.7%-75%

.85-1.11

.84-1.01

Average

40.00%

50.3-52.9%

75.1%-79.7%

1.12-1.43

1.02-1.24

Above Average

63.00%

53.0-57.3%

79.8%-84.2%

1.44-1.98

1.25-1.56

Good

82.00%

57.4-67%

84.2%-87.1%

1.99-2.90

1.57-1.99

Very Good

95.00%

67.1+%

87-2%+

2.90+

2.00+

Great

99.00%

How to use this table - simply find the range of scores that bracket your individual statistics and read to the right to find both your overall percentile as well as skill category (as defined by WoTLabs). For example, my own win rate of just over 54% puts me (barely) in the category of ‘Good’ players – meaning my win rate is better than that of 82% of active WoTB players.

Are these the stats the best measures of a player’s ability?

Spoiler

Likely not. Win Rate – while certainly a general indication of ability - does not completely capture it. ‘Ability’ is a complex concept that resists reduction to a single number. An individual player may be better or worse depending on vehicle or map. For example even though my average WR is 54% that is not the ability level you can expect from me in any particular battle. If I’m driving my E75 (57% WR) you can expect a slightly better performance; if I’m driving my T-54 (51% WR) you can expect slightly less (sorry team!). Similarly I know that I do better on some maps than others. At the end of the day, however, better players win more often.

Can this provide a ranking of players?

Spoiler

No. This is based on a sample rather than the entire population. The sample I collected does not allow for the calculation of WN8 nor do I have any interest in doing so. WoTLabs uses the multivariate WN8 stat derived from the API files of all players for this purpose. The table above simply provides a basic benchmark for comparing oneself against the larger universe of WoTB players. Only if/when the API data for Blitz is released will rankings through both WR and WN8 be possible.

Should you care?

Spoiler

Nope – it is entirely possible to enjoy this game immensely and not give a frog’s fat behind about your stats. However, given that I have seen lots of posts about how someone’s stats compare I thought there would be some interest.

For those who might be interested, the following sections provide more details on the mechanics of my analysis.

Sampling

Spoiler

The most difficult part of this was deciding how to sample the population given that virtually nothing was known ahead of time about the universe of WoTB players. Ultimately I chose to sample evenly from each tier – four games were played with a tank from each of the 10 tiers (using a mix of light, medium, heavy, and TD). These games were played on a variety of days (weekend/weekday) and times of day to reduce the possibility of any bias. Relevant stats were collected by accessing player profiles using the post-battle reports and then manually entered into a spreadsheet. Because of this sampling strategy the resulting data are best interpreted of as a sample of active players and not the entire universe of registered WoTB users. As a side note this was one of the more enjoyable data collection exercises I have ever done – aside from having to play at Tier I.

Data collection resulted in an initial sample of 521 players (13 x 10 x 4 + me). Any duplicate players were then removed from the sample (and not replaced). Initial inspection of the data indicated that it would also be necessary to remove players with very low (< 50) battle counts as they would have a disproportionate impact on the analysis – either because of atypically high or low win rates due to an insufficient number of battles. This arbitrary cutoff point was considered to be sufficient to negate any effects of random variation while still capturing data from low-experience players. This, coupled with the removal of duplicate cases, resulted in a final sample of 491 individuals.

Is the sample representative?

Spoiler

It should be given that it was collected in as random a manner as possible. There is no reason to suspect that any other complicating factor or underlying structure in the data would compromise the results. Other than considerations based on vehicle type and tier player the matchmaking algorithm should be random with respect to these variables.

Is the sample accurate?

Spoiler

The sample size should be more than sufficient to provide valid measures of each statistic’s variability. Although I have no way of knowing the total population of players nearly 500 data points is a very large sample for the purposes of this analysis. In populations where variables are more or less normally distributed (which is essentially the case for WR) a random, representative sample as small as 30 individuals is considered sufficient for discovering the basic structure of a data set. As an aside – in periodically looking at the number of players listed on the server during the time I conducted the sample at no time did I ever see a value higher than roughly 7500.

I am confident that the percentiles are quite close to the actual. The standard error of the means as well as the 95% confidence intervals for the means supports this fact. For example, we can be 95% confident that the mean Win Rate mean is between 48.42 and 49.41%. The only place where I am not as confident is in the upper percentiles (above 95%). I strongly suspect that the 99^{th} percentile (and possibly also the 95^{th}) is a point or two off of the actual.

The smaller sample size didn’t allow for the differentiation of the unicums (super or just regular) from the ‘great’ players (using the WoTLabs criteria). Given that they are ‘rare’ creatures by definition the likelihood of my randomly coming across one of the exceptionally high WR players was exceedingly small with this sample size (although I did have the ‘good fortune’ to be on the receiving end of a dddqqq and fullestnuke platoon in Desert Sands). I was hoping to bootstrap the sample to increase confidence levels for all of the percentiles but currently don’t have this add-on for my statistics software. This will have to wait until later. But really – isn’t it enough to be in the top 1 percent of players?

Yay - Stats and Graphs!!!

Spoiler

The following table shows what the various statistics are for the variables measured in this analysis.

Mean

Standard Error

Mean 95% C.I.

Median

Range

S.D.

Number of games

2184

97.2

1962.5-2375.5

1447

51-13,036

2154.6

Win Rate

48.9%

.25

48.42-49.41

48.9

32.14-82.33

5.6

Hit Rate

69.5%

.51

68.6-70.6

71.98

12.82-89.14

11.3

Damage Ratio

.96

.016

.93-.99

.92

.15-2.76

.36

Destruction Ratio

1.05

.026

1.02-1.12

.97

.06-3.78

.51

The following histograms show the distribution for each variable.

Number of battles does not have a normal distribution– nor would it be expected to. It is clearly a variable that shows a heavy positive skew with most of the cases at or below roughly 1500 games. Given that this is a relatively new game and assuming that there is a continuous stream of new players we would expect this shape. It would be curious to see how this may change as the game matures. It seems likely that it would assume a more normal distribution as time goes on (albeit with a continuing positive skew).

WR has a very normal, symmetrical distribution aside from a handful of outliers at each end of the distribution. This is not surprising - these are to be expected and do not significantly impact the overall results. These outliers are those individuals with win rates below 37% and above 61%. There are some in every sample.

Comparison to the results for WoT players. The average win rate of WoTB players (48.9%) is quite close to that of active players in WoT (49.97%). WoTB players have a greater spread – meaning there are more low WR and more high WR players. This more diverse talent pool is not surprising in a game platform designed for casual gamers. On the higher end Blitz is an easier game to be very good at – a 60+% win rate in WoT places someone in the Unicum category – in the top .1% of all players. In Blitz this is only enough to get you in the “Very Good” category. The ability to ‘carry’ is likely enhanced due the smaller size of the game (especially in the case of ‘power platoons’) – allowing win rate to more directly measure ‘talent’. Those who are familiar with WoT can add details to this suggestion.

Relationships between Variables

Spoiler

The sample data I collected also allowed me to look at the relationship between the different variables and overall Win Rate. These are shown in the five scatterplots below.

As the plots show, there is a general (positive) correlation between Win Rate and the # of battles, Hit Rate, Damage Ratio, and Destruction Ratio. Of these the connection between WR and # of Battles is the weakest. Playing the game more often clearly has an overall impact on WR (the general slope is upwards), but is highly variable. So in general people with more games tend to be better – but this tendency is fairly weak. Perhaps surprisingly, although there is certainly a positive relationship between WR and HR it is not as strong as I would have originally expected. Some very high WR players have low HR scores; some low WR players have high WR scores. DaRatio and DeRatio both have very strong relationships to overall WR. This is not surprising. The more damage you do and the more enemy vehicles you destroy clearly increase your (team’s) chances of winning. These two are also very strongly correlated with each other (also not surprising as they are not completely independent variables). You can't kill lots of tanks without doing lots of damage and vice versa.

If you’ve gotten this far – I’m impressed. Thanks for reading and I welcome any comments, feedback, or suggestions.

TwistedMetal_
#6
Posted 24 November 2014 - 03:52 PM

First Sergeant

Players

14290battles

2,741

[DFNT]

Member since: 06-26-2014

Nicely done! Love the part about not giving a "FROGS FAT ---" In the end it's only a game....One you will be back in 7 min or less to have at it again! + 1

Mere_Anarchy
#7
Posted 24 November 2014 - 03:54 PM

First Sergeant

Players

37233battles

1,118

Member since: 07-07-2014

TwistedMetal_1, on 24 November 2014 - 09:52 AM, said:

Nicely done! Love the part about not giving a "FROGS FAT ---" In the end it's only a game....One you will be back in 7 min or less to have at it again! + 1

Thanks, I appreciate it. At the end of the day its all about the fun.

It's interesting that win rate somehow means both more and less than it does on PC. With smaller teams, an individual can have a much larger impact, but the stat is confounded by platooning much more powerfully than on PC. Even though platoons are 2/3 the size, teams are less than 1/2 the size they are on PC. I am happy with my win rate, but would love to know what it could be if I ever platooned (I have maybe 10 platoon battles).

I am a bit confused by the mean win rate. 48.9 makes sense. That means on Blitz, 2.2% of battles end in a draw. However, a mean of 49.97 would mean only 0.06% of battles on PC end in draw, which seems unlikely.

Mere_Anarchy
#12
Posted 24 November 2014 - 04:06 PM

First Sergeant

Players

37233battles

1,118

Member since: 07-07-2014

Androyce, on 24 November 2014 - 10:01 AM, said:

It's interesting that win rate somehow means both more and less than it does on PC. With smaller teams, an individual can have a much larger impact, but the stat is confounded much more powerfully than on PC. Even though platoons are 2/3 the size, teams are less than 1/2 the size they are on PC. I am happy with my win rate, but would love to know what it could be if I ever platooned (I have maybe 10 platoon battles).

I am a bit confused by the mean win rate. 48.9 makes sense. That means on Blitz, 2.2% of battles end in a draw. However, a mean of 49.97 would mean only 0.06% of battles on PC end in draw, which seems unlikely.

In this case the mean win rate is by individual player - meaning the average player has won 48.9% of their games (not that 48.9% of all games have ended in a victory). In this case its not possible to differentiate draws from losses since they are both 'not wins' so to speak. Hope this helps to clarify things.

In this case the mean win rate is by individual player - meaning the average player has won 48.9% of their games (not that 48.9% of all games have ended in a victory). In this case its not possible to differentiate draws from losses since they are both 'not wins' so to speak. Hope this helps to clarify things.

I must be missing something. I would think the mean win rate would be the same as the number of games ending in victory. For instance, if draws were not possible then the mean win rate should be 50%, should it not? For every individual player's win, there is an individual players's loss. The mean win rate should be the same as number of wins ever in the game/number of games ever played. For every player with a 60% win rate! there must be a player with a 40% win rate! or two players with 45% win rates, etc.

Mere_Anarchy
#15
Posted 24 November 2014 - 04:18 PM

First Sergeant

Players

37233battles

1,118

Member since: 07-07-2014

Androyce, on 24 November 2014 - 10:11 AM, said:

I must be missing something. I would think the mean win rate would be the same as the number of games ending in victory. For instance, if draws were not possible then the mean win rate should be 50%, should it not? For every individual player's win, there is an individual players's loss. The mean win rate should be the same as number of wins ever in the game/number of games ever played.

Ahh, now I think I see what you mean. Are you arguing that in essence given all the players it should be like a coin flip - that given enough iterations the overall win rate should approach the statistical expected number (the law of large numbers)? In this case, I guess because of the human element this isn't the case making it not a totally random process. But to be honest - I don't know. Anyone else want to try?

DukeNukedem
#16
Posted 24 November 2014 - 04:20 PM

Lance-corporal

Players

58327battles

86

Member since: 09-18-2013

Fantastic analysis - while some will quibble with some of the results I for one really appreciate the effort. For a while I have quickly judged a player's ability using a ratio of their PR to total games played, knowing this to be flawed but certainly better than PR alone. Close to or over 1 for this ratio meant a unicum. For an "at a glance" number, this is still quite good but am using destruction and damage ratios for deeper dive.

Viper8757NC
#17
Posted 24 November 2014 - 04:21 PM

First Sergeant

Players

27016battles

2,215

[III-S]

Member since: 07-04-2014

>>Are these the stats the best measures of a player’s ability? Likely not. <<

Then what was the point of the exercise?

Don’t get me wrong, I applaud you for the effort. Nonetheless--and like you-- I urge caution for anyone attempting to draw any conclusions of ‘ability’ from your findings.

NOTE: and I see upthread that people are already--and mistakenly--doing so.

Question: were the players pulled from a random sample or just the games in which they participated?

Edited by Viper8757NC, 24 November 2014 - 04:23 PM.

This has a lot of effort put into it with a good-sized sample to back it up.

Not poking at your graph, but I've noticed that a majority of the great players on Blitz started around the same time, right when it was released, to be exact.

Tier Xs (in order of unlocking):T110E5, M48 Patton,T-62A, IS-7, E50M, IS-4, FV4202, T110E3, FV215b, Obj. 268, T110E4, Leopard 1, Obj. 140, STB-1,Obj. 263, T57 Heavy, AMX 50B, Bat Chat 25t

This has a lot of effort put into it with a good-sized sample to back it up.

Not poking at your graph, but I've noticed that a majority of the great players on Blitz started around the same time, right when it was released, to be exact.

When exactly was it released? I didn't find it until it was "Featured" on the app store.