Training Camp lvl 20 - Global stats summary

Hi there everyone!

First of all I’m not a statistician, but I’ve got my Master degree in Econometrics, so I’ve got some knowledge how statistics works
I decided to take a look at Hay Lee Chan’s spreadsheet with TC20 pull results (to which I’m a contributor as well!)

At the time beeing, there are almost 3000 entries (pulls). So it’s quite a sample! (equivalent of over 16 years of continuous legendary training from single TC20)
After some maintanance cleaning (e.g. the sum of global stats weren’t 100% due to some errors made by entering values by contibutors), I gathered below some of the global statistical factors.

So:

Total 3 Star pulls from TC20 - 74,65%
Total 4 Star pulls from TC20 - 20,13%
Total 5 Star pulls from TC20 - 5,21%

It’s heading straight to 75%/20%/5% in my opinion. And the global average difference from the average (for all the contributors) tends to confirm this distribution:

Average 3* pulls percentage of the players differ from global stat by -1,6pp (percentage points)
Average 4* pulls percentage of the players differ from global stat by +1,6pp (percentage points)
Average 5* pulls percentage of the players differ from global stat by +0,1pp (percentage points)

It’s very small difference. It means that on average, each player pulls almost the same ammount as a global stat says.
Of course it’s global statistic, so e.g. some players would have like +8pp/-7pp/-1pp which translates to 83% of 3*, 13% of 4* and 4% of 5* heroes pulls.
But it seems that it is leveling out for players with higher statistic samples (more pulls).

Then the most concerning part. Hero colors.

The global stat says:
Total Red pulls - 17,58%
Total Blue pulls - 20,89%
Total Green pulls - 23,41%
Total Yellow pulls - 16,82%
Total Purple pulls - 21,31%

The calculated global so called ‘stanard deviation’ is 3%, which means that the average of color pulls differ from the expected average value for even distribution (which is 20% obviously) by an average value of 3%.
In other words: how spread out numbers are. But this doesn’t represent the stats for each of the players.
Average standard deviation is over 8%! So almost 3 times bigger than global stat.

To illustrate how it works, here is example of 8% standard deviation:
Red - 22 (15,60% of total)
Blue - 47 (33,33% of total)
Green - 27 (19,15% of total)
Yellow - 17 (12,06% of total)
Purple - 28 (19,86% of total)
Total: 141

Okay, somebody would say, I see that blue’s have been favorite color for RNG here, but otherwise it looks roughly even. But it’s not.

I calculated how concentrated are those, so called ‘favored colors’ for each player.
I counted Top2 sum and Top3 sum.
For example above, it’s:
53,2% summed Top2 favored by RNG colors (blue and purple)
72,3% summed Top3 favored by RNG colors (blue, purple and green)

It turns out, that most of the players have those ‘favored colors’.
Average Top2 stat is 55,1%
Average Top3 stat is 73,8% of all pulls.

For an even distribution, those values should be 40% and 60%!
It means that pulling e.g. your sixth Kiril is almost 3 times more probable than pulling your first Wu…

For 38 contributors for the sample database, for only 1 (after only 17 pulls) yellow is the most favored color. For 17 of them, the favored color is green.
The worst part is that this doesn’t get better with increasing sample size.

17 Likes

P.S. For everyone interested, here are the calculations:

1 Like

Color bias isn’t surprising. Best guess in the TC20 results thread is that the first roll is for hero tier, then the second is from the total pool of heroes, of all colors. There are extra greens in both the 3* and 4* heroes when compared to yellow.

5 Likes

It was the same with troops and they fixed it by introducing new troops. I really hope they will introduce more standard heroes to even that out aswell and to bring some new content.

3 Likes

Yea, I just did the math and it matches up. Assuming 75/20/5 for tier 3/4/5. And given the possible tc20 heroes, you get the following probabilities:
Red - 18.05%
Blue - 20.26%
Green - 24.30%
Yellow - 17.14%
Purple - 20.26%

gibs’ results listed above are pretty close to that, each within 1%.

4 Likes

I guess you are right. I did the math and have the same theoretical stats of pulling colors:

R 18,0455%
B 20,2614%
G 24,2955%
Y 17,1364%
P 20,2614%

So it seems the differences within single player are caused by small sample… The colors are more distant from the theoretical values than heroes levels (on average 5,9% of absolute distance per color compared to 4,8% per hero level) but it’s close to statistical error. And there is yet the function of time - the data was gathered trough all of the game’s versions where there was different number of different colors/levels in the pool.

So… it’s best to assume, that with pulls goes to infinity, the stats will achieve the theoretical values.

Bookmarked.

1 Like

I’m a little slow in posting up my second 20…so a total of 43 pulls.

My two 5 stars? Obakan and Kadilen (oh well, at least I pulled some 5 star, right?). Oddly I pulled them one right after the other.

2 Likes

I’ve been tracking my TC 20 pulls since I started it up, and have kept it running 24x7.
Here are the summary results:
86 total pulls
3* = 72%
4* = 22%
5* = 6%
Dark = 20%, Holy = 17%, Ice = 16%, Nature = 29%, Fire = 16%, unknown element = 1%

I will upload these into the google sheet once I get a column assignment from the owner.