Serious Mathematics Pro In Need! : D (explain Something To Me)

I am fully aware that i may sound very very stupid in this post >.< , but ill accept it in the name of knowledge.

Do not read the spoiler below if you're only here for math

Spoiler: the situation i encountered the problem

I came home from school yesterday and saw my brother playing Hearthstone. He asked me if i thought his deck was good so i said i would make a spreadsheet for him that would automatically calculate his win rates . I made the spreadsheet and showed him where he needed to enter his values after every game . I had a column that calculated his total win rate .I also had a column for his win rate against different classes to find out which classes his deck was weak against. I had it calculate his win rate per class and check if it was above average . If it was above average the number would be blue , if it was below average it would be in red . (I also made a table for him that would show what is in meta but that is a secret to us >:P)

The next day , he had played a ton of games and he showed me his spreadsheet and something didn't add up. The program was turning things red even if they were above the total win rate so i calculated the "Avg of the Avg win rate per class " and it wasnt equal to the total win rate , which i had previously believed would be equal. And now i would like someone to correct me :D

P.S. The values below are not his actual win rates because he wants it to be a secret so that people don't copy his deck (Not like they know what OP Deck he's playing anyways >.<)

The Question:
*Avg=Mean

Class-----/Win--/Games Played(win+loss)|--Avg Win Rate Per Class
A_____/_2__/_5______________|___(2/5)*100%=40%
B_____/_1__/_2______________|___(1/2)*100%=50%
C_____/_3__/_3______________|___(3/3)*100%=100%

Totals__/_6__/_10________

Using Totals
Avg Win Rate = (6/10)*100%
_________=60%

Using Avg Win Rate Per Class
Avg Win Rate = (40%+50%+100%)/3
__________=63.33%

Why can i not use my avg win rate per class to find my avg win rate?
I think the one using totals is my "True Win Rate " .
I'd like for you to prove to me mathematically that i can't use avg win rate per class to calculate the avg win rate.

Thank you so much for taking the time to read my (badly written/Unmathematically written) question. :)
I would appreciate it soooo much if you take the time to help me correct my misconception :D

 

I'm not really good at that, but don't you have to multiply the chance by the amount of tries then divide it by tries? e.g:
(5x40%+2x50%+3x100%)/10 = 60%
I'm not sure though, I could be wrong!

 

You are right! :D
Thanks sooooo much for helping me !

I have the solution to my problem now and i would love it if someone wants to explain in more detail why the formula is like that or add anything extra or even have some interesting maths concepts :D

 

you're welcome! :D I have fun doing math, but I'm not the best at it so i didnt know if it was correct^^

 

I left this thread a lot less confident than before.