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October 17th, 2018, 07:26 AM   #1
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Math Focus: Multiplication
Fortnite math problem: is the average win rate exactly 1%?

At first I thought for sure it's 1% exactly, but then I realized I was wrong. Consider two cases:

Suppose there are exactly the same 100 players each game. In this case, since 1 player wins and the rest lose, the average win rate after n games is: (\sum_{i=1}{100} games won by person i / games played by person i) / total number of players and since the number of games played by all people is n (only 100 people), then this reduces to n / 100n = 1%.

Suppose there are more than 100 people, and people play an unequal number of games (as in real Fortnite), then it is not true. For a counterexample, suppose there are 101 people. Suppose the first has players 1,...,100, and player 1 wins. suppose the second game has players 2,..,101 play, and player 101 wins. Then the average win rate after these two games is is (100% + 100% + 98 * 0%) / 101 = 1.98%. Idk if anyone cares lol.
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October 17th, 2018, 02:43 PM   #2
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Please clarify description and question.
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October 20th, 2018, 11:46 AM   #3
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OK, bigchest01 (though it is 99*0% but the outcome is the same)

Now assume that you played the same games and players #50 and #51 won instead of #1 and #101. Then the average win rate would have been (50% + 50% + 99*0%)/101 ~ 0,99%.

Clearly, average win rates are not a constant factor in the group performance for this game (and games with a similar formula). Low participation winners up the group average, high participation winners do the opposite.

Last edited by Arisktotle; October 20th, 2018 at 12:08 PM.
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