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Adjusted win rate: why a 70% win rate can lie

On almost every infovgc table you will see «adjusted win rate» instead of the raw win rate. It is not a whim: without the adjustment, the top spots would go to Pokémon with a handful of games.

By @9shinny ·

The problem with small samples

Raw win rate is wins divided by games. A Pokémon that has played one tournament and won 7 of 10 games has 70%; one with 240 games and 140 wins has 58%. Is the first one better? Almost certainly not: ten games are won or lost by the player, the pairings or luck.

How we adjust it

We add 20 imaginary games at 50% to every Pokémon: 10 wins and 10 losses. The formula is (wins + 10) divided by (games + 20). Ties count as half a win.

With the example above, 7 of 10 becomes (7 + 10) / (10 + 20) = 56.7%, and 140 of 240 becomes (140 + 10) / (240 + 20) = 57.7%. Now the order makes sense: the one with many games barely moves and the one with few is pulled towards 50% until it proves more.

Why 20 games

It is a balance. With fewer, rare Pokémon would keep taking the top spots; with more, we would take too long to notice that something new works. In statistics this is called a Bayesian adjustment: we start from the idea that every Pokémon is average and let the results convince us otherwise.

What win rate does not tell you

A Pokémon's win rate is that of the teams that bring it, so it also measures its teammates and whoever plays it. Mirror matches (the same Pokémon on both sides) pull it towards 50%. And a high win rate with low usage can be a strong Pokémon or one only good players use.

That is why it is worth reading together with usage and the Top 8 index, which shows whether a Pokémon reaches the top cut more often than it is played.

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