# jemdoc: addcss{rbh.css}, addcss{jacob.css}
= elo scoring
~~~
{}
- Arpad Elo's expected-win-rate [https://en.wikipedia.org/wiki/Elo_rating_system scoring system] ~ e.g. [http://fivethirtyeight.com/features/how-we-calculate-nba-elo-ratings/ nba elo]
- converts between
-- difference {{D = P1 - P2}} of elo scores of two players, and
-- P1's expected winrate R when playing P2
- given D,
-- set {{R ← 1 / 1+10D/400}}
- equivalently, given R,
-- set {{D ←}} {{400 log10(1/R - 1)}}
- example, given P1\'s win rate vs P2 is .6, how much higher is her elo score ?
-- {{P1 - P2 ←}} ~ {{400 log10(1/.6 - 1)}} ~ {{≈}} 70.4
~~~
~~~
{}{}
def winrate(x,y):
return 1.0/(1.0+ pow(10.0,(x-y)/400.0))
def elo(r):
return 400.0 * math.log(1.0/r - 1.0, 10.0)
~~~
~~~
{score differences and win rates}{}
0 .50
50 .57
100 .64
150 .70
200 .76
250 .81
300 .85
350 .88
400 .91
450 .93
500 .95
~~~