Pythagorean Expectation¶
Expected Win % is proportional to ratio of square of my team's parameter and sum of squares of both teams' parameters. Parameter could be goals,points, etc. Regression analysis ensures right parameter(s).
$$ \text{Expected Win}\% \propto \frac{x2}{x2 + y^2} $$ where
- x = parameter scored
- y = parameter conceded
A graph for pythagorean expectation vs win % will show a strong relation. Relation is characterized by the following values
- correlation
- standard error smaller the better
- \(t\) statistic greater the better \(t = \frac{ \text{coefficent} } { \text{std err} }\), (coefficient = slope)
- \(p \le 0.05\) (statistically significant) smaller the better
- R-squared greater the better
Advantages¶
You might be thinking, why not just use the previous W% to predict future W%. The problem is that W% involves randomness. Meanwhile, PE captures the performance of the team.
Imagine a really good team which lost games because of some random events - let’s say opponent goal keepers were just too good; that doesn’t mean that we played bad. Meanwhile PE using shot scored on target/conceded will provide a better picture. Hence, past PE is a better predictor than past W%
Limitations¶
This isn’t ideal for
- small datasets
- games with smaller innings
- games like cricket where the chasing team has a target, so it cannot score to the best they can