## Why are the Orioles performing over their Pythagorean record?

This graph from Camden Depot showing the Orioles’ distribution of runs scored and runs against got me thinking:

Weird, right?  The Orioles allow very few runs frequently, and a lot of runs frequently, but don’t allow runs in that 3-4-5 range very often.  Their distribution of runs scored shows a much more ordinary shape.

Could this be explaining the Orioles consistent ability to win games despite allowing more runs than they score?  It’s not out of the question.  Imagine a team that allowed 0 runs 40% of the time and 5 runs 60% of the time; that team would allow 3 runs a game on average.  Suppose they scored exactly 3 runs every single game.  Then they’d score exactly as much as they allowed, so their Pythagorean WP would be .500.  But in fact they’d be a .400 team.

So I checked this for the Orioles — if each game had an RS and RA drawn at random from the distribution above (I got the exact numbers from baseball-reference, actually) it turns out that you’d get a winning percentage of .479, which gives 58 or 59 wins out of their current 122 games played.  Their Pythagorean WP is .456, which predicts 55 or 56.

So the Orioles’ weirdly bimodal RA distribution is indeed helping them beat Pythagoras, but only by 3 games or so; why they’re 10 over Pythagoras right now remains a mystery, and is probably just some combination of great bullpen and great luck.