+- International Simulation Football League (https://forums.sim-football.com)
+-- Forum: Community (https://forums.sim-football.com/forumdisplay.php?fid=5)
+--- Forum: Media (https://forums.sim-football.com/forumdisplay.php?fid=37)
+---- Forum: Graded Statistical Analysis (https://forums.sim-football.com/forumdisplay.php?fid=153)
+---- Thread: *Pythagorean Win Expectation (/showthread.php?tid=4168)
*Pythagorean Win Expectation - JuOSu - 09-05-2017
Pythagorean Win Expectation is a pretty cool thing that bases win and loss records on point differential. It basically shows how good a team was supposed to be based on the points they scored. It is said to predict win-loss records from season to season better than the actual record, according to people like Bill James, who many will recognize.
I decided to do the math on season 2. I used this formula:
PointsScored^2.37 / (PointsScored^2.37 + PointsAgainst^2.37) times 14 (games)
The results are the following:
Outlaws 12-2 real record, 11.96 Pythagorean wins
Otters 8-6 real record, 8.73 Pythagorean wins
Sabercats 4-10 real record, 3.44 Pythagorean wins
Legion 3-11 real record, 3.50 Pythagorean wins
In this conference, we see that the Legion actually performed arguably better than the Sabercats. The rest is all quite close to what it should have been.
Hawks 8-6 real record, 6.93 Pythagorean wins
Wraiths 8-6 real record, 7.14 Pythagorean wins
Yeti 8-6 real record, 8.75 Pythagorean wins
Liberty 5-9 real record, 5.87 Pythagorean wins
In this conference, we have one more proof that the best team missed the playoffs. All three teams had the same record, but with Pythagorean wins, there is a huge difference between them. Hawks vastly overperformed or got lucky, with the biggest difference in Pythagorean wins at 1.07 wins more than they deserved. Liberty are also notable as the team that was most unlucky with 0.87 less wins than they deserved, only about one win less than the Hawks who ended up in the final game.
Hope someone enjoyed this
*Pythagorean Win Expectation - 37thchamber - 09-05-2017
Based on these numbers, you'd expect the Yeti to bounce back next season and probably make the playoffs, if not win the NSFC while the Hawks to regress a bit, and the Wraiths and Liberty to stay around the same... but of course, this is ignoring personnel changes. So Yeti and Wraiths to make the playoffs, according to this.
This also shows the disparity between the NSFC and ASFC in a way. Sabercats and Legion weren't even close by any measure, whereas the NSFC teams were projected to finish within 3 games of each other. That's not a massive swing, I mean, if the Hawks hadn't beaten the Liberty on the road, they wouldn't have made the playoffs. Similarly, if the Yeti hadn't lost to the Legion at home, they would have made the playoffs. These numbers basically confirm those two results as being the crucial ones (Hawks ~1 win better than projection, Yeti ~1 win worse than projection)
That said, I'm wary of these numbers being applied to what is essentially a glorified random number generator. I'd perhaps adjust the coefficient to be lower, tbh, to account for a little more randomness. Though you could make the opposite argument for home games. Hmm... in that case maybe I'd make two calculations, for home and away games, and then sum the expected wins.
Interesting stuff anyway.