Pythagorean Differential Odds Question

[fauteuil7]

I just did a replay of the 1990 Yankees season for probably the 100th time over the past 30 years and however many versions of OOTP have come out since 5, and it's the first time I've won the division with Historical Transactions (but not Historical Lineups) turned on so I couldn't cheat by hustling the AI in trades; I wanted to deal with the same injuries and dumb trades Bucky and Stump dealt with (Dave Winfield for Mike Witt???), Deion disappearing for football, all of that. We finished 85-77, while the real life team went 67-95. I usually play to see if I can get to .500 and call that a victory, but this run was honestly miraculous.

We had the worst Run Differential in the AL and a +13 Pythagorean Differential; I'd like to know what the odds of that happening are since it seems so astronomically improbable. Our starting pitching and back of the bullpen were terrible so we lost 6 games by 9 or more runs and only won 1 game by that margin, and we were 28-12 in one run games and 51-30 at home with a number of walkoff wins so I know that skews the Pythagorean results but honestly, that looks like what happened to the 1905 Tigers when they had the record at +14.78: 7 losses by 9+ runs, 1 win by 9+.

What are the percentage odds of a +13 result? My hack math was to take the number of team-seasons since 1969 to 2023, 54 years times an average of 30 teams for 1620 team-seasons, then 16 teams by the 63 seasons between the 1905 Tigers and the Divisional Era, getting 1008, a total of 2628 team-seasons. Based on actual occurence, this looks like a 1 in 2628 result, a 0.00038% chance.

Does anyone better at math than I am know a more direct way using the equation to get the odds of each potential result, like a chart that shows +1, +2, etc. with the odds of each result happening? I couldn't find anything like that online anywhere.

[kq76]

I don't think the odds depend on what really happened. For example, say your league is only 9 years old and the event in question has never happened, but in the 10th year it does. Does that really mean it's going to happen at the same rate if the league ran for another 1000 years? No, not at all. If it's odd enough it might never happen again and so the % you calculated based on only 10 years would be wildly inaccurate over 1000 years.

A better way, I think, to calculate the odds would be to run OOTP 1000 seasons and see how often it happened in OOTP, but that'd be a lot of work just for curiousity's sake. I'd just take the win that something happened that you think you might never see again.

[Syd Thrift]

There was a year in the early 90s when the Giants were +20 in Pyth differential; they were outscored significantly that year, enough to have a a Pythagorean record of like 71-91 but they won 90 instead.

These instances are rare but they do exist.

ETA: I looked it up and the 97 Giants were “only” +11; however, the 1905 Tigers were +14 and the Rangers from a few years back finished +13.

[fauteuil7]

Here's a list I found:



I just checked the SF stats as you updated your post, this image I was using cut off with just one team at +10; '97 Giants won 90 with a Pythag of 80. That Giants team is crazy because they also won a few blowouts, 16-2, 16-4, 17-4, but lost 11 games by 9 or more runs. It looks like the same pitching staff composition as my run too, 2 1/2 okay starters and one guy at the back of the bullpen who had a 7.11 ERA but pitched in 63 games.