Tag Archives: pythagoras

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.

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More arguments about the Orioles and regression

David Schoenfield in ESPN:

However (you knew this was coming), only four teams have ever made the playoffs while getting outscored. Of course, the extra wild card changes that dimension a bit, as the necessary win total to make the postseason goes down. Here’s what I did. I looked at three of those four playoff teams and every team since 1969 that won 85 games while being outscored (leaving out the 2005 Padres, who won 82 games while getting outscored by 42 runs, but aren’t really germane to the Orioles since 82 isn’t getting them into the playoffs).

It doesn’t happen often, which is why us number crunchers constantly refer to run differential as a general sign of team strength and indicator of future results.

First of all — it’s we number crunchers.

More importantly:  yes, it’s rare for teams that get outscored to win 85 games.  But so what?  The Orioles are 9 games over .500 with 2/3 of the season already in the books.  Conditional on that, the chance of the Orioles winning 85 is not bad at all.

And it’s rare for 85-win teams that get outscored to make the playoffs.  But that’s because it’s rare for 85-win teams to make the playoffs!  If the Orioles end up with 85 wins, they probably won’t play in the postseason; but that has zilch to do with them allowing more runs than they score.

To his credit, Schoenfield ends up getting this right at the end of his piece:

Let’s say it will take 88 wins to make the playoffs; I think it will take a couple more than that, but, hey, maybe the Angels and Tigers aren’t as good as most people think and never get on a big roll. To win 88 games, the Orioles have to go 29-23 over the final 52 games. Can they go 31-21 to win 90? My argument is they can’t; Orioles fans will suggest that Miguel Gonzalez (3.80 ERA in 47 innings) and Chris Tillman (5-1, 2.38 ERA in six starts) help make the rotation respectable. Maybe so. Regardless, the Orioles will have to play better then they have; you can’t keep relying on extra-inning miracles.

You can usually count on FanGraphs for a more quantitatively savvy take, and Dave Cameron comes through:

But the odds are already stacked against the Orioles anyway. They are 60-51 despite being outscored by 47 runs, and everyone keeps expecting them to fall out of the race any day now. Instead, they just keep winning. Yes, they’ve built their record on unsustainable performances, racking up 12 straight extra inning wins and going 22-6 in one run games. The way the Orioles have put themselves in contention suggests that they’re not as good as their record suggests, and that of all the teams fighting for the wild card, they’re the one least likely to continue winning games at this pace.

But none of that should matter to the Orioles. The reality is that those 111 games are in the books, and no one is going to be stripping wins from them simply because they won more close games than we would have expected. Baltimore is tied with Oakland and Detroit for the lead in the wild card race with 51 games to go, and in that kind of small sample, the variation in expected record around a team’s true talent level is pretty large. Even if we accept that the Orioles are playing over their heads, that does not preclude them from continuing to play over their heads for the rest of the season.

It might not be the most likely outcome, but the Orioles shouldn’t give up on a playoff run simply because the results aren’t likely to turn out in their favor. Even if we thought the Orioles were a true talent .460 team, we’d still expect there to be a wide range of possible outcomes given their current situation. In general, standard deviations around a team’s true talent level are believed to be about eight to 10 wins per full season, so it’s completely normal for a 75 win team to win 65 or 85 games just due to normal variation. In smaller samples, the variations are even larger, so even if we analyze the Orioles as a true talent .460 winning percentage team, that just means that they’ll probably win between something like 39%-53% of their games in August and September. In other words, they could be good, they could be bad, or they could be anything in between. Their underlying stats suggest that the mean is shifted towards the losing side of the curve, but that doesn’t mean that the winning side doesn’t exist simply because they’ve already “gotten lucky” in terms of wins and losses. They are not more likely to underperform now simply because they’ve already overperformed in the first four months.

Lucky wins count!

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July math link dump

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Pythagorean doldrums

Since the All-Star Break the Orioles have scored 79 runs and allowed 93.  According to the Pythagorean formula we should have won about 7 of the 17 games we’ve played.  Instead we’re 4-13, with tonight’s 9th-inning loss to Detroit in a game we’d led 5-0 the latest sour little burst of dispirit.

If you need some cheerful Pythagoras to balance that out, look no further than the brand-new record from SF indie-pop outfit The Invisible Cities, featuring a hypnotic and slightly kooky track called “Pythagorean Theorem”:

‘a’ squared plus ‘b’ squared
the sum equals ‘c’ squared

opposite the angle ninety degrees wide
the hypotenuse likes saying it is the ‘c’ side
the other two keep stretching they don’t mind
they’re crafting copper etchings they’re just fine

For a limited time, their new album is free for download.  I recommend it (though my favorite song of theirs remains the older “Bumper Cars,” which you can listen to on their myspace page.)

Update: “Pythagorean Theorem” now live on YouTube.

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