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On run differential and the Pythagorean record

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Crazy as it sounds, the A's are playing better than their 36-22 record would suggest.

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The A's are on pace to win 100 games. That's the conservative estimate, though — they're actually on pace to win 101, if you round correctly. That would be Oakland's best regular-season mark since 2002, the year the Athletics won 20 straight in August and September en route to 103 total victories.

So 36-22 is beyond good; it's as good as any fan could have reasonably hoped for after 58 games, even after two consecutive division championships. But here's the crazy fact that you've all heard before: the A's, by most measures, are significantly underperforming.

Take Bill James' original Pythagorean record, for instance. The simple formula — runs scored2 / (runs scored2 + runs allowed2) = win — would give the A's an unthinkable win rate of .730, good for 42.35 wins through their first 58 games. Call it 42 and the A's are 42-16, on pace for 118.26 wins.

Here's the problem with Bill James' original formula for the Pythagorean record, though: it underestimates win totals, to the tune of about three wins per season. Call it 121.

So let's move to a more modern version of the Pythagorean record, the one that uses 1.83 as the exponent instead of 2.

It's back down to earth a little with that version, which spits out a winning rate of just .712. That's 115 wins and change over the course of a 162-game season, nothing too impressive, really, considering that the Mariners won 116 games in 2001. Adjusting for 58 games projects 41.29 as of now, which translates to 41-17.

Let's try another version. This one's a bit more math-y, but not to worry — I got a B- in calculus freshman year. Clay Davenport's "Pythagenport" formula actually takes runs scored, runs allowed, and games played into account when figuring the exponent used in the original Pythagorean record formula. Taking the log of [(runs scored + runs allowed) / games played] gives us .9214. Multiply by 1.50, add 0.45, and we get 1.8321. That's basically 1.83, but we'll run it anyway. Surprise, surprise — it projects the A's to be at 41-17.

Even Clay Davenport uses the most modern version now, known as "Pythagenpat". That one is surprisingly simple, deriving the exponent from the following formula: [(RS + RA) / G] ^ .285. That comes out to...1.8306. They're all 1.83. That has the A's at, unsurprisingly, 41.37 wins, or 41-17.

Obviously, what's done is done — there's no getting back the five or so "missing" wins that Oakland squandered, or at least, the ones that its run differential says it has. But if the A's can live up to that potential in the season's remaining 104 games, they'd manage about 74 wins in that span, upping their season total to 110.

This is a ridiculous conversation to begin with. The A's are 36-22, 14 games above .500 on June 4. To say that the team is underperforming would be ludicrous in almost any circumstance. Somehow, here, it's reasonable. Oakland has scored more runs, and allowed its opponents to score fewer, than any other team in the Major Leagues. The Athletics could play .538 baseball for the rest of the season and still reach 92 wins.

The other obvious school of thought is that the A's are simply in over their heads. Well, first let's consider that slightly different iterations of this team achieved 94 wins in 2012 and 96 last season. Is it possible for the A's to be in over their heads even though, from a win-loss perspective, they're on pace to win just five games more than they did a year ago?

Beyond that, no player is really screaming "overachiever". Jesse Chavez and Drew Pomeranz might not finish the year with ERAs under 3.00, sure, but no offensive player is doing more than he's capable of, especially now that Derek Norris is no longer hitting closer to .400 than .300.

That said, it'd be reasonable to expect a little more normalcy in the coming months. That doesn't mean bad baseball, or even average baseball. It just means baseball not played to the tune of a +118 run differential over 58 games. As some team from some other city on the shores of San Francisco Bay has demonstrated this year, even a +54 run differential in the same span can be very, very good.

The A's won't go 121-41 this year, not unless they one-up 2002 and break the record for longest winning streak. But they are, crazy as it sounds, better than 36-22. Only time will tell how much better, and if the season's last four months are anything remotely close similar to the first two, it'll be a lot of fun finding out.