May 8, 2007

Prospectus Today

Popping the Hood

by Joe Sheehan

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When do I have to shut up about it being too early?

I know there's a mathematical answer to this question, but it stretches my ability to do the math to find the answer. To try and figure it out, I asked the smart guys at BP a question:

I've read statements such as, "the chance that a .300 hitter would hit .400 over 100 at-bats is X," or "the chance that a .500 team would play .600 ball in 30 games is Y." I want to learn how to calculate these figures.

Is this as simple as an Excel function, or as complex as needing to take two semesters of math? I understand the principle behind the calculation, just not how to run the numbers.

Thanks in advance. Responses to the list, so we can all see how dumb I am.

Clay Davenport replied, a decision he would soon regret as I mangled my initial attempts and pestered him with followups over a 12-hour period. Clay's attempts to teach me about binomial distribution-one of the concepts that hastened my transition to the journalism program at USC-may have borne fruit. If they haven't, I'm pretty sure I'll hear about it from the smartest readers on the Internet. Note: if there are errors in this piece, they're mine, not Clay's. Clay doesn't make mistakes. Well, not since the incident with the Tri-Delt and the aardvark in Cabo, anyway.

Here's what I'm trying to find out: whose starts to the season, through last night's games, are least likely to represent chance, as compared to my preseason expectations for the teams. The lower the possibility, the greater the likelihood that I was wrong about the team.

To fill in the blanks from above with one example, there's just a 1.23% chance that the Brewers, projected by me to be a .475 team, would win 22 of their first 32 games. Given that, it seems likely that I've misevaluated the Brewers in some way, underestimating their talent or expected performance. In this specific case, the gap stems from the Brewers' excellent run prevention. As I mentioned last week, they're not walking hitters or allowing home runs, and that makes it very hard to score against them. I didn't see that coming, and it's changed the expectations for this team.

In the other direction, you have the Rangers, who I projected as a .548 team. The chance that a .548 team would open its season 13-18 is 10.39%, or about 1 in 10. There's a better chance that we're just seeing variance than with the Brewers' start, but a figure like that makes you look at the situation more closely. The Rangers' rotation has been disappointing, most notably the expensive duo of Kevin Millwood and Vicente Padilla, with the latter logging more walks than strikeouts. Rangers' hitters are striking out a bit more than once every five at-bats, and not hitting for enough power to make up for the .241 batting average that creates.

There are eight teams whose starts to the season show less than a 1 in 5 chance of occurring: the Brewers, Royals, Red Sox, Rangers, Yankees, Tigers, Cardinals, and Indians. The Yankees' start almost certainly reflects their poor pitching, both among the replacements for their injured starters and their overworked bullpen. The Cardinals suffered one critical injury to Chris Carpenter, but have also seen veteran position players age rapidly this spring. The Royals haven't hit or fielded to expectations, and the optimism about their young players seems to have come a year too soon. The Red Sox, Tigers, and Indians are good teams that have seen potential weak spots perform well in the early going. In all of those cases, I think you have to re-evaluate the preseason expectations.

Above that line, I think you have to take the results with a grain of salt; the Phillies' 14-18 record isn't that unlikely (24.08%) given their projected 83-79 mark, and the Dodgers' 19-13 mark, which paces the NL West, is even more likely (29.58%). Above the 20% line, we need more information, need to see more games. I'm not prepared to say that the 22 teams above that line have given me enough reason to alter my preseason expectations.

Now, this is using one set of preseason picks, my own. If you were to run these figures using Nate's PECOTA-driven ones, or the BP consensus, or the Predictatron average, you'd likely reach different conclusions. What if you changed the other side of the equation, though? Early-season results can be skewed by an odd distribution of runs, a poor or exceptional record in one-run games, or even a particularly easy or hard schedule. Instead of using actual records, what if you instead used the third-order records from Clay's Adjusted Standings Report?

With one notable exception, this pushes the curve upwards; there are fewer teams below the 10% and 20% lines (two and six, as opposed to three and eight), and there are more teams clustered above the 40% and 50% marks. The notable exception is the Diamondbacks, the team I have picked to go to the World Series, to be the best team in the National League. A .548 team by my reckoning, they've played to just a 15-19 record so far. With just a 3.83% chance of that occurring, it's time to think about what they are, as opposed to what I thought they were. Their young hitters have been a collective disappointment, and the power arms in the bullpen have pitched erratically. My optimism about both those elements seems to have been excessive.

The Red Sox, Rangers, and Cardinals all retain their spots as "real" over- or underachievers, but the Brewers, with a 19-13 third-order record, don't stand out. There's a 20.73% chance that a .475 team could start out with that mark, which opens the door to the possibility that they're what I thought they were. However, the one known way in which teams can outperform their projected record is by having a very good bullpen, and that's where the Brewers have excelled. Francisco Cordero and Derrick Turnbow are the main reasons for the three-game gap between the two records, rather than what we might call "luck" or "randomness." Despite their being barely over the line, I'm sticking with the idea that I underrated the Brewers this spring, if not perhaps by as much as it looks at the moment.

The point here isn't to get bogged down in specifics, although I will be taking a closer look at one of the overachievers later this week. The point is that by using this mathematical tool ("and hopefully not misusing it," thought the journalism grad), we can better identify the teams that have drifted far enough from expectations to allow us to let go of "it's too soon" and start doing some evaluations.

Joe Sheehan is an author of Baseball Prospectus. 
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