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# Daily Box Score 8/20: Things For Which I am a Sucker

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Everyone has their quirks. Joe Maddon has his hair. Statheads have their mancrushes. Drew Stubbs has sweet, sweet I-told-you-so. So I'm not afraid to admit that certain types of things fascinate me. Of course, articles about baseball on the internet are right in the wheelhouse. But today's box score features a surprising number of articles about baseball on the internet that are particularly interesting to me.

Baseball and Economics

I have to admit that baseball was a gateway drug to economics for me. I often find myself thinking about economics in baseball terms. So I've always been eager to read about new ideas that combine the two.

Shawn Hoffman has been blogging about baseball and economics at Squawking Baseball and Baseball Prospectus for a couple of years now. But he has really outdone himself this time. In his most recent article, he picks up where Doug Pappas and Nate Silver left off. In a classic article in BP's 2004 annual, Pappas devised a method to determine how much each team was paying for each marginal win (win above what a team of replacement level players would achieve). Here's Hoffman crystalizing the Pappas formula:

(club payroll - (28 x major league minimum)) / ((winning percentage - .300) x 162)

The only problems with that method were that it ignored the benefit of making (and doing well in) the playoffs, and it made the Marlins look like geniuses. In Baseball Between the Numbers, Nate Silver put a value on each win, demonstrating that the most valuable marginal win tended to be the 90th.

Now, Hoffman has combined these two insights and derived a new formula that accounts for the playoffs and doesn't just reward teams with very low payrolls (though the Marlins still rank 10th). Here's Hoffman's description of his method:

First, we need to know how much marginal revenue each team is likely to bring in, based on its win total and market size. To do this, we'll use Nate's MR/MW curve, updated for 2009 revenues. We'll then assign each team a market-size factor based on its 2007-2008 gate receipts. (We already know that this is the only short-term revenue source that significantly impacts a team's payroll spending). The Red Sox won 95 games last year, which should generally lead to \$108 million in marginal revenue. Multiply that figure by Boston's market-size factor (2.48), and we get expected revenue of \$267 million.

Next, we'll use a regression equation (MW = 0.1106*MP + 22.538) to determine how many games a team should win—and, therefore, how much revenue it should bring in—based solely on its payroll. For example, Boston's \$133 million payroll in 2008 should have led to 86 wins. According the win curve, multiplied by the team's market-size factor, that would create \$165 million in marginal revenue.

Then we just divide these numbers: 267 / 165 = 1.61. In other words, given their payroll and revenue potential, the Red Sox performed about 61 percent better than average in 2008.

It's pretty fantastic stuff, and the results definitely pass the smell test (the 2009 top three are Rays, Dodgers, Rockies). He has provided full results in a Google spreadsheet here. He even uses third-order wins to remove some of the element of luck. If you have a subscription, I highly recommend the article.

For a little more baseball and economics, here's a tidbit from Tyler Cowen of Marginal Revolution:

I see a few reasons why the evolution of sports rules may be less than ideal.

1. The rules may be geared toward the sale of merchandise, which implies an appeal to the young and to the least common denominator.  This is mostly an aesthetic objection, although you can tell a story about the purist being a neglected infra-marginal consumer.

2. The rules of the sport may be geared toward television advertising revenue, with the above argument repeated.

He's got four more but I'll leave it to you to head over there and read them for yourself. I would add that in response to #1, I think there's a tacit agreement among baseball fans that what is best for baseball is that which maximizes the enjoyment of the (let's say) 10 year-old fan. Am I right about that?

Probability

It was a banner day at BPro, as Hoffman wasn't the only one to chip in a nice piece. I had linked previously to this piece by David Pinto on the probability that Albert Pujols would win the triple crown. Pinto's method had a few limitations, though, including the fact that it assumed Pujols would definitely finish the season leading the league in RBI and home runs.

So Eric Seidman put on his skeptic's hat and did a little legwork of his own. He found that Pujols is only roughly a 50-50 shot to win each of the non-AVG categories (as he has to compete against a field of strong competitors in each column), and an even slimmer shot in batting average:

Multiply the 0.034 to the other two legs of the Triple Crown, 0.503 and 0.435, and Pujols ends up with a miniscule 0.74 percent chance of winning the Triple Crown this season—or odds of 134 to 1—an astounding number and odds ratio given that he may very well finish the year with a final line of .326-53-148. If the rest of the current season were replayed over and over again, on average Pujols would win the Triple Crown once every 134 replays.

...so you're telling me there's a chance? Truly, if it weren't so hard to do it wouldn't be nearly so fun to root for.

The List

Okay, so lists aren't so hard to come up with (especially if you have SQL or b-ref's Play Index). But still, they're wonderful to look at and good for starting discussion.

Here's an especially good one from THT's Chris Jaffe: the last pitcher to win 20 games for each team (except the Rays and Rockies, who haven't had 20 game winners yet). Here are the bottom five:

1986 MIL Teddy Higuera
1984 BAL Mike Boddicker
1982 PHI Steve Carlton
1978 SDP Gaylord Perry
1978 MON Ross Grimsley

One bonus of a list like this is that it's a great way to remember just how AWESOME Ross Grimsley was.

Here's another fun list, courtesy b-ref's blog. The top active players with 100+ career HR, sorted by PA/HR. The top five:

```              	PA/HR    	AB/HR
Ryan Howard	14.23   	12.13
Marcus Thames	16.21    	14.75
Alex Rodriguez	16.46		14.23
Albert Pujols	16.51		13.98
Jim Thome	16.71    	13.59   ```

Nicely done, Marcus Thames.

Discussion Question of the Day

What kind of articles about baseball pique your interest most? As a bonus for answering, you'll probably get to see more of them in the Daily Box Score, so have at it!