David Wadler’s Assorted Thoughts

Remember when you were in 7th grade, thinking to yourself, “Why do we have to learn all this math? I’m never going to use it.” If you indeed tuned out, then perhaps you should take a job in baseball. (You’ll have a hard time working for the A’s, Dodgers, Red Sox, Blue Jays, and a few other teams, but there are jobs aplenty in and around baseball for the mathematically challenged.)

Many baseball fans have voiced their frustration at watching pitchers intentionally or quasi-intentionally walk Barry Bonds repeatedly. Typically, the decision to give Bonds first base comes from the manager. Considering a manager’s prime directive is to give his team its best chance to win, quite a few skippers should be on the chopping block. What strikes me as odd is that amid the discussion of rules changes for intentional walks (ludicrous for many reasons), rarely does the IBB for Bonds tactic get called into question. Bear in mind that the S.F. left fielder has received more intentional walks thus far in 2004 than Alex Rodriguez, a feared hitter in his own right, has in his entire career. Pardon the pun, but ask yourself, “Does that add up?”

The Chicago Tribune’s Phil Rogers recently touched on differences in managerial approach towards Bonds by current manager Phil Garner and their manager of a few years ago, Larry Dierker. Rogers looks at their tendencies and concludes that Garner will be more aggressive in facing Bonds. Fair enough. Although there is little quantitative analysis to support the writer’s conjecture, I’m inclined to give him a pass and examine the primary question that the article raises: Do all these intentional walks make sense?

In 2001, Dierker’s pitchers walked Bonds eight times in a three game series much to the chagrin of the fans who wanted to watch Mark McGwire’s home run record fall. Though the strategy was booed, Dierker — to this day — thinks that if one wants to maximize the chances of victory against the Giants, “an opponent would be wise to intentionally walk Bonds every time he came to bat unless the bases were loaded, the score was tied and it was the bottom of the ninth, 10th, 11th, etc.”

Dierker addresses the aforementioned strategy: “You can support that idea statistically. If you do the math, you’re better off walking him than pitching to him … I think over the course of time, you probably would be better off walking him every single time.'’

Before I take Dierker up on his offer and “do the math,” I’m going to share Rogers’s mathematical take on this: “If Bonds walked every plate appearances all season, he’d have a 1.000 on-base percentage and a zero slugging average. That’s a 1.000 OPS, which creates fewer runs than Bonds’ 1.378 OPS from 2001 or his 1.437 this season, when he’s been the best hitter in the history of the game.”

First, let’s take a look at what Phil Rogers said. It’s true, a 1.000 OPS will typically yield fewer runs than a 1.378 OPS or a 1.437 OPS. The key word, however, is typically. There are two things that are taken for granted in Rogers’s assertion. First of all, OBP is a far more significant factor than SLG in determining a player’s offensive efficacy. Using a number somewhere between 1.64 and 1.8 as a multiplier for OBP and then adding the resultant number to SLG provides a more accurate assessment than a conventional unweighted OPS. Perhaps more damning though is that Rogers never accounts for the edge case, but that is exactly the scenario he offers the reader.

The imaginary player the Rogers describes looks like this (I’ll use unweighted OPS for the sake of simplicity):

PA     H    BB   OBP     SLG      OPS
500    0    500  1.000   1.000    0.000

Imagine a player who was exactly the same, save for a single in his first plate appearance. Basically, the player gets a hit and then is intentionally walked the rest of the season. Here are his numbers:

PA     H    BB   OBP     SLG      OPS
500    1    499  1.000   1.000    2.000

And if that hitter were to have hit a homerun in his first trip to the plate?

PA     H    BB   OBP     SLG      OPS
500    1    499  1.000   4.000    5.000

Each of the previous scenarios describes seasons that are quite close to identical, but the OPS is ridiculously skewed by the small sample size of at-bats.

OK, ready to do the math? Here we go…. The most important thing a batter can do is not make an out. Outs are precious as a team is only guaranteed 27 of them (24 for a winning home team) over the course of a 9-inning game. By offering a batter an intentional pass, a team is eliminated the chance of the batter’s generating an out. Bonds is an extremely dangerous hitter, but a good part of the threat he poses derives from the opposition’s unwillingness to pitch to him.

Let’s take a look at some stats. According to the formula for runs created per 27 outs (i.e. how many runs a team composed of nine instances of a particular hitter would score), a lineup of nine Barry Bondses would score almost 21 runs/game. (To put this number in context, only two other NL players have managed double digits and those players — Todd Helton and Jim Edmonds — are still below 11.) Now, take the batter Phil Rogers offered a figure out how many runs a team composed of nine of him would score. The number? Infinity. Intentionally walking every batter in the order repeatedly would eliminate all outs. The lineup would bat around until the end of time. While Bonds’s almost 21 runs created/27 outs in impressive, the imaginary player’s infinite runs created/27 outs would eliminate the need for a pitching staff in road games.

Dierker — a very good pitcher in his day, but clearly not mathematician — concluded by saying, “Over a long course of time, the math would be borne out, but in a three-game series, I don’t think you can count on it.” Taken by itself, this statement is accurate: Over a small sample, one can’t expect outcomes that are 100% consistent with the law of averages. Understanding this, Dierker should have played his hand the smartest way possible, pitching to Bonds with much greater regularity while realizing that though he may get burned a time or two, he is playing the odds. Besides, the odds are that, given enough series, Bonds will also experience less-than-favorable results on occasion.