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Dan Malkiel 

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March 14, 2010 1:45 pm

Great Expectations

16

Dan Malkiel

Sometimes a single is just a single, but sometimes it's worth much more.

In the A’s-Rangers game last Sept. 15, Oakland's Mark Ellis led off the fourth inning with a single to left. Daric Barton followed with a double to deep center, sending Ellis to third. Next up was Cliff Pennington, whose fly ball to left was too shallow to score Ellis. Adam Kennedy then struck out, and the A’s were on the verge of squandering a terrific run-scoring opportunity until Rajai Davis saved the day with a bloop single to right, driving in both runners.

Whose contribution to the rally was most valuable? This question is rather subjective and open to interpretation. Most fans would probably choose Davis because of his clutch two-RBI knock, but it’s possible to make cases for others as well. Ellis’ single got everything started, and we all know how crucial it is to get the leadoff man aboard. Barton’s long drive turned a promising start into a potentially huge inning; it wasn’t his fault that the two subsequent batters failed to cash it in.

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September 22, 2009 1:39 pm

Solving the Rookie Dilemma

9

Dan Malkiel

Popping the hood to dig down into when to let it ride with your rookie hitters, and when to worry.

In my previous article, I modeled the choice between a stable veteran and a promising but unproven rookie as a "multi-armed bandit" problem. To solve it, I devised an algorithm that computes the expected value of each choice and discovered that provisionally starting the rookie usually yields a greater expectation. The intuition behind this result is that it's usually worth investing a few plate appearances in the hopes that a rookie might be highly productive, even if that is improbable according to his PECOTA projection; after all, the veteran can always replace him if the experiment fails. But what constitutes failure? In other words, how long should the rookie be allowed to struggle?

To answer this question, we'll need to go under the hood of the model I described the first time out. In the model, the rookie's productivity is described by a probability distribution on his OBP based on PECOTA's projections. The probability distribution in question is a beta; in order to understand the methodology I am about to describe, we'll need to grasp the basics of this distribution. The beta ranges over the interval [0, 1] and is defined by two positive parameters (α, β). Its mean is α/(α+β); thus, if α goes up, the mean goes up, while if β goes up, the mean goes down. Also, the greater α and β are the more "peaked" the distribution will be around this mean. Let's see how this looks:

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September 10, 2009 4:18 pm

Solving the Rookie Dilemma

12

Dan Malkiel

Exploring when they should start versus when they should head for farm country.

Willie Mays famously started his career 0-for-12 before hitting a home run off of Warren Spahn. This season, Orioles ber-stud catcher Matt Wieters has struggled to live up to expectations, posting a feeble .264/.310/.368 line since being called up in May. Talented rookies such as these present a twofold challenge to their teams: first, how to identify when they're ready for promotion, and second, how to react when they fail to produce. These decisions can be driven by subjective considerations, such as a scout or manager's evaluation of the player's poise and confidence. Such things are certainly important, but it's worth investigating what a purely objective mechanism for making these decisions might look like.

So, today we'll try to answer the first question: How do you decide when a prospect's ready? Let's consider the common scenario in which a rookie player is competing with a veteran for the vet's job. The veteran's productivity is typically well established, while the rookie's productivity is not known as precisely. Thus, we're faced with a choice between a so-called sure thing, and an unknown but possibly superior alternative.

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August 23, 2009 10:43 am

Keeping Them Honest

32

Dan Malkiel

Repeated pickoff attempts may be an exercise in tedium, but what are the real costs and benefits to keeping the runner close?

We're all familiar with the chorus of boos that often rains down on a pitcher making repeated throws to first base. To fans, such throws are an annoyance, serving to slow down an already slow game. To pitchers, however, they are a valuable means of curtailing the running game. In his New Historical Baseball Abstract, Bill James proposed a rule he hoped would resolve this conflict: each team should be allowed two unsuccessful throws to the bases each inning, with all subsequent unsuccessful throws counting as balls.

I've always been fond of this suggestion, which is based on the simple and logical idea of assigning a cost to a resource that seemingly has none (or very little). But is this the case? That is, what is the benefit of throwing to first, and what, if any, is the cost? Regarding the first question, James refers to a study by STATS Inc. that found that throwing to first reduces the number and the success rate of stolen bases, and that throwing repeatedly is more effective than throwing once. He provides no details of the study, however, which by now is at least a decade old; it therefore seems worthwhile to revisit the issue.

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August 5, 2009 12:14 pm

Red Light, Green Light

29

Dan Malkiel

Once you've got the pitcher on the ropes, should you swing for the fences or hope the pitcher hangs himself?

Conventional wisdom dictates that a hitter take a pitch on a 3-0 count. The pitcher has thrown three straight balls, so why not make him throw a few strikes in a row? On the other hand, the 3-0 pitch is probably the easiest to hit, as the pitcher has no margin for error and can't afford to try anything fancy. Which is the more compelling argument?

Let's begin with some descriptive analysis: who swings on 3-0 and who doesn't? I looked at all 3-0 counts between 2003 and 2008, excluding intentional walks; below are the 20 players who swung most often (minimum 50 PA).

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