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August 23, 2009

Keeping Them Honest

Who Pays for Pickoff Attempts?

by Dan Malkiel

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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.

I generated a list of all 93 players who stole at least 15 bases in any year from 2005 through 2008. I then looked at every plate appearance in non-blowout situations (meaning a five-run lead or less) between 2006 and 2008 that began with one of these players on first base and the other bases empty; my thanks to BP's Bil Burke for an assist with the data. There were 22,570 such plate appearances, during which a total of 19,614 throws to first were made-an average of .87 throws per plate appearance. Any throw to first qualifies; there is no distinction in the data between casual tosses and genuine pickoff attempts.

To assess the impact of throws to first on the running game, we'll look at three statistics: attempt rate AR, defined as (SB + CS)/PA; success rate SR, defined as SB/(SB + CS); and pickoff rate PR, defined as PO/PA. First, let's see how not throwing to first compares to throwing at least once.

Throws         PA     SB    CS   PO    AR     SR      PR
    0        13721   1561  587  132  15.65%  72.67%  0.96%
    1+       11705   1915  472  307  20.39%  80.23%  2.62%

Surprisingly, runners attempted to steal less frequently and with less success when no throws to first were made. There are several explanations for this. First, runners who draw no throws tend to be less effective basestealers, go less often, and succeed at a lower rate. Second, runners have fewer opportunities to steal during shorter plate appearances, which tend to have fewer throws to first; in particular, when the first pitch is put into play the runner never has a chance to steal. Reshaping the data to reflect the number of pitches thrown produces the following results:

	            No Throws        At Least One Throw 
Pitches       AR       SR      PR     AR      SR     PR 
    2         6.89%  68.31%  0.49%  5.68%   79.35%  2.04%
    3        12.59%  67.52%  0.89%  13.13%  79.85%  2.50%
    4        21.87%  75.69%  1.21%  20.18%  83.08%  2.54%
    5        24.90%  75.05%  1.39%  26.10%  80.93%  2.86%
    6        32.70%  79.79%  1.12%  36.21%  80.78%  2.59%
    7+       33.79%  71.02%  1.24%  33.70%  75.74%  4.18%

Indeed, the fact that throws to first tend to occur during longer plate appearances explains the discrepancy in attempt rate. Given the number of pitches thrown, attempt rate with no throws is roughly equal to attempt rate with at least one throw. It seems, therefore, that throwing to first at least once has no discouraging effect compared to not throwing at all. Furthermore, success rate is higher across the board during plate appearances with throws to first. Again, this is likely not caused by the throws; still, these two facts cast some doubt on the efficacy of throwing to first.

Perhaps throwing to first just once is not enough; maybe throwing repeatedly sends a stronger signal to the runner that he's being watched. Let's check the rates for each number of throws:

  Throws      AR       SR       PR
    0       15.65%   72.67%   0.96%
    1       19.31%   81.04%   2.09%
    2       21.72%   80.09%   3.35%
    3       22.07%   76.95%   3.69%
    4       23.39%   79.31%   3.23%
    5+      20.33%   80.00%   0.81%

This perspective also fails to demonstrate that throws to first discourage runners from taking off or reduce their success rate if they do. We do, however, find an increased likelihood of picking the runner off, the reason for which should be obvious. Note, however, that this benefit offers diminishing returns; runners were picked off less frequently on four throws than three, and even less so on five or more.

My final attempt to establish the value of throws to first was to consider the handedness of the pitcher. Intuitively, one would expect lefties to have less motivation to throw to first, since they already have their eyes on the runner. Do only righties derive any benefit from throwing over?

Throws      % of PA      AR      SR       PR
    0         75.11%    9.68%  68.64%   0.86%
    1+        24.89%   17.90%  72.39%   4.12%

Throws      % of PA      AR      SR       PR
     0        52.74%   18.30%   73.61%   1.01%
     1+       47.26%   21.35%   82.66%   2.07%

It appears not. Though right-handers do throw over considerably more often than lefties, we still see increased attempts and success rates during plate appearances with throws to first in both cases. Perhaps these rates would be higher if the pitcher hadn't thrown; in other words, since better runners tend to draw more throws, it is quite possible that not throwing during the plate appearances involving throws would have resulted in even worse numbers. This explanation only carries so much weight, however; recall that we're only looking at situations with good runners on first base.

This analysis has discovered little benefit to throws to first; what of their cost? The immediate risk of throwing over is the potential for an error, either by the pitcher or the first baseman. Let's have a look at the error rates:

Throws         PA   Errors   Pickoff Rate    Error Rate
    0        13721     6        0.96%           0.04%
    1+       11705   107        2.62%           0.91%
    1         6801    57        2.09%           0.84%
    2         3190    38        3.35%           1.19%
    3         1219    10        3.69%           0.82%
    4          372     2        3.23%           0.54%
    5+         123     0        0.81%           0.00%

Not surprisingly, there were few errors when pitchers didn't throw to first. One thing to note is that catchers have an excellent pickoff-to-error ratio, as they only throw to first when there's a good chance of catching the runner napping. In other plate appearances, the error rate hovers around one percent, which is always less than half of the pickoff rate. Since the cost of allowing a runner to advance is far less than the gain of removing him from the bases (except in specific circumstances), the possibility of picking a runner off more than outweighs the cost of error.

Another potential cost of throws to first is the loss of focus a pitcher might suffer when he can't give the batter his undivided attention. I'll call this the "distraction theory." Despite its ardent espousal by broadcasters everywhere, the data offer no support of the distraction theory; in fact, the opposite may be true:

Throws      AVG    SLG    OBP   HR/AB
    0      .294   .361   .473   .038
    1+     .282   .362   .452   .034
    1      .286   .359   .462   .037
    2      .283   .368   .456   .035
    3      .271   .360   .405   .021
    4      .266   .364   .427   .035
    5+     .238   .336   .314   .010

Hitters got more hits, drew more walks, and hit more home runs in plate appearances with no throws over than in plate appearances with at least one. There is also a general downward trend in these stats as the number of throws to first increases. We can't be too confident in this last observation, however, as the sample sizes of 4 and 5+ throws to first are on the small side. Still, it seems that if anyone loses focus due to repeated throws to first, it's the hitter.

Returning to the two questions this piece was intended to answer, this analysis has found no evidence that throwing to first is an effective means of curtailing base stealing. Indeed, the numbers indicate that runners do better when throws are made, though it's difficult to believe that they do better because of the throws. There remains, however, a good reason to throw to first, namely the possibility of a pickoff. Since there is little cost to throwing over-the risk of an error is negligible and the batter's performance may even suffer-pitchers have a strong incentive to throw repeatedly to first when it's occupied by a speedy runner. Thus, James' proposed rule remains a viable idea, if not for the reasons he had in mind.

Dan Malkiel is an intern with Baseball Prospectus.

Dan Malkiel is an author of Baseball Prospectus. 
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