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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.

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Does this control for the fact that many "pickoff throws" at the beginning of an at-bat are intended not to get the runner, but to find out whether the batter (particularly if the batter is a pitcher) is going to be bunting for a sacrifice?
No, it doesn't. All throws to first are treated the same way in the data.
I'm sure it is a small subset of the numbers, but I wonder too what effect there would be if you could control for the "pickoff throws" by pitchers who were just wasting time in order for a reliever to get ready.
I would think the chance for a balk would increase with pickoff attempts
Why is the pickoff rate near 1% when there are no throws to first base?
Catcher throws.
Since no throws includes catcher throws, I presume we are unable to determine what percentage of outs of the other categories are affected by catchers?

It's a shame we cannot track the effectiveness of catcher throws. That play can be exciting.

With the caveat that I have no statistical background, it seems to me there are so many variables at play here that isolating the effect of pickoff attempts is all but impossible. Who the batter is, the exact score, the inning, etc. would all probably have far more impact on steal rates than the number of throws to first.

As you note, runners tend to steal more when more throws to first are made. Which makes me think that the explanation is that those were obvious steal situations.

Wouldn't it be better to look at more specific situations? Such as, when high steal guys are on first in the first inning with no outs (major steal situation), what is the effect of throwing over?

I don't know if that makes any sense, but that was my thought.
Putting a cost or cap on a pickoff is an interesting idea. I've often wondered what the reward is of a pitchout, since it obviously already has a cost. Have there been in looks into the effectiveness of pitchouts?
Do you think that controlling for only runners who have more than 15 SB removes the selection bias inherent in this? Jacoby Ellsbury or Carl Crawford will draw more throws and be more successful and attempt more SB than the guys who only get 15 SB/ yr.
To be really thorough, one could look at lots of different cutoffs for SB. I just wanted a minimum number of SB such that a player can be considered a legitimate SB threat, and 15 seems like a reasonable choice. There are no slowpokes in the group.
There may be issues, like with sample size, but did you consider narrowing down the list to not just players with X# of steals, but also possibly by X% for steal success?

I like the originality of your breakdown. I happen to have the 1989 study from STATS, Inc. in a book of mine. I was hoping to see a direct comparison to that study in order to see how tendencies have changed in the last 20 years.

Also, what are the AR, SR, and PR for the Top10 basestealers and pickoff pitchers from each year studied?
Interesting analysis - a nice look at something that's never really talked about in a critical way.

I would not be inclined to institute the rule change however. One of the things that I find so appealing about baseball (as opposed to football) is the simplicity of the rules: there are few arbitrary or complicated restrictions on what a player's allowed to do. Imposing a throw-over limit seems unnecessarily cumbersome. I don't see the delays caused by throwing over as being all that problematic.
I recall Orel Hershiser giving a rationale for pickoff throws that had little to do with actually catching the runner. His reason? Throwing to first gave him a little more time to think and plan out how he was going to approach the hitter at the plate.
Bill James's rule idea is creative but it seems to me that it could change the pitcher/runner balance in possibly unpredictable ways, and for no compelling reason. The pitcher wouldn't dare throw over a second time, because thereafter the runner could indulge in a big lead, knowing that few pitchers would pay the cost of a ball for a throw over. But if there would never be a second throw, then the runner can start making this assumption to some degree after the first throw. Therefore it might be better for the pitcher never to make that first throw, in order to maintain at least some doubt in the runner's mind. I don't know where the balance would really settle, but probably it would be different from today's. I'd like a better reason than saving probably a minute or less per game before I'd be keen to meddle with the game's balance.
I don't think it's true that the runner would be able to indulge in a big lead. He can still be picked off (that's no ball), and in fact the pitchers would probably stop throwing over the first time just to be on the safe side.

The saving in time could be rather large, and I think the fans would enjoy the tension of the situation.
I think it's possible to account for the throws to first as a cause in making it easier to steal. The runner gets a look at the pitcher's move to first, so after a pickoff attempt he can steal on it. Yes, that's speculation, but it fits the data.
I was thinking the exact same thing. I don't think it would be an unreasonable assumption that the more throws to 1st a pitcher makes, the more likely the runner learns the pitchers move. Allowing him to confidently leave for 2nd, and steal it successfully.
I have heard that there are some basestealers who like to see the pitchers pickoff move once so they know exactly how large a lead they can get.

Another observation on why basestealers are caught more often with no throws may be because they don't get a large enough lead to begin with. Lefties throw to first far less often and runners are thrown out more often attempting to steal on them. I think it is safe to say that the correlation at least in that scenario is due to shorter leads.
In the last table, looking at batter performance, I assume that the PAs are the same as the previous table, for number of throws.

First, even the 3190 PAs with 2 throws is probably a questionable sample size - the 1219 for 3 throws most likely is, so 3+ or even 2+ should have been the last line.

Second, these may not be the same batters. It's possible the number two batter is more likely to get more multiple throws, with the leadoff batter on base, than the number four batter with the number three guy on base. You would need to control for batter ID, comparing how each did with various numbers of throws, and then seeing the changes for the group.

Overall, interesting and thought provoking study.
I enjoyed this analysis. I'd love to see more of this type of thought process. Even if it's not perfect, you can read through the work and get your brain going.
If a baserunner knew that the pitcher could only throw to a base 2 times without paying any price he would have a strong incentive to entice the pithcer to throw over twice and then try to steal every time after that. The only defense against a steal the pitcher would have is a pitchout (which would be a ball anyway. Bill James must be a liberal as this proposed rule attempts to solve one problem by creating an even worse problem.

We already lowered the mound, allow batters to wear armor (encouraging them to crowd the plate), and warn the pitcher for throwing inside which he has every right to do (also encouraging batters to crowd the plate). Let's stop punishing the pitcher by destroying baseball as it was designed.

Modern hitter's wear a cup for aesthetic purposes only.
I hoped you'd address pitcher fatigue in the costs section of the analysis. A starting pitcher who allows, say, 10 baserunners, could end up making 30 throws to first base during a game (a guess). How many pitches is that equivalent to? I seem to recall that some older pitchers, when asked why they were able to throw so many more pitches in an average game than modern pitchers, gave that as a contributing factor.
I am amused by the fact that you could intentionally walk a batter by throwing to a base 4 times instead of throwing to the catcher with the rule proposed by Bill James. This would make a lot of sense to do considering I have seen wild pitches and grooved changeups on intentional balls before.
If you want to speed up games, forget about throws to first to try to dissuade a steal, just raise the mound to give back some of the hitters' advantage back to the pitcher. That way a pitcher can just concentrate on the hitter, knowing he now has a better advantage against the hitter whether the runner on first stays there or steals 2nd. Games across the board would take a lot less time and make for a more enjoyable game to boot.
@OkayFine - you may well be right that it would work out, but I fear the chance that it will go goofy somehow. I'd be willing to take that chance if there were a compelling reason, but I'm not sure there really is. I'm skeptical about the time savings. If we assume that it worked OK and there were still some PO attempts, then we're talking about saving the time of some percentage of the small handful of throws over in any given game. So we come down to annoyance among fans, which is important, but people ought to be able to survive a modest number of these plays, says I.
I am afraid you're not going to find out anything here without controlling for the two things: One, the exact stolen base talent of the runner and two, the game situation.

The reason is that you cannot separate cause from effect. Obviously, no throws to first regardless of the number of pitches in the AB suggests that it is not a base stealing situation (maybe the game is a blowout or the batting team is down by more than a run late in the game). It also suggests that the runner is not such a base stealing threat, even if you only looked at runners with at least 15 steals (not all 15 steal players are created equal).

The other thing is let's say that throwing over to first had no effect on the runner attempting a steal or being safe on a steal? Why would the pitcher waste his time with throws? Because you can't pick anyone off unless you throw over!

Basically, I don't see the data telling us anything at all for the reasons articulated above.
There are certainly limitations to this analysis, but I think the data are telling us *something*.

Regarding (1), the question of how to derive the set of SB threats was a difficult one. Do we select those with a minimum # of SB in every season? That would exclude good base stealers who missed time or effectiveness due to injury. Do we raise the threshold for any given season? That would exclude efficient base stealers who don't rack up gaudy SB totals but choose their spots prudently. I think the simple method I used has merit; it generated a list of 93 players that nearly all observers would agree are legitimate SB threats.

Regarding (2), no throws to first do not necessarily imply that it is not a SB situation. There are many possible reasons for this: a short PA, a pitcher (especially a LHP) with an effective pickoff move, a negligent pitcher, etc. Since it's impossible to rigorously define a "SB situation," it seems reasonable to consider all situations that could possibly be considered as such. I did ignore blowouts; as I said in the article, situations with a 5-run lead were excluded.

Finally, I don't see how your third paragraph is a criticism; in fact, it's exactly the point I make in my final paragraph
Good work, Dan. Overall this was a nice analysis, and certainly an interesting topic for research.

First, I would echo MGL's two criticisms. Even though you attempted to control for both runner quality and game situation to a reasonable degree, perhaps even tighter controls could have been applied to tease out additional insights.

Second, the other factor that I don't believe has been mentioned yet is the throwing arm of the catcher. Specifically, is it possible that pitchers with weak-throwing battery mates are more apt to throw to first (once or more) to compensate for their catcher's otherwise poor ability to control the running game himself? I imagine that there is some correlation there that could be skewing your attempte rate and particularly your success rate numbers.
How does this jive with John Dewan's stat of the week showing a drop from 75% to 64% when throws are made to first base?
I don't know what Dewan's methodology was that led him to that conclusion. One possible difference is that I only considered "fast" runners, while he may have been looking at everyone.