# The wonderful world of throwing to first

Remember earlier in the spring when everyone was all abuzz over the fact that Jon Lester hadn't thrown to first base since the Carter Administration? Lester's nonexistent pickoff move became a story for a few reasons, not the least of which was the fact that he had signed a contract with nine digits in it over the offseason. But for the most part, it was just strange.

Throws to first aren't anyone's favorite part of a baseball game, since they generally accomplish "nothing" and they take up time. Still, everyone understands that there's a certain sense to those throws. If they were outlawed, then runners would be at liberty to take as large a lead as they wanted. They could walk halfway to second base with no consequence. A throw to first isn't likely to actually pick off the runner, but it does keep him a few feet closer to the base. Even the fact that a throw to first is a legal play is enough in some cases to keep the runner close. It's probably the one thing that Lester had going in his favor. He hadn't thrown over in a year ... but he could.

But really, what's a throw to first worth? Anything?

Recently, we've learned that stolen bases are actually much more of a reflection on the pitcher than the catcher. We often rate catchers by their stolen-base percentage. We should really be looking 60 feet, 6 inches away from them. We also know that there seem to be certain pitchers who are good at stolen-base prevention and some who aren't. Maybe throwing to first isn't just a giant waste of time. Maybe it actually serves a useful purpose.

**Warning! Gory Mathematical Details Ahead!**

This is actually an update of something that I did (gulp) eight years ago. (It was one of the first topics I ever looked into as a sabermetrician!) But a fresh look at an old investigation never hurt anyone.

For 2010-14, I gathered all plate appearances in which a runner was on first while second base was open. I did not filter at all by whether there was a runner on third. Note that I am counting each plate appearance in which a runner stood on first as a separate event. For example, if Omar Infante reaches first to lead off an inning but then has to stand by helplessly as three fellow Royals strike out, he had three chances to do something, but didn't. And the pitcher had three chances to throw over to "check in" on him.

In 2014, there were 17,459 throws to first base. Only 283 resulted in a pickoff (1.6 percent), and 108 ended up as an error (0.6 percent). So, your average pickoff throw isn-t really going to do much on the scoresheet, but if we look closely, we can see that it does ... something.

*Which runners are more likely to draw throws?*

This one will surprise no one. In 2014, the top five "throw-getters" (per time at first base; minimum 100 times) were Dee Gordon, Billy Hamilton, Carlos Gomez, Starling Marte and Melvin Upton, all drawing throws more than 60 percent of the time that they were on first. The bottom five? Well, no one at all bothered to check on Mark Teixeira last year. At all. Billy Butler, David Ortiz, Jose Abreu and Miguel Cabrera were all at 1 percent or lower. I'll leave it to you, reader, to figure out the pattern there.

One thing we do know is that over the five years in the data set, among runners who were on first with second base open at least 100 times during the year, the rate at which they drew throws (and the average number of throws they drew) were very consistent from year to year. I used an AR(1) intra-class correlation (it's like a year-to-year correlation, but instead of two data points, you can use multiple points!) to look at this and for both metrics got an ICC over .90. That means over time, those rates stay remarkably stable.

*Which pitchers are more likely to throw over?*

We know that Lester didn't throw to first base at all in 2014. Who was the second-most reluctant? Dallas Keuchel got that prize, checking on only 3 percent of runners. Kevin Correia, Wei-Yin Chen and Matt Garza were also throw-averse, all under 10 percent. On the flip side, Stephen Strasburg and Chris Capuano both checked in on more than half of the runners that reached first against them. Jason Hammel, Justin Verlander, and Jose Quintana were also checkers. Over time, rates of throwing to first were consistent using the ICC method to the tune of a correlation of about .65. Not as strong as for runners, but it's clear that pitchers tend to be pretty set in their ways about throwing to first.

What's interesting is that the rate at which pitchers threw over to first was only moderately correlated (r = .26) with the rate at which runners attempted to steal on pitchers and not at all correlated (r = .04) with their success rate. Whether pitchers are Strasburgs or Lesters has less to do with outcomes than their preferences on the matter.

*Do throws to first actually keep runners from trying to steal?*

This one is a little tough. I started by figuring out whether a runner had received a "check-in" throw from the pitcher during a particular plate appearance. (I later coded for the exact number of throws to see if that made a difference, but got basically the same results.) I also looked to see how often a player tried to steal as a percentage of the number of opportunities he had (i.e. how many plate appearances happened with him on first and second base open). This allows us to control for the fact that some guys just run more, and since they are more likely to draw throws, we don't want to confuse the two.

Because we know that stolen bases are more likely in some situations than others, I controlled for the inning (entered categorically; steal attempts are more common earlier and later in the game), the number of outs (again, categorical; attempts are more common with fewer than two out), whether there was a runner at third, and whether the game was within three runs in either direction. Even controlling for all that (in a logistic regression), we find that when a pitcher threw over, that runner was *more* likely to go. In fact, I found that a throw to first was associated with (and the initiated will know exactly why I picked the phrase "associated with") about a three-percentage-point-greater likelihood that the runner would try to swipe second, controlling for the situation and the runner's own tendencies.

There are a couple of reasonable theories for this, none of which we can directly prove. One would be the "challenge theory," which says that a runner might see the throw from the pitcher as a challenge to run. ("Oh ... you think I'm going to run? I'll show you.") We've seen that managers are actually more likely to send a runner after they've had one caught stealing; maybe there is a bit of pack animal challenge that goes into all of this.

The other option would be that pitchers are actually picking up on a runner's intent to go, even beyond the analytical, "Well, Smith likes to run and this is the sort of situation where a stolen base would be helpful to his team, so I guess I need to pay closer attention to him." Even after we control for all that, we still find that pitchers throw over more often in situations where the runner eventually takes off. If that's the case, we need to tip our cap to pitchers everywhere because they are clearly picking up on something that our regressions aren't.

*Do throws to first affect a player's success rate when he does try to steal?*

Do they ever!

Similar to the method above, I controlled for a runner's success rates on stolen-base attempts. The one drawback was that I had to use a sample of stealers who had at least 10 attempts within a year, which means we're dealing with a slightly faster caliber of runner. But once we control for a player's success rate, as well as the situation (number of outs, whether the game is "close," the inning, and whether there is a runner at third, all of which had at least some effect on success), whether the pitcher had thrown to first prior to the stolen base attempt actually made a big difference. According to the regression, the effect size is actually more than 12 (!!!) percentage points.

On this one we can also be a little more direct about causation. The runner, seeing that the pitcher is willing to throw over, might lean a little less or might stay a bit closer to the bag, and on stolen bases, a tenth of a second can be the difference between safe and out. We know that frequent throwers are not necessarily better or worse at allowing steals, but when they do throw over, that one move makes it tougher for the runner to get there safely when he does try.

Strangely enough, it means that after a throw to first, we are more likely to see a runner try to steal, but since we've knocked the anticipated success rate below the commonly accepted 70 percent "break-even" point for the "average" runner, it means that a throw to first makes it more likely that the runner will try something that turns out to be a bad strategic play.

*What about other "stolen" bases?*

Even if that runner on first doesn't try to steal second, he might try to "steal" third on a single. Using a method similar to the above, I found that when the pitcher throws over to check on the runner, the runner is *more* likely to try for third on a single (again, even controlling for his own tendencies) and less likely to succeed. The effect isn't quite as strong, but it's there.

*Does a pickoff attempt affect what happens at the plate?*

For this one, I used the log-odds ratio method to help me out. This creates a control variable over how likely we expect an event to happen, based on the batter's, pitcher's, and league's tendencies. Then, I selected only cases with a runner on first and no one on second and coded for whether the pitcher made a throw to first during the plate appearance. I also controlled for how likely it was that a pitcher (in general) threw over to first. It's possible that pitchers who throw over a lot are in some way different than other pitchers in what they generally gave up (e.g. maybe high-strikeout pitchers throw over more).

There was no effect on BABIP or OBP, but the types of outcomes that happened changed when a pitcher had thrown over. Specifically, rates of singles, doubles, and triples went down, as well as outs on balls in play (compared to expectations). Rates of walks and strikeouts went up. We know that it's not a matter of there being runners on base, because all of the plate appearances in the sample I used have runners on base. The only difference here is that in some of the plate appearances, the pitcher throws to first. It's hard to parse what this means. Strikeouts are better than outs in play (for pitchers) and walks are better than singles or extra base hits, so pitchers are better when they throw to first. But what causes this?

One possibility is that throwing to first doesn't actually cause anything. It's just a marker that a pitcher is able to deal with everything that's going on. It might also be that his throw to first means he's concerned about the speed of this particular runner, and he figures that an approach that minimizes contact (and the runner's chance to use that speed) is better in this situation. Maybe the *batter* is reacting somehow.

My own personal pet theory (that I can't prove) is that with a runner on base who is worth a throw, the stakes are a little higher and that gets the adrenaline pumping a little more. That's not always a bad thing. People actually do their best on a task when they are slightly (but not totally) pumped up. It's known as the Yerkes-Dodson curve. Too much at stake is bad. Not enough at stake is bad. But this might be a little sweet spot in the middle.

*Do pitchers who make a bad throw become shy about throwing to first later?*

As we saw above, sometimes it happens that a pitcher throws to first, but the ball ends up down the right-field line or in the stands. Rarely, but it happens. I was curious whether pitchers who make a bad pickoff throw are scared to make another one later in the game. I identified all cases where a pitcher had made a bad throw earlier in the game, and used his "normal" pickoff-attempt rate as a control. It turns out that a pitcher is a little less likely to make an attempt, but the effect is not significant. Runners, on the other hand are significantly more likely to steal if a pitcher has thrown a wild one, and this time, it *doesn't *affect their success rate either way. We also see that if a pitcher makes an errant throw, he's no more likely to make a second one. Pitchers who had not previously made a bad throw had an "airmail rate" of 0.3 percent. Those who had already made one earlier in the game? 0.3 percent.

*Are pickoffs good deterrents?*

The happy side of a pickoff throw is that sometimes, you actually pick off the runner. But what happens after that? We see that pitchers are actually significantly more likely to throw over (compared to their usual rate) if they have picked off a runner earlier in the game, and it does tamp down on runners trying to swipe a base, even once you control for runner tendencies, situational factors, and whether the pitcher threw over to first. It doesn't seem to affect steal success rates.

There's also a tiny bit of evidence that pickoffs lead to more pickoffs. The pickoff rate for a pitcher who had not earlier picked a guy off was 0.7 percent. Afterward, it was 1 percent. That's a small bump up, and the chi-square is not significant (p = .10), but it's close.

*So what is a throw to first worth?*

Every time the "average" pitcher throws to first, he has a 1.6 percent chance the runner will be excused from the basepaths (and an out will be recorded). In 2014, going from a runner on first with no outs to no runners and one out is worth 0.58 runs. With one out, it's worth 0.39 runs. With two outs, itâs worth 0.19 runs. Let's call that 0.30 runs or so.

There's also a 0.6 percent chance that he will throw the ball away. From 2010-14, when this happened, 1 percent of the time, the runner stayed at first, but 72 percent of the time, he went to second, and 26 percent of the time he went to third. One percent of the time, he scored. Let's just focus on the runner-to-second situation for now. With no one out, that's a negative of 0.22 runs, with one out, it's 0.14 runs, and with none out, it's 0.10 runs. Let's call that 0.15 runs on average and bump it up to 0.20 runs total because of the chance of going to third.

On that throw, there's a 1.6 percent chance that something worth 0.30 runs will happen, a 0.6 percent chance that something worth negative 0.2 runs will happen, and a 97.8 percent chance that "nothing" will happen. Except that we've seen that a throw to first really does affect the running game. We saw that throwing to first actually increases steal attempt rates by 3 percent (from about 9 to 12 percent) and reduces steal success rates by 12 percentage points. We can infer from above that the difference between a stolen base and a caught stealing is about 0.45 runs. So by throwing over to first, an extra 3 percent of the time (12 percent total), the runner is going and an extra 12 percent of those times, he does something that loses his team 0.45 runs. There's also some value from the situation where there's a single and the runner is more likely to try for third (and more likely to be thrown out), although those effect sizes are small as well. That means that for an average throw over to first, the pitcher gains something like 0.0064 runs. All together, throwing to first is worth 0.01 runs, even if "nothing" happens.

**Should All Pitchers Throw to First?**

I don't think the moral of the story is that all pitchers should throw to first any time that there's a runner over there. Most throws are halfhearted anyway, just a way to say "I'm watching." There are other ways to communicate that, but, for what it's worth, throwing over does appear to be a pretty effective strategy. The fact that pitchers tend to be fairly consistent over time in their throwing to first and the fact that it doesn't seem to be associated with stolen-base results suggests that throwing might actually have more to do with a pitcher's routine or approach than anything. With some pitchers, if you start to tinker with the approach, things can come unraveled.

The effect size of a hundredth of a run might seem small, but that's a credit that a pitcher can pick up just about every time there's a runner on first. Still, even for a starter who has 200 or so of these opportunities, we're talking about what could be two runs worth of value over the course of a season. Then again, the most throw-happy pitchers only throw over half of the time, So, we're talking about maybe a half a run for a more average pitcher over the course of a year. And that's it.

So really, throwing to first doesn't actually add much in terms of value to the game. Not much, but it's there, and it basically costs nothing to do, so the pitcher might as well seize what value is there. Coming back to Jon Lester, it's very likely that because he's such an extreme case, the rules discussed above melt away; but for those pitchers who are somewhere in the middle, there's not a lot to be gained from throwing more often to first, but just enough to gain that the play is not going away either.