When to Give Up an Out on the Bases

With just 27 of them per team in any game, outs are a rather precious commodity. It’s important not to give them away, as letting them go often decreases the chance of scoring. Even so, there are some situations in which outs are given away and it’s regarded as advantageous. For example, a pitcher, who is likely quite bad at hitting, is often called to sacrifice bunt, moving a runner over as opposed to the more likely outcome of merely recording an unproductive out by means of strikeout, pop up, ground ball, etc.

There are other so-called “productive outs,” like moving a runner from second to third with a ground ball to the right side or hitting a sacrifice fly, but those situations are more likely to be a happy accident than intentional — i.e. a player was attempting to record a productive hit, but made an out that happened to provide an ancillary benefit. Finally, there’s still another form another potential productive out, in which a base-runner gives himself up so that another runner has a a better chance to score. Let’s explore whether that move is productive or beneficial.

While you’ve likely seen this type of play before, let’s go through a brief example. Earlier this season, Jhonny Peralta stepped to the plate with one out and runners on first and third. Brandon Moss, the runner at third, doesn’t possess great speed and has produced a negative base-running figure over the course his career. Yadier Molina, the runner on first, is a Molina. Peralta hit a fly ball to shallow center field. Coco Crisp, the center fielder, doesn’t have a very strong arm, but given how shallow the play was and Moss’ lack of blazing speed at third base, there was a reasonable chance to throw Moss out at the plate if the latter ran. Moss did run, the throw was slightly off line, and it was cut off by Yonder Alonso, who threw to second base. Max Muncy then chased after Molina, who was running back towards first, caught up to him for the out, but not before Moss was safely at home.

The embedded video below shows the play in full.

So did Molina make the smart play by giving himself up? It’s difficult to know for certain. With the benefit of hindsight, we can see that the throw likely would not have gotten Moss at the plate, rendering Molina’s sacrifice unnecessary. However, that’s not information Molina had at the time he decided to run. If you listen to the clip above with sound, you can hear broadcaster Ricky Horton say, “I don’t know” as the play began to materialize, questioning aloud whether Moss should run. The play itself did not do much to increase the Cardinals’ chances of winning, moving them from 81.5% win expectancy to 83.3% in the game. Of course, those numbers come before and after the play, and the decision we are discussing occurred in the middle of the play after an out was made.

Before we get to Molina’s decision, let’s first address the decision by Alonso to cut off the throw from center field. Given where the throw was heading, it looked like a pretty easy decision for Alonso, but we can dig into the numbers a little bit and determine exactly when a fielder should be cutting off a throw home to get the sure out. The play doesn’t have to be identical to the example above. A player could hit a single with a runner on second and then go for second to try and help the runner score. A similar situation could happen at third base, as well. Using run expectancy numbers given the number of base-runners and outs, we can find the optimal times for fielders to cut off the throw to take the sure out.

This is the chart we will use for run expectancy:

Run Expectancy (2010-2015)
Base Runners 0 outs 1 outs 2 outs
_ _ _ 0.481 0.254 0.098
1 _ _ 0.859 0.509 0.224
_ 2 _ 1.100 0.664 0.319
1 2 _ 1.437 0.884 0.429
_ _ 3 1.350 0.950 0.353
1 _ 3 1.784 1.130 0.478
_ 2 3 1.964 1.376 0.580
1 2 3 2.292 1.541 0.752
SOURCE: http://www.tangotiger.net/re24.html

To determine if a cutoff should be made, we need to look at the run expectancy in certain situations. For example, with a runner on second base and two outs, the run expectancy is 0.319 runs. If, in the play above, the sacrifice fly is successful and Alonso does nothing, then one run scores and 0.319 more are expected. If Moss is thrown out at the plate, the inning is over and no runs are scored. In this scenario, I will multiply 1.319 by the theoretical percentage likelihood that Moss will score. For example, if we assume a 50/50 shot at Moss scoring while Molina moves to second, that adjusted run expectancy is 0.660 (or, 1.319 * 0.5). Once that number exceeds 1, then the fielder should consider a cutoff and attempt to record the sure out on the bases. The graph below shows the numbers for a player going from first to second with no outs, one out, and two outs.

WHEN TO TAKE THE SURE OUT AT SECOND ON A THROW HOME

The percentages in the graph document those points at which the run expectancy crosses the threshold of one run, essentially indicating when the fielder should simply concede the run at the plate and take the out. In the example from the clip above, if Alonso believed Moss had at least a 76% chance of making it home, then the smart play was to go for Molina. Now, this does not factor in the possibility of Alonso or another player not getting Molina out. If there were, say, a 10% chance that Alonso couldn’t get Molina out, that would adjust the percentages up to closer to 80%.

As you can see in the chart, there’s a pretty big difference between two outs and no outs. Without any outs in the inning, it is better most of the time to get that first out while conceding a run. This is especially true given that, in most cases, a runner at third isn’t going to be sent unless he has a decent shot at scoring in the first place. With two outs, a third-base coach might be a bit more aggressive, and the fielder needs to be pretty sure that the throw won’t get the runner at home before cutting the ball off. Here’s a similar graph, except with the runner moving from second to third.

WHEN TO TAKE THE SURE OUT AT THIRD ON A THROW HOME

The results are substantially similar at third with two outs, but the fielder should be even more encouraged to cut the ball off and throw out the runner if there are less than two outs. In tabular form:

When to Cut Off the Ball on a Throw Home
Situation Cut the Ball Off if the Chances of Runner Scoring Are
Runner on 1st and 2 outs At Least 76%
Runner on 1st and 1 out At least 61%
Runner on 1st and 0 outs At least 48%
Runner on 2nd and 2 outs At least 74%
Runner on 2nd and 1 out At least 52%
Runner on 2nd and 1 out At least 43%

Those numbers are general guidelines and would need to be pushed up if the fielder is less certain about getting the trail runner out. While fielders don’t have the luxury of calculating these exact probabilities in real time, as a general rule, if there are two outs and the runner will probably score, take the out, and if there are fewer than two outs, unless the runner will almost certainly be out at the plate, cut the ball off to get the out.

The above show the parameters for the fielder. The runner, meanwhile, is working under slightly different circumstances. A player like Molina, above, has much less certainty when it comes to determining if the runner is likely to score. He can consider the placement of the outfielder and the speed of the runner, but he’s not likely to see as much of the throw before he makes his decision. What we can do is set up run expectancy if the runner doesn’t move, and then compare it to the expectancy he gives himself by taking an extra base.

The graph below has two lines. The blue line represents the run expectancy for the runner who stays at first base depending on the chances of the runner from third scoring. The orange line represents the run expectancy if the runner moves, with the line changing at the point where a throw is expected. The graph below only shows the situation with two outs and a runner moving from first to second.

WHEN TO GIVE UP AN OUT ON A THROW HOME (2)

Here, I gave the runner a 10% chance of making it to second, leading the horizontal portion of the orange line to appear just above the one-run marker as opposed to right at it, but those numbers could be moved around a little depending on the situation. There’s also the slim chance that the runner gets tagged out before the runner from third reaches home, nullifying the scoring opportunity. The line with the runner moving to second is ahead of the runner staying on first line for most of the graph. If the runner at home is out, nothing has been lost, but if he is safe, then the extra base gives the offensive team a slightly higher run expectancy.

If, at any time, the fielder cuts the ball off before 75%, that’s a win for the offensive team, as they’re guaranteed one run in that case. Even though it makes sense for the fielder to cut off the ball at 75% — as that is the point at which the fielder can stop the upward trajectory of the run expectancy — it still makes sense for the runner to move up to 85% chance of scoring because, while the upward trajectory stops, the flattened portion of the line doesn’t get lower than the alternative for a while longer.

We can repeat these scenarios with other base and out states, and the results are in the table below:

When to Take the Extra Base on a Throw Home
Situation Run if the Chances of Runner Scoring Are
Runner on 1st and 2 outs Less Than 85%
Runner on 1st and 1 out Less Than 71%
Runner on 1st and 0 outs Less Than 60%
Runner on 2nd and 2 outs Less Than 79%
Runner on 2nd and 1 out Less Than 72%
Runner on 2nd and 1 out Less Than 59%

For the runner, the issue is less cut and dry than the fielder. If there are two outs, the runner should generally try to take the extra base unless the run at home is close to being certain. With fewer than two outs, there are still situations when running into an out makes sense, but these scenarios are likely to be pretty rare. Most coaches will not send runners home with fewer than two outs unless the runner has a pretty good chance of making it, leaving the intersection of smart outs and opportunities for those smart outs uncommon. If a runner is faced with that decision when there are fewer than two outs, it probably means the runner on third and the third-base coach made a poor decision by trying for home.

Nobody likes to see his or her team run into outs on the base paths, and it can often seem like a frustrating rally killer when it happens. However, there are a decent amount of scenarios, particularly with two outs, where running into an out on the bases — if it ultimately nets a run for the team — makes a lot of sense.





Craig Edwards can be found on twitter @craigjedwards.

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Anon
7 years ago

I would think game state (score & inning) would also heavily influence the decision.

Runners giving themselves up is one of my pet peeves in baseball. Way too often I see guys give themselves up needlessly when clearly the run is going to score anyway. To my eye, it’s not entirely clear that the play even works for the offense. If the defense thinks they might get the runner at home, they’re letting the throw go through (unless it’s a blowout – then to some extent, everyone is just trying to get the game over with).