**The Setup**

Consider the following situation: Jimmy Rollins is on third base with no outs. Jayson Werth hits a fly ball to medium deep left field; this is, essentially, a sacrifice fly waiting to happen. Jimmy knows what to do. He retreats back to third, puts his head down and waits for third-base coach Sam Perlozzo to yell-*what?*

Should he stay or go? How does Perlozzo make that decision? And how do his all-too-human failings mean that he’ll probably end up costing his team, the Philadelphia Phillies, runs in the end?

The answer comes in understanding a good bet, as opposed to a bad bet. If offered the chance to lay $1 on a heads/tails coin flip with the chance to win $10, would you take the wager? What if you could call it in the air? Suppose you could play this game several times. You’d probably take that bet, even though you have a 50 percent chance of losing each time. Why? Because if you play the game long enough, you have a chance come out slightly ahead. You’ve instinctively applied what’s known as expected value theory. You might lose an individual coin flip-but if you play over and over, you know you’ll eventually be ahead of where you would be if you just held on to your dollar bills. This is how third-base coaches in MLB need to work and think.

**The Proof**

In our situation above, Perlozzo is playing the same sort of game-only he’s not playing for money, but for runs. Let’s go back to our potential sac fly. If Perlozzo yells “Stay,” then the Phillies will have a runner on third with one out. In 2009, whenever a team was in this situation in an inning, the team scored 0.965 runs on average. That’s the equivalent of hanging on to your dollar bill. If Perlozzo yells, “Go,” one of two things will happen: Rollins will either be safe or out. If he’s safe, the Phillies get that run, and have the bases empty with one out-which on average produced 0.279 runs, for a grand total of 1.279 runs in the two situations. If Rollins is out, there will be no one on base with two outs, which had an average run expectancy of 0.106 runs.

There’s a run and an out at stake, both valuable in baseball. How can you tell if it’s a good bet? Without going into all the algebra, it says that Perlozzo needs to be *73.2 percent sure* that Rollins will make it before he sends him. So, if third-base coaches league-wide are playing the game correctly, we should see that about 73 percent of the runners in this situation wind up scoring.

In 2009, there were 97 instances where this sort of situation occurred: no outs, runner on third, fly ball to the outfield. When the runner tried for home, he was safe 96.2 percent of the time (75-for-78). In fact, Perlozzo himself was perfect in 2009: 100 percent of the runners he sent in this situation (and in all sacrifice fly situations) reached home safely.

This seems like a good thing on the surface-but it’s actually not.

A 96-percent success rate means that third-base coaches are being far too conservative-and *only* sending the sure things. Suppose that after considering the speed of the runner on third, the distance of the fly ball, and the strength of the outfielder’s arm, the third-base coach figures that the runner has an 80 percent chance of scoring. There’s a 1-in-5 chance that he’ll be gunned down, and we already figured out that anything over 73.2 percent is a good bet-so being rational, the runner with the 80 percent chance should make a mad dash for home. If third-base coaches are only willing to send the runners who have a 95 percent chance or better, they’re leaving a good chance at extra money, er, runs on the table.

Why don’t Perlozzo and his brothers of the third-base line send more runners? It’s a human failing to which everyone falls prey. People are very loss-averse. We tend to see things not in a rational cost-benefit analysis, but in terms of how much chance of failure we’re willing to stomach. On top of that, if a runner gets thrown out at the plate, who usually gets blamed? The third-base coach. If a runner goes for the extra base and makes it, who usually gets the credit? The runner. From this perspective, the coach has everything to lose and nothing to gain from yelling “Go,” so it’s best only to send the sure things. It’s called blame avoidance. People do things not because they are the best things to do-but because they have the least chance of something being traced back to and blamed on them. It happens in your office too, doesn’t it?
If you use that same formula on several other similar situations (different configurations of runners, one out as opposed to no one out, etc.), they all show the same pattern. The “break-even” point is usually around 75 percent, but actual success rates are well above 90 percent. Through a little more complex math (it involves a technique called binary logistic regression), the average team *leaves about four runs on the table per year* on potential sac flies alone. Sacrifice flies are just one thing that a third-base coach does: He also has to decide whether to send a runner from first to home on a double, second to home on a single, and first to third on a single. All of these situations show the same gap between the break-even point and actual success rate.

If we look only at rates of runners being safe, there were actually seven third-base coaches who had perfect records sending runners on sac flies in 2009, oddly enough, all in the National League: Perlozzo, Pat Listach (Washington Nationals), Tony Beasley (Pittsburgh Pirates), Tim Flannery (San Francisco Giants), Dave Clark (Houston Astros), Larry Bowa (Los Angeles Dodgers), and Bo Porter (Florida Marlins); Porter is going to coach for the Arizona Diamondbacks this season. Only one third-base coach (Dave Owen of the Kansas City Royals) dropped below 90 percent success-but that’s not the number you should be looking at.

Which third-base coaches said “Go!” the most in 2009? Across all potential sacrifice flies (runner on third, less than two outs, fly ball or line drive caught by an outfielder), Tom Foley of the Tampa Bay Rays was most likely to send a runner (88.9 percent), followed by Rich Dauer of the Colorado Rockies (88.4), Brad Fischer of the Milwaukee Brewers (87.9), Scott Ullger of the Minnesota Twins (87.9), and Chip Hale of the Arizona Diamondbacks (87.8). The coaches most likely to yell “Stay!” were Glen Hoffman of the San Diego Padres (70.9), Owen from the Royals (70.6), Mike Quade of the Chicago Cubs (70.5), Listach from the Nationals (69.6), and in last place, our friend Mr. Perlozzo of Philadelphia (69.2).

**The Conclusion**

Here’s an interesting one: What would happen if third-base coaches just sent everyone, playground-style, on these potential sac flies, regardless of whether it was a good idea or not? It turns out that teams would probably score *more runs* than they do now.

Indeed, it was very rare that it was a bad idea to send the runner, even after controlling for the distance of the fly ball and the speed of the runner. It was almost always the case that the chances of the runner succeeding were above the break-even point. The runner might get thrown out this time, but if a team really committed to an old-school playground style, it would come out ahead.

Thus, the ideal third-base coach is a sign on a stick featuring the words *“If the gentleman currently holding the ball is an outfielder, please turn left and run an additional 90 feet.”* It’s counter-intuitive, but the third-base coach doing the most for his team is not the one who has the highest safe-rate, but the one who has the highest go-now rate.

*A version of this story originally appeared on ESPN Insider .*

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Quick question - your article says "In 2009, there were 97 instances where this sort of situation occurred: no outs, runner on third, fly ball to the outfield." Is that number accurate? If so, that specific situation would only occur about three times per season per team, which doesn't sound right.

How do we know that Perlozzo isn't 96% successful b/c he can almost always tell when to send the runner? Let's say that there's usually a 100% chance of success and sometimes a less than 70% chance and only very rarely is the chance of success between 70-100%. (btw, I think this is likely the case; there are very few "tough calls" on sac flies usually it's fairly obvious) In this case, a 3rd base ump might make all the right decisions and have a success rate (like 96%) FAR above the break even rate.

The break even rate should be his marginal rate of success not his average rate of success. His average should be considerably higher than his marginal. If a coach has a 73% (or lower) success rate he's definitely making bad calls.

There's other things to control for that are not stated: the quality of the outfielder, the quality of the upcoming batters, the quality of the pitcher.

Could you talk about another type of flaw in the way we observe events? Not only are humans loss averse, we also do a very poor job of recollecting the occurrence rate of events. With a runner on 3rd and no outs, we take great notice of the rarest outcome (the runner getting thrown out at home), take good notice of the desired outcome (run scored), but perhaps fail to appreciate how often the runner gets stranded. Do you have a number for the strand rate of runners held at 3rd during a potential no-out sacrifice fly?

There is an article on Bill James Onine by Dave Fleming "Utley's Perfect Season" address the exact situation.

http://www.billjamesonline.net/ArticleContent.aspx?AID=1182 (subsciption only)

Guess it is closer than I expected.

Look at your original numbers.

68 = cannot be made out

10 = good chance (seven made it)

19 = cannot be safe

You're article theorizes that by giving the other team an additional 19 free outs, you'll score more runs.

The theory is wrong.

If your math is correct, anyone with a greater than 27% chance of getting thrown out shouldn't be sent (game considerations aside). Think about it, 19 times in 100, the chances are about 1 in 3 that a guy gets thrown out - does that really seem out of line to you?

You're taking 97 different decisions and trying to apply the same equation to each of them. That's just wrong.

All those easy scores push the success rate upward. The coach would have to be sending a lot of runners with the chance of scoring is well below %73 to end up with a success rate of 73%.

It sounds like you've done deeper analysis here so I'm really hoping there's a follow up article.

Which still means that they're too conservative, but not by all that much.

Pretending every baserunner and outfielder is an identical aggregate of league-average statistics, and every play has a league-average outcome, just doesn't translate to the real world.

Thus, the ideal third-base coach is a sign on a stick featuring the words "If the gentleman currently holding the ball is an outfielder, please turn left and run an additional 90 feet."

is far too strong. At least until you can convince me that you have controlled for these factors.

* the ballpark (run-scoring environment ... is it a bandbox where one more run doesn't mean THAT much, or a canyon where one more run can stand up)

* the flyball/ball-in-play tendencies of the next batter (if the next batter puts many balls into play ... and puts then in the air, there should be less of a tendency to send the runner)

Note that the Phillies are far and away the most successful team in baseball at the art of the stolen base for several years running (pun intended). Most analysts attribute this to the sagacity of one Davey Lopes, 1st base and baserunning coach extraordinaire, but perhaps a modicum of credit is due to the baserunning skills of Messrs. Utley, Rollins, Victorino, Werth, Howard (8 SBs, only 3 of which were back-ends), et al; and Mr. Perlozzo's success rate is a result of smart, speedy runners who give outfielders a reason to hurry their throws.

Feliz, Ibanez, Ruiz - them he don't run so much, for obvious reasons.

What am I missing?

It may be true that teams on average leave runners on base over the course of a year, but are all those runs of equal value? Wouldn't the break even point be context dependent?

Plus, there are all sorts of other decisions involving sending runners (advancing on singles) where you may want to hold or advance a runner based on the interaction between the probability of drawing from the thick right tail of the distribution and the inning. A four run bottom of the second is valuable, but you shouldn't include that possibility in your calculations in the bottom of the ninth if you're down by less than four runs.

This is a very simple, well-defined decision (stay/go), that has definable outcomes (via the run expectancy matrix... if you want to monkey around for some other context, fine) and if the goal is maximizing the number of runs scored (which is kinda the point of the game) then this is a way to maximize run scoring.

It's not easy, but somewhere in the back of his mind, the 3BC is doing some sort of calculation. It's just skewed toward keeping the runner there more than it should be.

Conventional baseball "wisdom" is that you don't send the guy with no outs. You've got evidence that shows the coaches are going against that convention 80% of the time, and you conclusion is that they're being overly conservative.

(but of course, the ump COULD call the runner out without even seeing if he left the base early or not, as in last year's playoffs)

Situation 1. Michael Bourn is on third base and Juan Pierre makes a diving catch running up the hill in center field at the Juice Box, slamming into the flag pole.

Conclusion: Runner should be sent, because he has a 73.3% chance of scouring, and thus a positive outcome.

Situation 2. Jorge Posada is at third and a pop fly is hit 150 feet from home into right field which Ichiro catches running at 70% of maximum speed directly facing home plate.

Conclusion: Runner should be sent because he has a greater than 73.3% chance of scoring, and thus a positive outcome.

If the article was done correctly it would have disregarded all of situation 1's above (plays where throws aren't attempted or reasonably done so), and weighted situation 2's to the correct chance of the runner actually scoring, (say 5% for that particular scenario up to 99.9% chance were an outfielder could theoretically throw someone out).

Then further weighted those numbers against the game situations mentioned by others.

Good idea, very poor execution.

A third base coaches job in this scenario is, on some level, to assess the chances of the runner reaching home. The problem is that the statistics suggest that third base coaches are seeing the threshold for sending runners as being somewhere around 90%, rather than being somewhere around 73%.

The "always send" is probably not optimal, but is meant to show that it would be better than what teams currently do in these situations.

I used the "always send" to have a little fun with the data. The results surprised me. I went with it. It's not actually going to happen (and it isn't optimal), but it's better than what's being done now.

I will put the question to you again and to others. Does it seem likely that 30% of the time the third base coach felt that the player had less than a 73% chance of scoring?

To me that number seems perfectly in line with what I would expect. It may be a little high, but it's not outrageously high.

No, no, no.

He needs to be *at least* 73.2% sure. If he's greater than 73.2% sure, he will send the runner. If he's 100% sure 50% of the time, 73.2% sure 25% of the time, and 0% sure the rest of the time, he's going to send the runner 75% of the time at an 86.6% success rate.

You could think of the events in three baskets:

-no doubt safe

-no doubt out

-grey area

This analysis should only involve the grey area, but you include the no doubt safe in the analysis.

(BTW, if your analysis in this article is correct, then the best base stealers are those who succeed 73% of the time and guys like Ichiro should stop with their 82% success rates and steal more.)

Using Russell's numbers of 97 events, 78 runners sent, and 96.2% success rate, 3B coaches delivered (75/97)*1.279 + (3/97)*0.106 + (19/97)*.965 = 1.182 expected runs per event.

Change those numbers to 97 events, 97 runners sent, and an 86.6% success rate, and expected runs is just 1.122 per event.

What it seems like is 3B coaches have this about nailed.

One thing to note: it seems to me that it's pretty rare to even see a close play at the plate in these situations. Nearly every fly ball seems to end with the outfielder lobbing the ball to second while the runner trots home, or the runner taking three steps towards home and stopping while the ball reaches the catcher on a couple of hops.