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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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