Pebble Hunting: A Billy Hamilton/David Ortiz Race

On April 16th, Johnny Cueto singled against Francisco Liriano, which brought up Billy Hamilton, who grounded weakly to shortstop Jordy Mercer, which sets up a question we don’t ask very often but, in this case, must: Should Mercer have taken the out at second, or ignored Cueto and thrown Hamilton out at first?

Eric Hartman phrased the question a bit differently in an email to me this spring: “Down 1 run in the 9th, would you rather have David Ortiz on 2nd base, or Billy Hamilton on 1st?”

Most of the questions we get aren’t this simple. All I have to do is go to a run-expectancy table, and I can see that with nobody out and a runner on first this year, the average team has scored .48 runs; with nobody out and a runner on second that team has scored .62. So I’ll take the runner on second. Asked and answered!

But, alas, a Billy Hamilton run expectancy table is very different. With a runner on first and nobody out, according to the Billy Hamilton run expectancy table, the most likely result is mayhem; with a runner on second and nobody out, it’s madness, and with a runner on third and nobody out it’s hysteria.

So while the question seems silly—Hamilton and Ortiz aren’t even on the same team, for starters—it’s actually somewhat tied to reality. Mercer didn’t seem to think twice about his play, flipping it casually to second, where a disinterested Cueto never even entered the frame. But Mercer had just loosed Hamilton in a one-run game. Did he do wrong?

In one sense, there might not be a bigger tools gap in the sport than that between the speed of Hamilton and the speed of Ortiz (or some similar slug). Ortiz will hit considerably more home runs than Hamilton, for instance, but Hamilton will also hit some home runs; any home run Ortiz hits Hamilton might also have hit, so there is never a situation where Ortiz’s power is infinitely better than Hamilton’s. But when Hamilton does something like this,

it is virtually impossible to imagine Ortiz ever doing that. David Ortiz will never, ever, ever, ever score on a sacrifice fly 30 feet beyond the infield. Ortiz can't be taught to do that, and he can't be repositioned to do that. He'll never do that.

And yet, it’s also very hard for Hamilton to turn his infinite speed advantage into infinite runs. We’re nearly two months into the season, and this is as far as he’s been able to run:

• Billy Hamilton: 1.2 baserunning runs above average
• David Ortiz: -2.0 baserunning runs above average

That gap seems impossibly small—two months of running and he’s produced a value differential roughly equivalent to three triples. Let’s break down what happens when each guy gets on base.

Advancing on hits, from first.
As soon as we start this process, we run into a problem. Say you want to know how often each guy scores from first on a double. That’s easy enough: Since 2011, David Ortiz has almost never scored from first base on a double:

• Ortiz: 4 times out of 32 opportunities, thrown out at home once

Since Billy Hamilton came up to the majors, he has never scored from first base on a double.

• Hamilton: 0/0, attempts to steal second every stinking time he gets to first.

This is a big problem if we want to model Billy Hamilton’s baserunning. He doesn’t stay at first. So he doesn’t have a lot of “from first base” outcomes to his name. We’ll do the best we can.

Ortiz practically never goes from first to third, either. Hamilton—well, who really knows, but at least we have some numbers to go on:

• Ortiz: 10 out of 81, thrown out at third once
• Hamilton: 3 out of 7

Hamilton’s opportunities have been so rare that they’re skewed by context. Of the four times Hamilton hasn’t gone to third, one was an infield single, one was to left field, and the other two were line drives to center. He has never not reached third on a single to right—Ortiz goes to third on about a third of those.

And, from second base when a single is hit:

• Ortiz: 28 of 61, thrice thrown out at the plate
• Hamilton: 7 of 7

Advancing on outs.
From second, on a groundout:

• Ortiz: 62 percent, including one fielder’s choice/out
• Hamilton: 80 percent

From second, on an air out:

• Ortiz: 21 percent
• Hamilton: 71 percent

From third, on a groundout:

• Ortiz: 71 percent, including two outs
• Hamilton: 86 percent, including one out

From third, on an air out:

• Ortiz: 42 percent, including one out
• Hamilton: 50 percent

Advancing on wild pitches/passed balls.

• Ortiz: 11, since the start of 2011
• Hamilton: 6, since August 2013

OK, so we’ve established that, no matter what happens around them, Billy Hamilton is a substantially more productive baserunner. If there’s a hit, he’s roughly three times as likely to take the extra base. If there’s an out, he’s 50 percent more likely to advance. If a ball gets away from the catcher, he’s about four times as likely to advance a base. This is not surprising. The relatively small margin between their baserunning value is what’s surprising, so what’s up with that?

Well, for one thing, baserunning is often redundant. We know, for instance, that when the Pirates opted to erase Johnny Cueto they were inviting Hamilton to advance to second on a wild pitch or a fly out, or to go first to third on a single, or to steal a base, or to steal two bases. But what actually happened next was Joey Votto homering. The difference between Johnny Cueto and Billy Hamilton in that scenario is neutralized. There are enough home runs on the way that it’s hard to really impact a situation with one extra base.

But the other thing, at least with Hamilton and Ortiz, is the final category of baserunning: Stolen bases. Hamilton has been caught six times this year, out of 22 tries; Ortiz hasn’t tried, and thus hasn’t been caught. That closes the gap in their baserunning by a little bit—about a tenth of a run, by our measures. But in reality it has closed the gap even more than that. Our measures are based on the lost value of a typical baserunner, but as we established way up in paragraph three, Hamilton is not a typical baserunner. When he’s on base and something happens, he’s very likely to separate himself from Ortiz. But every time he takes off on a stolen base attempt, he’s costing himself opportunities to really let his speed separate itself from Ortiz's—by scoring from first on a double, for instance—without the same risk of an out.

That’s not to say that Hamilton shouldn’t be trying to steal bases. It’s just noting that, in a sense, this is the least efficient way for Hamilton’s speed to show, at least statistically. And it’s the one way that Hamilton’s speed can actually bring his stats back down to Ortiz’s level.

So back to the original question. The easiest way to answer this question is, indeed, a run-expectancy table, but one that is specific to each player. So here’s the likelihood of each runner scoring based on all the base/out scenarios they’ve been involved in–Ortiz going back to 2011, Hamilton in his career:

David Ortiz Run Probability:

Billy Hamilton Run Probability:

Well, it would be the easiest way to answer this question if we had enough data to really trust. As we can see by Hamilton’s table—where moving from first to second with one out actually hurts his run expectancy—there are still some problems with extrapolating at this point. He's stood at second base with one out, for instance, only nine times in his career. But the most common scenario—Hamilton on first, with nobody out, a situation he has been in 25 times—produces a 64 percent chance of Hamilton scoring. There are other factors–the outs Hamilton spends getting to second hurt the rest of the team's scoring chances that inning; the hypothesized (if unproven) Hamilton Effect on pitchers—but If that turns out to be accurate, it's practically identical to Ortiz’s 63 percent chance of scoring from second. (With one out or two outs, the run expectancy tables would suggest Ortiz at second is the better bet, but, again, unreliable at this stage.) I hope it turns out to be accurate. Watching Jordy Mercer try to decide what to do next time he’s faced with a Cueto-or-Hamilton choice will be much more fun if the answer is this debatable.

In lieu of complete data, I'll answer Eric's question (and Jordy's question) like this: I'd take the out at first and hope the numbers backed me up.

Thanks to Rob McQuown for research assistance.