Let’s imagine a baseball player.

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Let’s imagine a player who has a unique and freakish skill: he can only hit doubles. No homers. No singles or triples. He can’t even walk…he just hits doubles. If a pitcher tries to walk him, he ends up on second base anyway. Our guy is Earl Webb, imagined through a Matt Christopher book.

Let’s go a little further in flushing his character out. Let’s say he has an on-base percentage of .300. Three out of every ten times he comes up to the plate, he gets a double. The other seven times he’s an easy out. That is an abysmal on-base percentage, of course.

But he would also have a .600 slugging percentage. If he collects six total bases per ten at-bats, that’s a .600 slugging percentage. You can probably live with a .300 on-base percentage if you’re getting a .600 slugging percentage, right? Let’s bat him fifth or sixth and call it a day.

Well hold on. Hold on for just a second. I have another twist to throw at you.

Because the best superheroes have layers of complexity, we’re going to throw in one moredetail about our guy’s oddly specific power: his ability to hit doubles only works if there is no one on base when he is batting. If someone’s on base, he’s a nearly useless hitter.

So maybe he’s not worth playing. I mean, it’ll be great to have a .600 slugging percentage in the batting order, but it’s not that great if he can’t use that slugging percentage to actually drive in runners. And he’s going to have a lot of at-bats where he’s hitting below replacement level. So he’s probably not worth it.

Except it turns out that he is a superlative defensive player at a key position. He saves a good number of runs on defense.

And he comes cheap. His annual salary is less than what Clayton Kershaw makes for one start.

What do you do with a guy like that? Would you want that kind of a headache? And how would you use him? What would be the best way to cash in on his particular skill set?

I think, if you thought it all the way through, you’d decide that he should play. Because you’d want to maximize the possibility of a double, you’d probably slot him in the leadoff spot. And because you’d want to maximize the chances of him hitting leadoff, you’d want him to play for an NL team.

* * *

Which is handy, because Billy Hamilton does play on an NL team.

I was thinking about Billy Hamilton last night, and I was thinking about the fact that his on-base percentage just does not do justice to who he is as a player. It is the one statistic that almost everyone who writes about Hamilton focuses on: his abysmal on-base percentage. Almost every article you read about Hamilton will be about:

a) How he might improve his on-base percentage by trying one thing or another, or

b) Why the Reds cannot bat him leadoff, because his on-base average is so terrible.

Billy Hamilton certainly does have a terrible on-base percentage: his career mark is .298. But he scores a lot when he gets on base. In an off year, Hamilton ranked 16th among qualified players in the percentage of times he scored after reaching base:

Rank Name H BB ToB Runs Run% 12 Aaron Judge 154 127 281 128 45.6% 13-t Jose Bautista 119 84 203 92 45.3% 13-t Cody Bellinger 128 64 192 87 45.3% 15 Billy Hamilton 144 44 188 85 45.2% 16 Paul Goldschmidt 166 94 260 117 45.0% 17 Jose Ramirez 186 52 238 107 45.0% 18 Curtis Granderson 95 71 166 74 44.6% 19 Byron Buxton 117 38 155 69 44.5%

The year before that, Hamilton ranked tied for fourth among qualified players:

Rank Name H BB ToB Runs Run% 1 Ian Kinsler 178 45 223 117 52.5% 2 Adam Duvall 133 41 174 85 48.9% 3 Rougned Odor 164 19 183 89 48.6% 4-t Charlie Blackmon 187 43 230 111 48.3% 4-t Billy Hamilton 107 36 143 69 48.3% 6 Kris Bryant 176 75 251 121 48.2% 7 Ian Desmond 178 44 222 107 48.2%

The reason for this is very obvious: once he reaches base, it is extremely difficult to keep Hamilton from scoring. He is pretty bad at getting on base: he doesn’t have the power to knock one into the cheap seats, and he doesn’t have the contact skills to reach base regularly. But Billy Hamilton is excellent at moving around the bases.

Hamilton’s speed doesn’t show up in the traditional equations for on-base and slugging percentage, of course. But it’s possible to tweak those formulas to give him a leadoff slugging percentage.

How do we do that?

We convert his stolen bases into total bases, and we penalize him for the times he has been caught stealing. The result is a player who had a slightly worseon-base percentage, but a much better slugging percentage:

2017 Actual OBP Actual SLG Leadoff OBP Leadoff SLG B. Hamilton .299 .335 .279 .414

When you factor in the times he was caught stealing, Hamilton’s on-base percentage drops twenty points. But his slugging percentage, once you factor in his stolen bases, jumps nearly eighty points. He becomes last year’s version of Mark Trumbo:

Player OBP SLG B. Hamilton .279 .414 Mark Trumbo .289 .397

Let’s just stop a moment and appreciate the historical nature of this article: we’ve reached a point where we’re comparing Billy Hamilton to Mark Trumbo. Uncharted waters, I suppose.

But that measure actually undersells Hamilton, because it considers all of his at-bats. What about just looking at his at-bats as a leadoff hitter?

This gets trickier, because while we can get his hitting splits as a leadoff hitter, I can’t find anywhere that lists his stolen base numbers split on leading off an inning versus not leading off an inning. But we can at least make an approximate guess of things. 246 of Hamilton’s 633 plate appearances came when he was leading off an inning last year, or 39%. We can run his numbers leading off an inning, swapping in 39% of his stolen bases and caught stealing events, and figure out the kind of hitter Hamilton was at the start of innings.

We get:

2017 Actual OBP Actual SLG Leadoff OBP Leadoff SLG B. Hamilton .358 .404 .337 .487

Leading off an inning, Hamilton was…not bad.

Player OBP SLG B. Hamilton .337 .487 Trey Mancini .338 .487

He was opposite-world Trey Mancini…he was Trey Mancini if you took Mancini’s power hitting and converted it to speed on the bases.

In an ideal world, you wouldn’t want a hitter like Trey Mancini batting leadoff. In an ideal world, Trey Mancini would be hitting at the back of an offense, where that slugging percentage could convert into runners being driven in.

This is where the trick loses its magic. We can pretend all we want that Hamilton is a pull hitter all we want, but the reality is that the bases he advances don’t do the same thing as the bases that Mancini or Trumbo collect. Hamilton is the living incarnation of one-run strategies, and trying to understand him using multiple-run metrics like slugging percentage is a little like trying to understand a fish by looking at clouds.

* * *

There is nothing conclusive about the numbers I’ve shown you so far: I’m just trying to get us out of the mindset that a metric like on-base percentage doesn’t tell the whole story about Billy Hamilton.

But I am going to come around to a conclusion: I think the Cincinnati Reds should absolutely bat Billy Hamilton in the leadoff spot.

Hamilton hit leadoff in 135 games last year, and the Reds went 61-74 in those games. That’s not good, of course…that translates to a .452 winning percentage.

But the Reds went an abysmal 7-20 in games where Hamilton didn’t lead-off. That’s a winning percentage of .259. They played like the 1962 Mets without Hamilton.

They scored 660 runs with Hamilton batting leadoff, an average of 4.9 runs per game. Without Hamilton, the Reds scored 92 runs in 27 games, or 3.4 runs per game.

And their pitchers did appreciably worse without Hamilton in centerfield. When Hamilton played, the staff allowed 5.2 runs per game. When he was out of the lineup, the Reds pitchers allowed 6.2 runs per game.

Let’s table that:

2017 Reds W-L W% RS R/G RA R/G With Hamilton Leading Off 61-74 .452 660 4.9 703 5.2 Without Hamilton Leading Off 7-20 .259 92 3.4 166 6.2

Most of Hamilton’s days off were rest days, but there was a stretch in September when Hamilton missed fourteen straight games. The Reds record without him was 5-9, a .357 winning percentage.

I don’t want to put too much stock in those run differentials: it is unlikely that Hamilton generated 1.5 runs in production more per game than whomever the Reds substituted in for him. And though I’m sure Hamilton’s stellar play in the outfield is a contributing factor to the difference in runs allowed, it is a big stretch to say that he is worth a run per game on defense.

But the Reds do seem to play betterwhen Billy Hamilton leads off. Maybe they shouldn’t do better - maybe the math suggests that Billy Hamilton is a liability - but it is difficult to argue with the results.

* * *

I’m not impartial on the subject of Billy Hamilton. He’s my favorite player to watch in baseball, and I root for him every year. I root for him because he is so different, and because sometimes it is difficult for teams to know what to do with players who are different. What do you do, really, with a kid who can only hit doubles?

The Reds efforts to win baseball games with Billy Hamilton on their roster has been one of the most interesting storylines I’ve followed over the last few years in baseball. Let us all remember, for a moment, that when Billy Hamilton first blipped on our radar as the guy charging at Vince Coleman’s minor league record for stolen bases, he was a right-hand-hitting shortstop prospect. He has transitioned to a centerfielder who now hits mostly left-handed. Let’s remember, too, that Hamilton developed those skills simultaneously, under a great deal of scrutiny and competing at the highest levels of play. At times, Hamilton’s story has been a frustrating story, and I’m sure that no one is more frustrated with the annual conversations we seem to have about Billy Hamilton than Hamilton himself.

Billy Hamilton is a good player. He isn’t going to win any MVP awards, but his presence on the Reds is a net positive on a team that is lacking in positives. Let him hit where he’s comfortable. Let him hit where he’s useful.

Dave Fleming is a writer living in western Virginia. He can be reached on this site and at dfleming1986@yahoo.com.