You probably didn’t exclaim angrily on the morning of December 10th when Billy Hamilton signed a one-year contract with the Royals. You probably didn’t do much of anything, if you even saw the news. I was the one exclaiming angrily. Why, you ask? Well, I was about 90% through writing a fun article about what the Cardinals could do with Billy Hamilton. Realistically, what the Cardinals could do with Billy Hamilton, even before he signed with the Royals, was basically nothing. Theoretically, though, the possibilities were endless. For a week or so, my ambition was thwarted. What was I going to do with this twee little BIlly Hamilton article when the man himself was out of play? This week, though, inspiration struck- and by inspiration, I mean writer’s block during a slow offseason. So here’s the deal- here’s an article about platooning Billy Hamilton and Jose Martinez to create a super-centerfielder. Even if they could, right now, the Cardinals would never do this. They theoretically could, though, and I think the results would be pretty amazing. Consider this a thought experiment- how good of a defender would you have to be to justify an EXTREMELY early defensive substitution? How good of a hitter would you need to be to justify a full-time role as a pinch hitter? Billy Hamilton and Jose Martinez are the logical extremes of their respective archetypes- if it’s not going to work with them, it’s not going to work at all.
First, let’s define the parameters of our experiment. The Cardinals, in this hypothetical, sign Billy Hamilton and retain Jose Martinez. Then the fun begins. The team sits both players down and gets full cooperation on a rotating system that will maximize both players’ skills. Here’s how it works: Jose Martinez is going to be batting for Hamilton whenever possible, and I do mean whenever possible. In away games, this works out pretty easily. Martinez hits third, and Hamilton enters as either a pinch runner or a defensive replacement immediately afterwards. That’s nine glorious innings of Hamilton patrolling center field, and one plate appearance he gets to skip. Jose Martinez has reached base about 37% of the time in his career- that’s some juicy Billy Hamilton baserunning opportunities. Home games are slightly more complicated- Martinez needs to field, after all. In this case, Harrison Bader starts in center field with Martinez in right, and Hamilton enters after Martinez bats in the bottom of the first. There are a few more wrinkles to cover. In AL stadiums, Martinez DH’s and the outfield works more or less normally aside from him. Last but not least, Martinez gets a game of full-time play once a week.
Those are the rules- they’re basically what you’d expect for a time share. It’s a neat concept, but how good would this hybrid player actually be? First, we’ll go to the numbers to approximate how good Billse Hamiltinez would be as a hybrid player. Next, we’ll try to work out a reasonable amount of playing time for our hybrid ‘outfielder.’ Last, we’ll do some very qualitative guessing at the cost of a roster spot- this setup requires five outfielders on the roster, and it’s going to cost some roster flexibility to do that.
Bullet With Butterfly Wings
First things first- what kind of batting line does our strange hybrid have? We can actually get a pretty good idea by looking at each player’s line and then working out a quick approximation for how often Hamilton will be forced to bat. The average number three hitter in the NL came to the plate 4.14 times per game last year, so that gives us an idea of how many plate appearances we’re working with. Martinez is taking up exactly 1 PA per game, with Hamilton grabbing the other 3.14. Let’s further stipulate that Hamilton is later pinch-hit for one in every ten games- he’s a pretty terrible hitter, after all. This leaves us with 3.04 PA from Hamilton every game. There are two ways to go about this- we can either look at a blended wRC+ to approximate a park-adjusted batting line, or just construct a triple-slash line and basically ignore park effects. For the sake of completeness, we’ll do both. The wRC+ math is easy- Martinez sports a career 130 wRC+ and Hamilton sits at a comically low 70. Blend those together, and we’ve got an 85 wRC+ hitter. That’s not amazing, but still leagues better than Hamilton by himself. What does that look like in a triple slash line? Call it .261/.316/.369, an unexciting line but at least serviceable.
Okay, so our new player is a pretty blah hitter. How about his base-stealing prowess? To figure this out, I’m going to do some absolutely terrible approximating. Billy Hamilton has been worth 54.6 baserunning runs above average over his career per Fangraphs. He’s reached base without hitting a home run 784 times. By extremely dubious commutative property, we can say that he’s been worth roughly .07 runs above average every time he’s set foot on the basepaths. Well, how many times per game will Hamilton have a chance to unleash baserunning hell? After accounting for combined on-base percentage and home run rates, we can expect Hamilton to get 1.22 opportunities to run a game. If that doesn’t sound all that exciting, it’s because it’s not. Hamilton gets about 1.17 opportunities per game already. In fact, over a 125-game set, that’s only an additional seven opportunities on the basepaths when piggy-backing with Martinez rather than just having Hamilton bat himself. That’s about half a run a year- basically just a rounding error. Still, while the increase from Billy Hamilton alone to Jose+Billy isn’t high, Hamilton’s overall baserunning value is still pretty high. Our strange hybrid would have been the second-best baserunner in the majors last year.
Wait ‘Til You See Him Play Defense
We’ve got the per-plate-appearance hitting squared away, but what about our hybrid defense? This is a little trickier to measure, but I’ll certainly still give it a try. The first thing to estimate is how many innings of Hamilton and how many innings of Martinez we’ll get. Luckily for us, a loose estimate is pretty workable given our assumptions. The Cardinals get to pick which days Hamilton rests, and let’s assume they always give Jose his full day in the field on a home game. This means that our hybrid is going to play three road games and two home games a week (assuming five games a week, one of rest, and one for Martinez to play). The road games are easy- we get Billy Hamilton’s defense for all nine innings. The two home games are a bit trickier. We need to use positional adjustments here to compare the value of Hamilton’s defense and Martinez’s ‘defense.’ The math here is straightforward, though a bit abstract. There’s a 10-run difference in centerfield and rightfield defense over 162 games. Ever wonder how many runs that is per inning? Of course you didn’t, because it’s going to be meaningless. Meaningless except in this madcap exercise, of course. Those 10 runs per 162 games are .007 runs per inning.
Next, let’s add the defensive values for each player. Jose Martinez is a TERRIBLE defender. Like, just terrible. What is that in runs per inning? Well, -.008 runs per inning (that’s a UZR/150 of -10.6, which is truly abysmal). Billy Hamilton, on the other hand, is worth POSITIVE .008 runs per inning in center. That’s all we need to do the math. In road games, the team is getting 9*.008=.072 runs per game worth of centerfield defense. In home games, they’re getting (-.007 - .008 +8*.008) or .049 runs worth of defense. These are, I want to emphasize again, tiny numbers. Let’s convert it into UZR/150, which is roughly what you’d expect a player’s defense to look like in a full season. In road games, we get defense 10.8 runs above average for center. In home games, we’re looking at 7.35 runs above average- worse, but still excellent.
Both Sides Now
Where is this dumb experiment going? Well, now that we have all the constituent parts, we’re going to stitch it together to get one number. First, we’re going to assume 125 games- 5 a week for the whole season. That comes out to 505 plate appearances, as well as 125 games worth of defense. The hitting is relatively straightforward- we’re looking at an 85 wRC+ over 125 games. Jamming that into the formula for WAR (explained in my appendix here) gives us an approximation of the hitting value- an otherwise-league-average player with this batting line would be worth .6 wins per 505 PA. With that baseline, we can start plugging in other values. We’ve got 10.7 runs of baserunning value from the baserunning section up above- up to 1.75 WAR now! Next, we’ve got defense. Blending 60% away games and 40% home games, that’s another 8 runs of defensive value above average, 2.55 WAR total. Lastly, there’s the positional adjustment for centerfield, which is pretty close to 0- 2.5 runs over 162 games. This gets us up to a 2.75 WAR player over 505 plate appearances. To round out the season, we’ve got the 25 games where Jose Martinez plays the whole game himself. That’s easy enough to figure out- we can just plug in his career statistics, which gives us a further .5 WAR in those games. Altogether, then, our hybrid is a 3.25 WAR player in 600 PA. We’ve manufactured an above-average player out of two glass cannons. Rejoice!
At What Price?
Well, yeah, manufacturing a three-plus win player doesn’t come for free. I feel pretty confident that my math is right on how good this hybridized player would be. That slots in as the fourth-best projection on the Cardinals for next year, just behind Matt Carpenter and Marcell Ozuna and just ahead of Paul DeJong. The problem, though, is in the knock-on effects. Jose Martinez and Billy Hamilton are two different people (breaking news!). They take up two whole roster spots. There’s only one way to free up enough space to carry five outfielders (necessary in this hypothetical): carry one fewer pitcher. That is absolutely not something the Cardinals have been willing to do in the past, and it’s at least believable that the extra pitcher is worth one win to the team over the course of the year through increasing rest on the rest of the bullpen (though there has been little public work on the knock-on value of extra relievers). In the end, the Cardinals didn’t sign Hamilton, and I’m not even convinced that they should have. The returns, though positive, are marginal. The communication and morale issues the team would face are real. Still, though, I wish they had done it. It would be a hell of a fun plotline for next year.
I’ve never exactly respected the fourth wall in these articles, but I’m just completely ignoring it for this section. I hope you enjoyed this largely nonsensical rabbit hole. I had a pretty decent time writing it, and I really didn’t want to let it go to waste, so this total news-blank week was too good to pass up. Should you take it seriously? I mean, basically no. It was a pretty fun exercise no doubt, but I think that’s pretty much all it was. The Cardinals shouldn’t sign Billy Hamilton. Insane platoons are, yeah, insane. Still, if nothing else, it gave me something to write about in December. That’s not really fair- I think it’s also a good blueprint for how to approach truly outside-the-box lineup ideas. I had this problem to solve, and I had literally no idea how to approach it. I spent quite a while with the Hamilton-Martinez plan in my mind but no real angle of approach. Turns out, what I should have done all along is just brute-force it. Wonder about a situation? Do the math. Will the math be right? Probably not! It’s going to be a ton better than just guessing, and if nothing else it will get you in the right ballpark. Enjoy the article! Depending on what time you’re reading this, I’m either asleep or in a hot tub right now. Those are pretty much the only two options when you head to southern California for New Years. See you guys next year. Bryce Harper one time, Mo!