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A (Pseudo-)Mathematical Proof

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It's time we get this straightened out once and for all.

We know for a fact that some players hustle more than others. For example, you'll hear that, say, John McDonald is "leaving everything on the field" or "getting his uniform dirty" more than you'd hear the same about Wily Mo Pena or Adrian Gonzalez. A part of this is announcer exaggeration, but there's also an element of truth to it; guys like McDonald tend to do the things most frequently related to effort and tenacity more often than some of their teammates. If "hustle" is a human construct, than humans should be well-suited to evaluate who has it and who doesn't, and the result is that the Darin Erstads and Scott Podsedniks of the world are considered to be among the scrappiest players in the league.

That's about as far as you can take the idea and have it still make sense, though. Because, you see, something we hear all the time is that these same scrappy, blue-collar athletes do "all the little things that don't show up in the box scores," and that just isn't true. Things like diving stops, long at bats, legged-out infield singles - these are all numerically-recorded events. If Willie Ballgame hits a roller to short and sprints to first before the throw, that gets entered as a "1" under the "Hits" column. Had he not hustled down the line, he would've had a "0" to his name instead.

The same basically goes for every little thing scrappy players do in earning (and maintaining) their reputation. Additional hits go into their batting line. Stolen bases and sac bunts are shown on their player profile pages. Great defensive plays are individually reflected by their UZR or PMR. And so on and so forth. The only - only - thing these players are said to do that can't be measured is "make everyone around them better," which I'm convinced is something some coach made up on a whim because it can't be disproven, and coaches always love having the last word on a subject.

If we accept that a player's hustle shows up in his stats, then we're able to take the point further. We can't make any predictions about the future, since there's no way of quantifying the "hustle" contribution to a player's overall numbers, but this does lend itself to a little retrospective analysis. Historical numbers are static. They don't change. If a player was worth 80 runs in a season, then that's it, end of story. And this is where it gets fun.

The best runs created metrics in the world take as much as possible into account, from singles to steals to strikeouts to defense (defense is usually added to offense to get a "total" player value). It makes sense, then, that a player's hustle will show up somewhere in his final calculated value. Since effort is put towards making good plays that help a player's team win, it will make up a certain fraction of a player's total worth.

So let's take two guys - Player X and Player Y. They were both worth the same amount of runs to their respective teams in 2006.

Player X: +100 runs
Player Y: +100 runs

Player X, however, is a skinny white middle infielder, while Player Y is a fat, lumbering corner outfielder (we'll call him 'C. Lee'. Or maybe 'Carlos L'). Player X's extraordinary hustle over the course of the season was worth +15 runs, while Player Y cost his team 5 runs by candyassing on the basepaths and in the field. That's a pretty substantial gap of 20 runs in Player X's favor. The difference has to be made up by natural talent. So, to recap:


Player X: +15
Player Y: -5

Natural Talent:

Player X: +85
Player Y: +105

They both come out the same in the end, but Players X and Y arrive at their 100 runs by taking vastly different routes. Player X got less from his talent and more from his hustle, while Player Y got more from his talent and less from his hustle.

This analysis can and does apply to any collection of players in the history of baseball. A player's total value will always depend on (A) talent and (B) hustle, and that's pretty much it. And if it applies to everyone in the past, then - because nothing about the game is changing - it therefore applies to everyone in the future as well. It may not be the most mathematically-appropriate assumption to make, but for our purposes, it works. If a player has a given total value, then a fraction of that will come from his hustle, and the rest from his talent. As you get more from one, you get less from the other. This inverse relationship leads to the following simple expression:

In English: hustle is inversely proportional to talent. A player who derives a lot of his value from one will get comparatively less from the other. Guys like David Eckstein and Jose Vizcaino are constantly lauded for their scrappiness and balls-to-the-wall style of play because relative to the rest of the league, their natural talent sucks, and their hustle is the only thing keeping them employed. Meanwhile, you don't hear any stories about how Travis Hafner took an extra base or that Gary Sheffield made a diving attempt at a foul ball, because these guys have so much natural ability that they don't need to go 100% on every play. Nor would it really do them much good; "hustle" is all about maximizing your ability, and you'd have a tough time convincing me that Hafner or Sheffield could significantly up their value by running a little harder.

The better a player is, the less he tends to hustle (or do the things that announcers think count as hustling, anyway). This is true for a number of reasons, the most predominant being that there isn't much to gain. It's a simple principle, but an interesting one, and something to consider when you're watching a ballgame. For example, rather than complain the next time Rick Rizzs washes Willie Ballgame's dirty uniform with his drool, understand that Rizzs is basically saying that Willie's ability sucks. It'll give you a whole new perspective.