Yes, Of Course We Should Feed Rapists and Murderers. Oh, And We Already Do

Sen. David Vitter (R-LA) recently added an amendment to the farm bill to prevent those convicted of violent crimes from receiving food stamp benefits. Kevin Drum wrote a blog post on the subject of this amendment, in which he quotes someone else saying that, once such an amendment is proposed,

Then the tacit question arises: Does anyone in this chamber want to stand up and say that taxpayers should feed murderers, rapists and pedophiles? No? Of course not.

Okay, fine, I'll say it: of course the taxpayers should feed murderers, rapists, and pedophiles, at least those who qualify for taxpayer-feeding by the normal criteria. They are still human beings, and society has not decided that they have forfeited their right to live. If it had, it would have executed them, which I'm against in any case but which is by no means implausible in practice. By releasing these people from prison, society is signalling that it still considers them members of itself. Thereafter leaving them to fend for themselves against the prospect of starvation, while not forcing others similarly situated socioeconomically to do so, is incoherent.

Also, it's worth noting that taxpayers feed murderers, rapists, and pedophiles all the time, when they're in prison! Actually taxpayers pay less to feed an imprisoned murderer for live than they would pay to have that murderer executed, but taxpayer money, typically at the state level, is responsible for every calorie a prisoner ever consumes. Because, until and unless the state decides to kill a prisoner, it still recognizes its basic obligation not to let that person starve, and while imprisoned they rather plainly have no other means of sustenance. The percent share of convict-food that's taxpayer funded is way, way lower for the set of released-from-prison convicts than for the set of still-imprisoned convicts. So, given that, as Kevin Drum notes, this has zero impact on either the fiscal picture or the future violent-crimes rate, the actual philosophical message being sent is entirely incoherent: while the state is in the act of punishing these people it will respect their right to sustenance by providing their entire diet, but once it formally releases them back into society it will insist that they be allowed to starve if they are unable to find food themselves. It's pointless cruelty for the sake of pointless cruelty. They're people just like everyone else, and until you decide to kill them you have the same responsibility for their non-starvation as you do everyone else's.

Fractal Dimension for Hits

Not all hits are created equal. This is, of course, obvious: a single and a home run aren't even approximately equal in any relevant regard except constituting a base hit. But I mean more than that: not all singles are created equal, not all doubles are created equal. (Actually, all triples and all home runs are kind of equivalent to each other, so let's focus on the less-flashy kinds of hit for now.) For instance, often when a runner is on first and a double is hit, the runner will manage to score, especially if there were two outs or it's a fast runner. However, I recently saw someone fail to score from second base on a double. The hit was a high fly ball to the shallow outfield, so the runner on second had to stay near the base in case it was caught, but the batter could just keep running during all that hang-time. So, when the ball dropped in, the batter made it to second, but the runner from second could only get as far as third. (With two outs that couldn't have happened, you'd just run on contact.) Similarly, one will occasionally see a runner from second advance zero bases on a single, if it's an infield single to the shortstop hit in just the right spot. Ordinarily, though, runners from second often have a good chance of scoring on a single.

To describe these differences in the impact of a base hit on the existing runners on base, I hereby invent the concept of fractal dimensions for base hits. This is defined as the average number of bases advanced on the hit (excluding any bases taken on throws or due to errors), with the modification that any runner who scores while advancing fewer bases on the play than any runner behind him is given credit for the same number of bases as that following runner. Any hit with the bases empty has fractal dimension equal to its number of total bases, i.e. 1 for a single, 2 for a double, etc. All home runs are of dimension 4, as every runner on base scores on the play and had a runner behind them advancing 4 bases. (This is why it is necessary to give lead runners who score credit for the advances of trailing runners; otherwise a grand slam would have dimension 2.5, less than a bases-empty triple let alone a solo home run, which is obviously unsatisfying.) All triples are also, I believe, of dimension 3; while the batter does not score, every baserunner will score, and will be able to take credit for the three bases taken by the batter. This is a slightly undesirable property of this metric, as ideally I'd like to be able to distinguish different triples, but as I mentioned above, I guess there just aren't different kinds of triples: they are all bases-clearing, every single time.

A bases-clearing double, however, has dimension 2.75, because the runner from first advanced three bases, giving the runners from second and third credit for three bases as well, but the batter only made it to second. The play I described earlier, where a runner from second failed to score on a double, would have dimension 1.5: two for the batter and one for the runner, averaged together. (Note that in this case the lead runner does not get credit for the advances of the trailing runner, since he did not score.) An infield single that fails to advance a runner from second has dimension 0.5. A single that scores a runner from second, on the other hand, is dimension 1.5, the same as the double that doesn't score that runner. Note that this is all very context-dependent, of course, and also not remotely related to any sort of statistical estimate of the run-value of different hits. The double that turns -2- into -23 without a run scoring and the single that turns -2- into 1-- with a run scoring are not in any obvious sense equivalent, as the bases they create are in different configurations and in one case but not the other you bank a run. Still, I think this is an interesting way to describe a hit, and to note when a single or double was leveraged well or poorly by the existing baserunners.

One can also extend the concept to something other than a hit. A walk, for instance, or a hit-by-pitch, always gives one base to the batter, and may or may not advance the existing baserunners at all. So a bases-loaded walk has dimension 1, as everyone moves up 90 feet, but a walk with runners on second and third has dimension 1/3, since two of the three baserunners involved in the play (counting the batter) stay put.  Sacrifice bunts, sacrifice flies, and productive outs of all kind are the reverse: the batter does not get a base, not even one, but other runners might. A sacrifice fly that drives in the sole baserunner from third has dimension 0.5. This also lets us distinguish between a sac-fly with, say, runners on second and third that only scores the runner from third or one that scores that runner and also advances the runner from second to third base, a difference that can be crucially important if there were zero outs prior to the play. (The former has dimension one-third, the latter two-thirds.) Grounding into a fielder's choice at second base, say, gives one base to the batter while subtracting a base from the baserunner; if there were no other runners who advanced on the play, then, this results in a dimension of 0. Grounding into a double play has negative dimension, as it subtracts an existing base and doesn't add anything in return, unless, of course, there were other runners, say a runner from third with no outs who came around to score on the play.

Now, we do get a situation where the batter is penalized, in a sense, for having an extra runner on first or second who doesn't advance on his sacrifice fly. There are two possible ways to go about correcting for this. One would just be to look at the total base-advances generated on by a play. One could leave off, in this case, the thing about giving lead runners credit for the bases taken by their trailing runners if they score; then a grand slam would be worth 10 bases, the highest possible. Or one could keep that feature, which would give a slam dimension 16 and might leave some numbers between 0 and 16 as impossible dimensions. I'm not sure how you'd get 15, for instance; a bases-loaded triple would be 4*3, since each scoring runner would only get credit for 3 bases of advancement.

The other possibility would be to, in essence, pretend that the bases are always loaded, and subjectively estimate what would've happened to any of those runners who happen actually to be fictional. This can encounter difficulties, however, because with the bases loaded I think it's not possible to have a hit of lower dimension than its total-base number. For instance, take the double that didn't score the runner from second. What happened to our fictional runner from first on that play? He can't have would up at second, since the batter finishes there, but he also can't have wound up at third, since the runner from second finishes there.

So, I'm not sure there's a way to perfect this system, but I still think it's useful. We do subjectively feel, I think, that a ripped line drive to right field that allows a runner to go first to third on a single is a stronger and better hit than an infield hit that only gets the runner to second. Fractal dimension is a nice conceptually-simple way to quantify that sense.

Miguel Cabrera is Good at Hitting

Last night, Miguel Cabrera of the Detroit Tigers hit three home runs. They were the three longest home runs of the night. After winning the Triple Crown last year, Cabrera leads the American League in runs batted in with 47 (after 42 games!) and in batting average at .387, and is only one behind the four-way tie for the league lead in home runs with 11. It is, at this point, tough to doubt that Miguel Cabrera is the best hitter in baseball. He turned it on in 2010. Well, okay, he's been pretty good for his entire career, and even better during his stay in Detroit, but since 2010, well...

Cabrera's batting average is .339, the best in baseball among those with at least 1000 at-bats. The next best is Joey Votto, at .324.

Cabrera's on-base percentage is .423, the second-best in baseball, behind only Votto's .438.

Cabrera's slugging percentage is .609, the best in baseball. Next best is Jose Bautista's .587.

That gives Cabrera an OPS of 1.033, noticeably ahead of Votto's .999 for the best in the game.

Cabrera has his 123 home runs over the past four seasons, trailing only Bautista's 133.

Cabrera has 145 doubles, just one behind Robinson Cano's 146 and second in baseball.

Cabrera has 649 hits, the best in baseball. Cano is second with 636.

Cabrera has driven in 417 runs, the best in baseball. Adrian Gonzalez is second at 355.

Cabrera has scored 365 runs, the most in the game, ahead of Ryan Braun's 341.

All this adds up to 195 Runs Above Average from Batting for Cabrera, according to Baseball-Reference. The next best over this period is Votto, with 165 RAAbat. I'm pretty sure that the categories I just listed are all the statistics that you want a great middle-of-the-order bat to excel at. For what it's worth, he has the sixth most walks in the game over these years with 284, behind Ben Zobrist (287), Carlos Pena (299), Jose Bautista (316), Joey Votto (332), and Prince Fielder (336). So, I suppose one could wish that he led the league in walks as well as hits. But it's awfully tough to complain when you're leading baseball in batting average by fifteen points. It's also probably not a coincidence that his walks dropped off from 108 in 2011 to just 66 last year, when he gained the threat of Prince Fielder behind him in the order; if Prince had signed elsewhere, he might've been closer to the lead there. But, seriously, first or second in average, on-base, slugging, home runs, doubles, hits, runs driven in, and runs scored. That's the best hitter in baseball. It's tough, at this point, to see Cabrera not making the Hall of Fame: this is only his age 30 season, it's only May, and he's got 332 career home runs, 1869 career hits (so he should hit 2000 later this year), 398 career doubles, 1170 career RBI, 995 career runs scored, and, oh yeah, 50 career Wins Above Replacement, despite being an absolutely incompetent defensive player. This guy is scary good. If anyone can do back-to-back Triple Crowns, it could well be Miggy.

Golf is a Zero-Sum Competition, Guys

Phil Mickelson just (i.e. several hours ago, but they just showed it on a tape delay) missed a par putt at the Wells Fargo Championship at the Quail Hollow Club. One of the announcers commented that that was not the visual that Nick Watney, Phil's playing partner and up-until-then co-leader, wanted to see before stroking his own par putt. Watney, of course, sank his putt, and is now ahead of Phil and, in fact, the outright leader. The announcer's comment is a common genre, most frequently heard on the intensely watery par-3 holes like the 12th at Augusta or the 17th at TPC Sawgrass. If the first two players in a group, say, have hit the green, or have gone in the water, the announcers will say something about how that gives the third player a good/bad visual. Now, on a Thursday or a Friday or something, where the pairings are pretty much random and the odds that two players in the same group will be in direct competition come Sunday are pretty small, I can sort of see that. But on Sunday? In one of the late groups, among people vying for the tournament? They're in a cut-throat, zero-sum competition for millions of dollars. Every stroke your competitor throws away is money in your pocket. If I were in contention at the Masters on Sunday, say in the final group or something, and my playing partner hit in the water ahead of me, I'd be ecstatic. I wouldn't feel like that meant I was going to do the same thing, or something: I'd feel like it meant I had an opening to make up some serious ground on one of my chief rivals just by hitting a non-disastrous shot. Now, at the same time, I never have been in that situation, so I could be wrong. Maybe the PGA Tour professionals, the guys who, after all, are playing the game for a living and are supposed to have good competitive mindsets, really do get rattled when things happen that, on paper, ought to be pretty directly beneficial to them. But it would kind of surprise me.