First, let me thank the many readers who have commented these past few days. I did not know what to expect when I accepted Eugene’s invitation to blog about my article, and have been impressed by, and grateful for, the number and incisiveness of the comments. Unfortunately, there have been too many to permit me to respond in a systematic manner, let alone in a comprehensive one. So here are a mess of somewhat random reactions.
1. I’ve agreed with many of the posts, and have been gratified to see that many readers anticipated arguments to come.
For example, Assistant Village Idiot observed that my analysis “would suggest that a possible strategy would be to reduce the penalty late in the game but call it more closely. I don’t know if that would actually play out well, however.”
Agreed on both counts. See p.1349 n.73 of my article for some remarks on just this score.
Soronel Haetir remarked on Tuesday: “I can see some argument for allowing more contact later in a game (an argument I don’t particularly agree with), but I don’t see any reason whatsoever for relaxing the basic rules of ball possession.” I hope that this morning’s post revealed my full agreement that the argument I offered on Tuesday would not support relaxing “the basic rules of ball possession.” Those are constitutive rules.
Justin agreed with Tuesday’s analysis but added: “except for fouling out in basketball and red cards in soccer. Two fouls called on a key player in the first 5 minutes of a basketball game can change the entire contest. And a soccer team playing 80 minutes while a man down is almost certain to lose.”
So true. Wait for Friday. Incidentally, Friday’s post will simplify matters by ignoring Visitor Again’s observation that soccer refs might already respect temporal variance in the issuance of red cards. This is addressed in the article at p.1368 & n.116.
Guy and I seem to be on the same page. I agree with his observation on the regulative/constitutive distinction that “the distinction is less something that can be derived by objective observation of the law in operation, but more by how people understand the law and what its purposes are.” He then added: “the most obvious distinction between foot faults and zone faults is that most people think of the game as being a test of skill with respect to hitting the ball, not where you place your feet. Foot faults only exist because the game needs to prescribe a spot for you to serve from, but minor variations in the rule are unlikely to change the difficulty of performing a proper serve. Rigid adherence to the rule is probably thought of as more penal by the audience than rigid adherence to zone fault rules because the game is ‘testing’ your ability to hit the ball precisely to serve to a particular spot, but it isn’t ‘testing’ your skill at putting your foot close to a line without going over.”
Yep, that will a core piece of tomorrow’s argument. Incidentally, Justin agreed with Guy, but added: “Unfortunately, I think one of the problems with your analysis is that you are looking at it through a legal philosophy prism when the answer you are looking for is an anthropological one.” This puzzled me. Anthropology and philosophy needn’t be at odds. I understand my philosophical analysis to point out which anthropological facts are relevant, in what ways, and why. Perhaps Justin might further explain why he thought his observation showed a problem with my analysis (or with Guy’s?).
Lastly, I think Martinned is right, as against both Noah and Gentleman Farmer, that the relative distinction is not objective/subjective.
2. The problem of time-sensitive impact.
I received fewer challenges than I anticipated to my claim that outcome-affecting events have greater impact the later they occur in a close contest, holding closeness of contest contest. I believe only Bruce Boyden and Tom Swift objected.
Here are a few additional thoughts on the matter. I think almost all of us feel comfortable saying things like Team A has a .X probability of winning this game. We believe, for example, that the U.S. women’s soccer team had a pretty high probability of victory immediately after Abby Wambach’s goal. We believe that the team’s probability of victory was lower once Japan equalized. Almost all probability theorists believe that such statements are meaningful and that they must be some type of subjective probabilities. (The objective probability of a U.S. victory was, at all times, 0.)
If we then believe that events can affect outcome-probabilities, we must be comfortable assessing these things in terms of subjective probability. And once we’re in subjective probability land, my claim that late events change the probabilities more than early events do is quite sound as a generalization, though there can be exceptions. (See, e.g., p. 1350 n.74.) Given all this, I’d need to hear more from Bruce Boyden regarding why he believes that the perspective of an omniscient observer supplies the “more relevant comparison.”
Tom Swift is surely right in one sense that “points count the same at the beginning of a game as they do in the last 2 minutes.” They count the same in terms of nominal additions to the score. But they don’t count the same in terms of changes to probability of winning so long as the relevant probability is subjective — which, I’ve just said, it must be so long as we continue to make claims about probability less than 1 and greater than 0.
3. Miscellaneous thoughts.
Many of the remaining posts raised ideas that might not be strictly germane to my arguments thus far, but which I found interesting enough to merit some reaction.
I’ve never understood how an official not calling a violation late in the game is “letting the players and not the officials decide the game.” A non-call of a violation is an official influencing the game, perhaps decisively. I think the comment from James about uncertainly in the determination of an infraction is a good one, however, particularly in basketball. Perhaps some “temporal variance” is justifed in terms of the degree of certainty the official should have in making a late call (I’ve done a litte refereeing, and I’d say it’s kind of a “felt” thing rather than a conscious decision).
I wonder whether the ideas in this post are in tension. Temporal variance in degree of certainty (actually, the NBA has a rule about this!) would make sense if the costs of false positives and false negatives differ toward contest’s end. But tbaugh seems to deny that. I happen to agree that temporal variance in the standard of proof makes sense. But the judgment that a false positive is worse than a false negative is (and must be, I think) parasitic on the supposition that the sanction and the penalty are differently costly as measured against the competitive desideratum. (Incidentally, James’s different argument for why uncertainty might lead to temporal variance seems largely dependent upon omission bias.)
duffy pratt observed that “Baseball has a different time element than other games” and asked for examples “where this idea of “temporal variance” would apply in baseball?”
I’m disposed to think that baseball has few good examples not because it has a different time element (see 1336 n.32) but because it has few duty-imposing/regulative rules and many power-conferring/constitutive ones. I do think that balks provide a good potential example, though.
baseball announcers advocating a form of situational (if not strictly temporal) variance with balls and strikes. For example, on 0–2 counts when the batter takes a close pitch, I have heard announcers talk about how the umpire either should have (when they call a third strike) or did (when they call a ball) take the situation into account. The implication is obviously that the penalty for a called strike to the batter is much greater than the penalty of a called ball to the pitcher, so I think this can actually fit into your analysis whereas you claim that it does not.
The analysis in a book I mentioned earlier, Scorecasting, reveals that umpires do take the situation into account in must this way. I am disposed to believe that they ought not to. More interestingly, as some commentators observed previously, Steven Jay Gould thought that home plate umpire Babe Pinelli rightly gave Don Larsen a few extra inches on his last called strike to end his perfect game in the 1956 World Series. I differ with Gould here. (See pp. 1352-54)
Lastly, Byomtov opined that “calling a pitch a ball is a penalty, or at least can be seen as one. If we say the idea of the game is for the batter to try to hit the ball, etc., then there needs to be a rule requiring the pitcher to throw it where the batter actually can reach it. The penalty for violating the rule four times is a walk.” I think that’s an interesting analysis. Balls could have arisen as Byomtov conjectures and still count as constitutive rules today. I’ll think more about this.
Byomtov also remarked, presumably tongue-in-cheek, that he “wouldn’t be surprised if the rule was established — by Abner Doubleday no doubt — precisely for this purpose, though of course it turned out that it often makes sense to violate it and suffer the penalty.”
Interestingly, early baseball had no bases on balls. There were balls, but no number of balls resulted in a free pass to first. I believe that bases-on-balls were introduced in 1879. At that time, though, a pitcher had 9 balls for a walk. The current rule that awards a walk on 4 balls was introduced ten years later.
That’s it for now. See you tomorrow.