Go for broke
Last night's NBA playoff action between the Miami Heat and the Detroit Pistons very nearly went to hell for the Pistons in the final two minutes. This may be in part due to (dare I say it?) officiating. Not only were some questionable fouls called after blocked shots by first Chauncey Billups (of Gary Payton) and then Rasheed Wallace (of Antoine Walker), but the refs also let Payton and James Posey ride Billups all over the court whenever Detroit wanted to in-bound the ball to him. Dick Bavetta even jumped out of the way as Posey sent Billups out of bounds on one such play, only to ignore Tayshaun Prince's plea for a time-out and call a five-second violation a moment later.
But that's not the point. The point is, the Heat almost did the right thing, and almost pulled off an improbable victory that almost gave them a commanding lead in the series, in which they're now headed home for two games. Almost, but not quite.
Remember many years ago when Reggie Miller single-handedly pulled out a last-second victory against the Knicks by pushing one of them (John Starks, maybe?) out of the way on an in-bound pass (after Miller had made one three) and then retreating beyond the line to make another three-pointer? It should have been called a foul, yes. But it wasn't.
Some time ago, in a source I doubt I could find, I read an opinion about football that, I realized yesterday, has managed to stick with me. Basically, it said that football coaches are too conservative. Big surprise there. More specifically, it said that when trailing late in the game, football coaches should pull out all the stops. Go for it on fourth down. Try for the big play. Run a flea-flicker (or a "gadget" play, if you're the Steelers).
Why? Because you're probably going to lose anyway. Sure, fourth down is a big gamble. But not getting it doesn't hurt you that much, because there's already not much time left, and you're already behind, so punting is probably going to lead to a loss as well. (You have a better chance of converting a fourth down than of recovering an onside kick, and the difference in yardage if you fail is about the same.) You're not going to win every game this way. There's nothing you can do about that. But you might win a few games that you would lose by playing it safe. And that could be the difference, for example, between making the playoffs and not.
Back to basketball: I think the same approach applies. Don't listen to the guys on the sidelines who keep telling you to go for the two and then foul. That's a low-variance solution that will almost always result in you scoring about the same number of points as the other guys, and thus you losing, because they already have more. The more free throws you let them shoot, the more likely it is they'll hit about 75% of them (unless it's Shaq or Ben Wallace you're fouling). And thus, the more likely that time will run out without you closing the gap.
Instead, take a tip from Reggie Miller. Take a tip from UCLA (vs. Gonzaga). (Hmmm, maybe there's a connection?) On offense, shoot the three-pointers! On defense, take the ball away! Three-point shots are lower percentage, yes, but they're higher variance. If you make them, you're golden. And experience tells me that if you just take the ball away and act like nothing is wrong, the officials might not know what to do. Sure, you're still going to lose most of the time. But in the playoffs, one game could make all the difference.

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