Was Ray Allen's performance in the first half of Game 2 evidence that a player can get hot?

Even though it's entirely celebrated as a reality of hoops at all levels, serious research has cast doubt on the very existence of "the hot hand."

Does Ray Allen's hitting seven straight 3-pointers blow all that research to smithereens?

Allen has shot close to 7,000 3s in his career, and has made about 40% of them. (Going into the game, he was 2,685 of 6,768, regular season and playoffs combined.)

Given that -- how lucky is seven in a row? Is this a case of a guy who has something special and strange and almost religious going on? Is the zone holy ground?

Or if you have picture perfect shooting form that you practice incessantly like he does, will makes show up in a seven-strong posse once in a while, because that's just how life is?

If you flip a coin enough times, it'll come up heads seven times in a row, without ever being anything other than random, right?

All kind of research has shown that people tend to see trends where in fact things are random. It's just how our brains work. People will watch a coin land on heads again and again and assume that's a fishy coin. We think random things should look random, as in all mixed up. But in fact, truly random things sometimes look organized.

I invite those of you with better math heads than me to tell he how you'd assess Allen's performance. If you hit 40% of the time, and take 6,678 shots, how often would you end up with seven or more makes in a row?

Does Allen do that more often than you'd expect? (Bring on your probabilities!) If the answer is yes, then let's talk about the hot hand. But if the answer is no, well then let's appreciate this is the kind of night good shooters have sometimes, even without the supernatural.

And either way, there are a couple of lessons. One of them is that the most authoritative study to date found that if the hot hand exists, it's rare. And its effect is far smaller than an opposite "hunting shots" or "heat check" effect -- players hit a shot or two and then tend to take a really tough one. They apparently believe so firmly in the idea of the hot hand that after a few shots go in, they'll suspend their normal shot selection. And then they almost always miss.

(Allen may have done a little of that in the second half.)

Since digging into that research a year and a few months ago, I can assure you that if you want to see poor shot selection, make yourself a highlight reel of NBA players who have just hit two shots in a row. That third time down the court, the defense is ready for them, but they're almost always shooting anyway, no matter how horrible the look.

In the study, a player who had just hit a shot was less likely to hit his next one than a player who had just missed. The opposite of the hot hand is alive and well. That is why, as a coach, you don't just "feed the hot hand." It's an invitation for your players to suspend their best judgment, and that's no way to win.

Except for every now and again, like the first half of Game 2, when riding the hot hand -- or whatever Allen had going on -- won the Celtics a game and changed the tenor of these NBA Finals. On nights like that, it's worth remembering that even the authors of that big study say some players may get hot sometimes. And consider a newer, different study, that has found some new suggestions of the hot hand.

UPDATE: Some stats experts weigh in.