Wednesday, February 18, 2009

Hockey fights and the Bruins: a case study

Those of you who know me may be aware of the fact that I am a fan of hockey. Just a bit.

But one aspect of hockey that's never really captivated me is the fighting. I know, I know — fighting's one of the great parts of hockey, it shows how raw the emotions are, blah blah.

Yes, hockey's a very fast-paced, emotional sport. And if you get pissed off at a guy enough to throw the gloves down, I'm fine with that. What I don't like is the staged crap that starts with circling and has as much hugging as punching. If you have enough patience with the guy to "size him up" for 15 seconds before you try to land your first blow, my philosophy is to just forget the fight and give him an extra hard hit next time around.

The pro-fighting crowd always points to how it energizes the players and can give your team the one-up. To test that theory, I looked up all of the Bruins' fights for the season and looked at each one game by game. For each fight, I looked at what the score was before the fight, who scored the next goal and who won the game.

The tabulated results show that fights don't help the Bruins. My guess is that fights don't have much effect either way, but if you want to really nitpick the stats, they seem to show the Bruins at a slight disadvantage when fighting.

The Bruins are 15-10-4 for scoring after a fight. That is: 15 times they scored next after a fight, 10 times the other team did, and 4 times nobody did. The Bruins' overall goals for/against is 197-131, which is almost the exact same ratio as 15-10 (1.500 compared to to 1.504). So, no advantage there.

But it's actually worse than that for the B's. Most fights didn't have an effect on the game's outcome, in that the team that was winning before the fight ended up winning the game. Of the Bruins' 29 fights, only seven could be argued to have ended up changing (or setting) the game's momentum. In all of those games, the score was tied before the fight; four of them ended up as losses for the Bruins. Even if you account for OTLs, a record of 3-1-3 isn't too great when your overall record is 40-10-8.

The lesson: if a guy's getting chippy at you and you feel the urge to throw the gloves down, fine. But don't pretend it's going to help your team, and don't do it just for the sake of doing it.

Wednesday, February 11, 2009

Multiverse theory and the two die allegory

In my last post, I described an allegory I'd created that illustrates why life on Earth, even if it is extremely unlikely, does not serve as evidence that God exists. (I emphasize "if" because there is actually no empirical data I know of that has established this probability.)

The same allegory can be used to understand a thought experiment which is one of my favorites. I forget where I read it and who it's by, but it serves as a proof of multiverse theory. That's the theory that says that there are infinite parallel universes. At each moment, every decision or random act that's possible happens in one of those multiple universes.

So, here's the thought experiment: Find a reliable pistol, load it, put it to your head, and pull the trigger. There is a high probability that you'll have just killed yourself, but a small probability that the gun will fail. Repeat this several times. For good measure, after you've pulled the trigger a few times, fire it at the wall to make sure that the gun really works; then put it to your head and pull the trigger a few more times.

If the multiverse theory is wrong, you're almost definitely going to die. In fact, you probably died at the first pull of the trigger.

But if multiverse theory is right, then at every pull of the trigger, you die in the vast majority of universes — but live in the very few in which the gun failed. "Very few" of infinity is infinity, so you're still alive in infinite universes. Moreover, you only go on testing out the experiment and analyzing its results in those [rare] universes in which you're alive. (That's where the evolution allegory comes in.)

The result is that, if you're still alive after having tried to kill yourself a couple hundred times, you can be relatively sure that multiverse theory is correct. You'd have a very, very small chance of being alive if it's not correct, but a 100% chance of being alive if it is.

The kicker, of course, is that you can't communicate with any of the other parallel universes. So while you can be fairly sure that multiverse theory is right, that information doesn't help the versions of you that are dead. Also, since outside observers haven't eliminated all versions of themselves in which you're dead, they won't be able to share your knowledge: even if multiverse theory is right, the chance that an outside observer is in the right universe to see you alive is the same as the chance that the gun has failed. So even if they do see you live, there's no way for them to know if that's because multiverse theory is right or if you're just very, very lucky.

Needless to say, for both your sake if multiverse theory is wrong and for your loved ones' sakes even if it's right, I highly recommend not trying this out.

Monday, February 9, 2009

Evolution and chance: to live, perchance two die

I recently came up with an allegory in a discussion over at on evolution that I'm a bit proud of. The question it seeks to address is: If God didn't create life on Earth, then how did it come about, given the minuscule chance of life evolving on its own?

For life as we know it to exist, you have to have the right mix of situations — a suitable solar system, a planet with liquid water, atoms that can form amino acids, amino acids that can self-replicate, etc. The chance of any one of these things happening is very small, and the chance of all of them happening in the same place is virtually nil. Only God, the argument goes, could have tipped the balance to create life here on Earth.

I should preface the allegory by stating that although I do believe in evolution (though I also believe it'll have to be amended, and possibly significantly, as any theory is), the following isn't a proof that God doesn't exist. As an agnostic, I don't believe such a proof exists. But I do treat this allegory as an illustration of the fallacy that God must exist for humans to have formed.

So, now: An allegory two die for

Imagine a simple game involving two players and a 100-sided die (hence the pun in the title, for which I apologize... kinda). The players each roll the die, and if one rolls higher than the other, the player with the higher number wins. Otherwise, they both lose.

Now consider a single-elimination tournament with a million players. At each round, you kill the losers and put the winners in the pool for the next round, randomly seeded. For simplicity, let's say that anyone who isn't matched in a given round (ie, the "odd man out") dies before the round starts. There's a minuscule chance that any one person will win the tournament, but a very high (99%) chance that somebody will win.

At the end of the tournament, you interview the remaining player, if there is one (if the last round was a draw, there's nobody left). Sure enough, that player says he's extremely lucky to be alive. There was less than a million-to-one chance he'd live, and it wasn't even guaranteed that there would be anyone alive at all. He's so lucky, in fact, that only the existence of God explains it.

In fact, God doesn't explain it. It's just that by the very nature of the game, you only get to interview the fortunate winner. God may exist and he may not, but the existence of a survivor isn't evidence one way or the other.

It's the same with us coming from evolution, except that the losers (those without suitable solar systems, or who didn't have water, or who didn't create amino acids, etc) didn't die — they never existed in the first place. We're left with us, the fortunate few survivors in a game of chance, who look at our situation and are fooled into thinking that the question was "will humans evolve on Earth" and not "will something evolve somewhere."

When people look out to the universe and ask, "if it's all just luck, how come we don't see any other life forms?" they're missing the point. The winner in our allegory could ask the same question, especially if he didn't understand the rules of the game he just played.