For you basketball lovers...

Here is Bill Jame's method for calculating whether a lead is safe at a basketball game:

[www.slate.com]

ps: I always wondered if the hockey version heuristically practiced at Lynah --the lead is safe when number of goals ahead is greater than the number of minutes remaining-- is rigorous enough, historically or statistically.

Huh. I don't think I've ever seen Bill James write about a sport other than baseball. If he's willing to publish this, I'm willing to believe it. Guy knows his stuff.

The only thing he's a little messed up on is his 'once a lead is safe, its always safe' thing, even if the game tightens up, because the whole series of events is unlikely to occur together. While true, its assuming that past events effect future ones.

That's like saying, the odds of 100 coin flips coming up heads in a row is incredibly unlikely, so if you've thrown 99 in a row, there's no way you're gonna get the 100th. Sorry, once the game tightens up, you have to reevalute. It doesn't matter if you had a 30 point lead with 2 minutes left, if its now 10 seconds left and you have a 1 point lead, the game is not safe.

I'd respond to the article, but I don't feel like registering with Slate to do so


Back to hockey, I think the Lynah heuristic is pretty accurate - if somewhat conservative - at least for the last 3 or 4 minutes. It may get a bit silly earlier than that (i.e. 10 goal lead is pretty darn safe with 15 minutes left), but at that point you're probably not thinking about jingling keys yet .

DeltaOne81
The only thing he's a little messed up on is his 'once a lead is safe, its always safe' thing, even if the game tightens up, because the whole series of events is unlikely to occur together. While true, its assuming that past events effect future ones.

That's like saying, the odds of 100 coin flips coming up heads in a row is incredibly unlikely, so if you've thrown 99 in a row, there's no way you're gonna get the 100th. Sorry, once the game tightens up, you have to reevalute. It doesn't matter if you had a 30 point lead with 2 minutes left, if its now 10 seconds left and you have a 1 point lead, the game is not safe.

You're not doing your logic any favors by picking those two ridiculous examples. Nobody with even the slighest basic knowledge of probability will tell you that the odds of the 100th flip coming up heads is anything other than 50% - and I dare you to find a basketball game where a team was up by 30 with two minutes left and allowed the other team to go on a (X+29)-X run in the ensuing 110 seconds.

Beeeej

You're not doing your logic any favors by picking those two ridiculous examples. Nobody with even the slighest basic knowledge of probability will tell you that the odds of the 100th flip coming up heads is anything other than 50%.

Actually, I disagree. Anbody with even the slightest basic knowledge of probability will tell you that the odds of the coin having two heads is approaching 100%. He never specified a fair coin.

schoaff

Beeeej

You're not doing your logic any favors by picking those two ridiculous examples. Nobody with even the slighest basic knowledge of probability will tell you that the odds of the 100th flip coming up heads is anything other than 50%.

Actually, I disagree. Anbody with even the slightest basic knowledge of probability will tell you that the odds of the coin having two heads is approaching 100%. He never specified a fair coin.

Heh... nicely played.

I mean, no, you need to lighten up!!

DeltaOne81
The only thing he's a little messed up on is his 'once a lead is safe, its always safe' thing, even if the game tightens up, because the whole series of events is unlikely to occur together. While true, its assuming that past events effect future ones.

James isn't making a probabilistic argument - he is making a historical one.

The only way this calculation will fail in the tournament is if UCLA is the trailing team; they haven't had a call go against them all year.

Beeeej
You're not doing your logic any favors by picking those two ridiculous examples. Nobody with even the slighest basic knowledge of probability will tell you that the odds of the 100th flip coming up heads is anything other than 50% - and I dare you to find a basketball game where a team was up by 30 with two minutes left and allowed the other team to go on a (X+29)-X run in the ensuing 110 seconds.

I don't disagree with what you said but that's not the point he's making (unless I'm misreading - weirder things have happened).

What he's saying is that *if* a team has a 30 point lead with 2 minutes left, and then *if* it becomes a 1 point lead with 10 seconds left (highly insanely unlikely I agree), that lead is still 'safe'. Whereas a 1 point lead with 10 seconds left under other conditions is not 'safe'.

Pick a less extreme example if you like. A 17 point lead with 3 minutes becomes a 1 point lead with 10 seconds, yet its still completely 'safe' by mere virtue of the fact that it *used* to be a 17 point lead?

Either way, he's implying that past events influence future ones. You could make a slight case for that in sports - more so than in coin flips - but as a fan of a team that just let the other team close 16 points in 2:50, I'm not taking much security in any correlation that may or may not there.

On further reflection, I think he is making a probabilistic assessment.

I think ugarte has it right, but Even though I think he is making a probabilistic assessment, James could still be more or less right about the safe lead staying safe bit. And you're right - he is essentially claiming that the events are not independent. That's the point.

Consider the team that goes on a 16-0 run to erase a formerly "safe" 17-0 deficit, cutting the lead to 1 point with 10 seconds remaining. The comeback team will not have the ball, will almost certainly have to foul, which will almost certainly result in 2 free throws (due to the many fouls given during the course of the comeback). The trailing team will then have to score in well under 10 seconds off a full-court play. Even if the shooter misses both free throws (unlikely, as the coach should have decent foul shooters in the game at this point), the odds are against the team down by 1 point.

Of course, before you even get there, the odds that the coach will not make any adjustments once the lead is no longer safe (i.e. 90 seconds earlier) are pretty much 0. Even if the coach doesn't make any adjustments, or those adjustments don't work, this kind of comeback would require an astonishing string of bad turnovers and missed free throws on the part of the leading team. It would be a meltdown of epic proportions, and it would have to continue for a full three minutes, during which the comeback team could not afford a single mistake.

He is overstating the claim - certainly for the marginal "safe" cases or the extreme limits of probability there is a point where a safe lead can become unsafe - but I think the basic idea is reasonable. The lead will remain "safe" because events aren't independent. The trailing team will put the leading team in the double bonus. They'll get tired, they'll get into foul trouble. The leading team will eventually put its starters back in the game, or load the line with good ball handlers who can shoot free throws, or make some adjustment on the inbounds play.

Tom! How dare you strikethrough the best part of your analysis?

The James Safe Lead Thesis is not being handed down a Holy Writ. He even includes an example of a Duke - UNC game where the formula didn't hold. His analysis of all prior games has led him to conclude that his formula works in 99.9999999999999999% of scenarios. He didn't state - and likely doesn't believe - that a Duke/UNC scenario will never happen again, but he does want those minutes of his life back that are spent watching desperation fouls in the closing minutes of games beyond reach.

ugarte
Tom! How dare you strikethrough the best part of your analysis?

The James Safe Lead Thesis is not being handed down a Holy Writ. He even includes an example of a Duke - UNC game where the formula didn't hold. His analysis of all prior games has led him to conclude that his formula works in 99.9999999999999999% of scenarios. He didn't state - and likely doesn't believe - that a Duke/UNC scenario will never happen again, but he does want those minutes of his life back that are spent watching desperation fouls in the closing minutes of games beyond reach.

Striekthrough? I thought that was the highlight button!

And I agree, but that isn't mutually exclusive with a probabilistic assessment. It's highly probable that the safe lead will hold, even if the other team closes the gap enough to make the eventual lead not-safe. It's not a certainty - it's been broken once and it'll be broken again - but it's so close to certain that he's willing to write a silly article on slate about it.

DeltaOne81

Beeeej
You're not doing your logic any favors by picking those two ridiculous examples. Nobody with even the slighest basic knowledge of probability will tell you that the odds of the 100th flip coming up heads is anything other than 50% - and I dare you to find a basketball game where a team was up by 30 with two minutes left and allowed the other team to go on a (X+29)-X run in the ensuing 110 seconds.

I don't disagree with what you said but that's not the point he's making (unless I'm misreading - weirder things have happened).

What he's saying is that *if* a team has a 30 point lead with 2 minutes left, and then *if* it becomes a 1 point lead with 10 seconds left (highly insanely unlikely I agree), that lead is still 'safe'. Whereas a 1 point lead with 10 seconds left under other conditions is not 'safe'.

Pick a less extreme example if you like. A 17 point lead with 3 minutes becomes a 1 point lead with 10 seconds, yet its still completely 'safe' by mere virtue of the fact that it *used* to be a 17 point lead?

Either way, he's implying that past events influence future ones. You could make a slight case for that in sports - more so than in coin flips - but as a fan of a team that just let the other team close 16 points in 2:50, I'm not taking much security in any correlation that may or may not there.

Hey, I've got two words for anyone who thinks a 1 point lead is safe: Randy Wilson.

Now keep your keys in your pocket, or purse if it applies.