Hi guys, there's a thread in SE discussing foul trouble and whether coaches should be less afraid of it compared to their currrent behaviour. In it a side argument sprung up about the value of possessions as a game progresses.

One guy said that it's justified to bench your best players early because possessions later in the game are actually worth more. The argument being that the outcome of each possession can influence the win probability more the closer to the final buzzer it occurs. That is, possessions later in the game are "higher leverage possessions", so you want your best players playing at those times.

That seems wrong to me, I think every possession in a basketball game carries the same weight. But as the potential number of possessions left in a game decreases, the importance of any given possession in a game has the potential to influence the outcome more. I think it's faulty to believe that this effect applies to possessions in order of their occurrence. I made a post in the thread trying to articulate this but I'm not educated in this area so it's a rambling.

You can read the thread here: http://forumserver.twoplustwo.com/46...-much-1167852/

You guys probably have a better handle on this stuff that your average sports fan, so if you would explain which viewpoint is right regarding the value of posessions has time expires in a bball game that'd be great. If you could point me in the right direction as to why whatever view is correct that'd be good too.

I found this blog post on the issue: http://www.backpicks.com/2011/06/17/...ts-count-more/

I skimmed page 1 and it appears to just be one moron making no sense while almost everybody agrees that it's generally stupid to bench players like that. Early points don't matter quite as much (games tend to regress to the spread- if a game is even, and Team A wins the first half by 10, team B will normally be favored in the second half), but what's missing from the leverage argument is basically what you see- the last minute well might have been ~0 leverage if the guy had been in the game earlier and scored enough points to put it away. You're a lot closer to right than the other position.

I didn't read any of the links, but this statement is absolutely false.

The underlying assumption in saying that later possessions are worth more is that the game will be close late in the game. This is often blatantly wrong. If you have a chance to make the game a blowout early, then the 4th-quarter possessions will often have a negligible impact on win probability.

That does not mean that either side of the original debate is right or wrong, though; it just means that that argument is invalid.

the thread itsself is a bit all over the place cos there are lots of legit bball reasons for either side, i'm mostly interested in the "leverage" argument specifically because i assume there's a provable right and wrong answer there

It's provable but hard. As I said in the thread, I've looked at a related issue in hockey, and what I've found indicates that leverage is very dependent on the state of the game. This alone isn't surprising; what may be is that optimal play varies according to the state of the game, and that this can be quantified.

That may go into scores regressing toward the mean, if what TomCowley says is correct, though actually it should probably cause them to go the other way more often; for regression to the mean to result from optimal play you would have to model multiple games at once (e.g., teams resting their stars a bit when holding a comfortable lead). But at that point it seems more likely that you're actually just talking dumbass basketball players being lazy, not anything optimal in any sense, and you can't model that in isolation — you need (a hell of a lot of) data to analyze.

Given those data, we could work out average leverage; adding that to data on relative player values, the effect of playing while in foul trouble (particularly on defense), whether it's true that a player getting in foul trouble shows that he's not playing well in other ways (an assertion being made in that thread, which strikes me as stupid but I suppose might be right), the change in different players' relative values in different game situations (particularly three point and foul shot shooting percentages), and some other things I'm not thinking of, it could all be worked out.

In other words, it really can't, not exactly, but we can get a pretty good idea at least that all those in that thread who are going "duh, of course Lebron is more valuable late in the game, it's obvious" are ****ing idiots. Beyond that, we can tell that while it's possible those idiots are right in some cases, there are reasons to believe it actually may be backwards, and strong reasons to believe that saving players for the end of the game is at best not nearly as valuable as many non-math people believe.

By the way, if scores don't regress toward the mean and tactics remain unchanged throughout the game (which is certainly false, but a good place to start modeling), then it is pretty easy to prove that the average value of a basket does not vary as a function of the point in the game at which it occurs. Early in the game, every marginal basket is worth some percentage change in the chance of winning (maybe 5%? maybe 10%?); at in the last second of the game the marginal basket is usually worthless but occasionally causes a 50% or 100% swing — and it exactly balances out. If everything else stays the same (which, as I said, isn't true), then a basket is a basket.


btw, no, what I've posted here isn't proof, but if you think about it you can see the form the proof takes.

Following the "leverage" argument, I guess if I were coaching a swim team, I would let my grandmother swim the first 300 meters of the 400 meter freestyle, and leave Michael Phelps for the last 100 meters. That way Phelps is fresh for the last 100 meters which is the "high leverage" part. And, really, these races are never determined in the first couple of hundred meters, so we can just let anyone swim that part.

Incorrect. As long as dispersion of individual player time allotted maximizes her efficiency, it doesn't matter when the player is on the ice/court.

This includes knowing the player's stamina so for the last 2-3 minutes of a game (hockey indeed, double/triple-shifting, futsal, etc. sports with high-tempo, fast rotating shifts yield better data) so when it's a close game, you make sure your most efficient players are at or near their most efficient.

That's the game theoretical approach and more suited to video game AI modeling rather than human beings (absence of emotion, external factors which really can only be accounted for as vagueness within a probabilistic range, etc.)

For historical NBA data, I'd look at Phil Jackson's career. NHL, I'd probably go with Scotty Bowman. Football is an order of magnitude more difficult to model in this fashion but it can be done. Just time-consuming.

Why is the anchorman (last runner) in a relay race the fastest guy?

I think it's psychology, mostly.

If you're coming from behind, you can generally push yourself harder than if you're out in front (as long as you think you have a chance). So you want someone in that spot who has the capacity to put up a stronger performance for you, if necessary.

Entertainment value, maximal audience absorption in the event at hand.

So yeah, psychology basically. No point in blowing teams out before the half-hour and all that. Makes the other hour meaningless.

Fun once in awhile, sure, but so demoralizing to them.

It might have to do with handoffs in that case. The last guy doesn't have to handoff, and the first guy doesn't have to get handed off to. I'd think the first guy should be the guy with the best acceleration, the last guy should have the best kick, and the fastest guy should be whoever has to cover the most distance aside from transitions. Swimming wouldn't have these complications.

Bruce,

Consider that in a sport like swimming where placing is determined by hundredths of a second, in the longer races, possum strategies are very much at play.

IOW, I wouldn't be too fooled by the apparent decline in Phelps' public performances or even Bolt's times post-Beijing. We'll see in a few months though.

The last runner should be the smartest, not necessarily the fastest. Do you see why.

I knew I swam anchor for a reason as the second fastest guy. It definitely wasn't because my gun starts were the worst and my leaning starts were the best.

Depends on definition of smartest. It's not a fixed variable but once you're last, you're always last.

The rest is trickle-down.

I thought he was supposed to be the nicest.

Ultimately, yes. But to correct fundamentally incorrect behaviors, being nice just doesn't work. Takes too long.

Way to kill 3 birds with one stone. You made a point (debatable :-) to those that understand, a riddle to those that don't, and really boosted Tom Cowley's self-esteem.