Volatility & Two-Point Shots

[mavsluvr]

Thanks, balls, for replying to my lonely, neglected thread. Maybe I didn’t explain the idea very well. I’m flattered that you read it several times.

And thanks to Luka and Scott41 for liking so I didn’t feel like a complete idiot.

It just seems obvious to me, when you have a 2 point lead and the ball near the very end of a game, a 40-50% chance of adding 2 points is better than a 30-40% chance of adding 3. Why? Because either score increases the difficulty of catching up by a lot. And the most important thing is to avoid giving the opposition the chance to catch up or take the lead.

Now, that example is extremely narrow. And it is somewhat unique in that either score (a 2 or a 3) changes a one-possession game into a two-possession game. But the principles involved should apply more broadly. As you approach the end of a game with a lead, scoring some points (for instance, 2) rather than none becomes increasingly valuable. In the same way, scoring more points (for instance, 3) rather than just some points becomes less important. 

The opposite is true early on. Whatever is most likely to increase your point total most efficiently is definitely best in the first half. And probably for awhile thereafter. But nearing the end, the point margin matters less and less. And maintaining the lead matters more and more.

Because 3-point shots are a lower-percentage shot than 2s generally speaking, the likelihood of a miss (and therefore, the likelihood of a scoreless possession) is necessarily higher when you shoot them. I believe the correct statistical term for this is concept is “volatility,” although I found a reddit thread and an article that seemed to be calling a related notion “variability.”

Volatility makes me think of the stock market and the typical advice from investment advisors that you want to decrease your exposure to volatility as you near retirement. Why is that? Because the risk of a big loss is significantly more consequential late in life, and preserving your assets, rather than necessarily growing them, becomes a more and more important goal. 

This seems right on point within a basketball game. Score as much as you can early. But late, as the end approaches, preserving your lead (if you have one) becomes the more important goal. 

Of course, this isn’t true in basketball or investing when you’re behind. If you don’t have enough money to retire or enough points to win, the roulette wheel becomes more and more appealing. But this is because you have less to lose when you’re already facing a likely loss. The more desperate the circumstances, the more that desperate measures are called for, right?

I also get that not all 3s and 2s are created equal. I’m not arguing that JJ Reddick should pass up open shots. What I am saying is that the calculus changes when you are protecting a lead. And I think that change (a) is due to volatility and (b) means 2-point attempts become more valuable and 3-point attempts less so.

And most importantly, I’m asking if anyone knows of any literature on this concept or has any insight. All that I can find deals with whole game/whole season analytics. None of it seems to address this idea that what is more valuable changes the closer you get to the finish.

Sorry about your thread being neglected, jommy. Sounded like you wanted a reference to an article, and I'm guessing no one knew of one. 

Sounds like your issue is shot selection in the clutch. Might be a good subject for a Sloane Conference presentation, but I haven't seen anything specifically on that to date. 

Might be because the answer is so situation-dependent. 

When your team has a lead, agree that it can be more important to score than to specifically hit threes. However, in the last minutes of a close game, the defenses have usually clamped down, and the offenses often have to take whatever shot the defense allows, be it a two or a three. 

I should say that my view on this was somewhat influenced by the Monta Ellis days, when the team blew a bunch of leads in the last few minutes even though they were so far ahead that if they had just run out the shot clock on each possession, they were far enough ahead to have won. He played the same fast pace no matter what. This resulted in more turnovers, giving up offensive rebounds, and more long shots with long rebounds enabling the other team to run on them. Just gifted the opponent the opportunity to win. Sometimes, discretion is the better part of valor. 

Of course, when your team is behind, they have to take more risks, and threes might be the only way they can catch up, especially if the leading team is still scoring. 

I can't claim any particular insight on the issue, but the question is interesting.