NBA Three Point Shooters - Who Gets Good? (261 views)

[eric]

The NBA introduced the three pointer before the 1980 season. Here is the rolling five year average of three point percentage since then.



The three red dots indicate the years where the NBA shortened the three point line. While the percentage of field goal attempts taken as three point attempts (three point ratio) has increased linearly since 1980, three point percentage itself has largely plateaued since the traditional three point line was restored: 33.1% in the five year period centered on 1998, 33.8% for 2014. As such, it is possible to define a good three point shooter over a wide era: did they make more than 33% from the three point line, yes or no? We will also add a three point ratio requirement of .15 to rule out people going 1 for 2 on the season and the like. While this rate is more forgiving of present day players, it was below average even in 1998 so we feel it is fair.

Let us take all the rookie seasons for careers including at least 4000 MP in the three point era - this is 1238 players.
Let us constrain ourselves to those whose careers began in 1998 or later - this is 562.
Because our regression can only take 248 entries, let us select the 248 entries with the highest MP in their rookie season.

Looking only at rookie season stats, can we produce a decent estimate of whether a player's career stats will exceed our criteria?

YES WE CAN



This is a graph of probability against a dummy variable (it's okay i'm a computer too i can say things like that) and the black dots are all the actual results. As you can see it's a pretty great regression, probably the best in the business. Top three. Alright, but how does it work?



That's it. That's all we need. Three point ratio, three point percentage, and free throw percentage. Using just those we get the right answer 83% of the time. Season, age, games, minutes played; field goals made and attempted, free throws made and attempted, assists, steals, turnovers, and points (per 36 minutes) are all completely irrelevant. If we add in the remaining stats (three pointers made and attempted, offensive, defensive, and total rebounds, blocks, and fouls) we get our accuracy all the way up to... 84%. Not worth it.

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So what does the equation mean? If our hypothetical player goes out and racks up billions their whole rookie season, their chance of being a good three point shooter for their career is 1/(1+exp(4.6)) = 1%. Everybody's got a shot!

If they never take a three but make 100% from the line, their chances are 1/(1+exp(4.6-3.8)) = 31%. Not great, but a lot better than if they were a free throw bricklayer.

What would they have to do to have a 100% chance of being a good three point shooter? What we have here is an asymptote so it's literally impossible. Even if they shot all threes and hit 100% of them and their free throws the formula only gives them a 99.96% chance. Way purer than Dove (TM) soap #notspon but there are no guarantees.

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Tomorrow I'm gonna go through specific examples because I think it'll be fun. If you have anyone in particular you wanna see and don't feel like doing the calcs yourself, leave their names below!

[Delap]

so are we asking for young players now or asking to see if current older players (or retired players) were predictably good or bad?

[eric]

May 25, 2017 17:12:50 GMT -6 Delap said:

so are we asking for young players now or asking to see if current older players (or retired players) were predictably good or bad?

either

[Delap]

Dirk, Kobe, Walt Williams, Malcolm Brogdon

[eric]

So as the formula indicates the best way to be a "good" three point shooter (33%+, .15 3PR+) is to come into the league that way: 147 of our 582 did, and 133 of those or 90% kept it up over their careers. The extreme reverse is also true: 211 players didn't make a single three their rookie seasons and only 19 or 9% went on to become good three point shooters. Can we find anything interesting in these extreme cases that might indicate a subtle correction to our formula?

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Let's start with the flashes in the pan.

First of all they were all given a better than 50% shot at making the grade, which is not surprising considering that someone who hit 33% and .15 exactly would need to hit only 73% from the line for the formula to generate a yes prediction.

The highest probabilities at 94% went to James Anderson and Amir Johnson, but they played 286 and 39 minutes respectively their rookie years so they're pretty clearly an issue of small sample size. (Also note that both are pretty close to making our marks: James shot 32% on .48 3PR and Amir shoots 34% on .06.) Let's go higher up the chain and find some people who had high probabilities and rookie minutes played.

Devin Harris had a 78% chance and is currently at 32.4% from three, so he didn't miss by much, not much to be learned there.

Marcus Smart (yes, Marcus Smart!) has an 89% chance and while he's currently way south of the mark he is only in year three. At the same time he could indicate an issue with the formula: certain teams have embraced the three to such an extent that everyone, even poor shooters, should take them. An infamous example of this is Corey Brewer of the Rockets, but Smart's chuckery fits as well. They have very high three point ratios due to their team styles, not their individual skillsets. Brewer is too old to be instructive, but it will be interesting to see how the Smarts of the world progress. It's plausible that practicing the three so much will lead to improvement. It's also plausible that practicing bad threes will only lead to more bad threes.

Finally we have Ray Felton, who the formula gave a 72% chance. Stay in school shape, kids. To be fair to Big Ol' Ray he's at 32.7% and a decent shooting season next year would slip him back in, too bad CBA stats don't count in this analysis ayyyyyyyyyyyyyy

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Okay, what about the guys who made zero threes but turned into three point shooters? Of the nineteen players to do so, fourteen played less than 162 minutes. Again, we should be wary of small samples, but what of the other five?

The equation gave them all less than a 20% of making it. We know the max for non three makers is about 30% so this isn't surprising. Is there any underlying similarity that would have hinted at their growth? Let's see.

The first intercontinental champion Pat Patterson dabbled with the three ball in his last year for the then-NBDL Kentucky Wildcats, but gave it up his first two years in the league, choosing instead to make it rain to the tune of 45% on long twos. A trade from Houston to noted analytics-oriented intellectual organization Sacramento set him off to the races, and he's been making 37% on threes with a .44 ratio ever since.

DeMarre Carroll was a bricklayer in college and kept it up his first three years in the league: 28% from three on .07 ratio, 37% on long twos on a hideous .42 ratio, 69% from the line. He learned to take free throws and long twos in year four, and extended that range to three once in Atlanta. Still, that was his fifth team in five years, sometimes a guy is just an outlier.

Lance Thomas is easily the best NBA player named Lance of all time, and remarkably made zero threes his first three years in the league and took none in four years of college on top of it. Over his first four pro years in total he was 7 of 23 from three, shot a brutal 34% on long twos, and abruptly shot 42% on almost 200 attempts the last two years. Sample size could still take him down to the mid 30s, but he's still well clear of our benchmark.

Brian Cook had a pretty decent career as a backup big with legit range, unfortunately he retired in 2012 and so nobody cared. He was a decent 34% three point shooter in four years of college that for whatever reason (triangle) eschewed them (Zen) his rookie year (how'd that goink). In 2005 he started jacking triples and never looked back, finishing his career with 38% on .33. Looking at his first season he was a fine spot-up guy from long two, making 47% on .45 of his total FGAs.

Wayne Gretzky Michael Scott is currently putting up 33.6% on .35. His rookie year he lived at the rim with 52% of his attempts and a robust .38 FTr. He flashed a mild long two game by making 43% but on only .19 of his attempts, following a college career where he only took 44 threes over five years. Pretty much as soon as his sophomore campaign started he out of nowhere was a fair to middling three point shooter.

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The only through line I see is large players who were good free throw shooters, and even that doesn't quite cover DeMarre. 6'9" 71%, 6'8" 62%, 6'8" 84%, 6'9" 75%, 6'8" 77%. This makes sense - large players even today tend to lag behind the little guys in embracing the three ball even when they can make 'em, and it's really hard to be a good three point shooter without being a good free throw shooter. This isn't a sufficient condition of course, there are plenty of bigs who shoot well from the line that never take a three, but it appears to be a (roughly) necessary one for players to buck the formula. Adding an explicit height variable would probably help the overall accuracy, but it's really difficult to scrape height from b-r, all NBA players lie about their height anyway, and I'm comfortable just keeping this conditional clause anyway.

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And now to requests, of whom only Kobe did not make it to "good" three point shooter territory:

Dirk 52%
Kobe 81%
Walt 62%
Brogdon 83%