A Stat to Capture Shooting Volatility

[PhoSita]

I have a challenge for any stat-heads out there -- we need a better way to quantify the relative badness of bad shooters.

By this I mean, we need a way beyond simply looking at overall shooting percentages to explain whether a guy is merely streaky and therefore unreliable but potentially dangerous as a shooter, versus somebody who is just a straight up bad shooter who should never take shots.

This is near and dear to my heart as a Celtics fan because one of the key young players on the team -- Marcus Smart -- is a guy who takes 4+ three pointers a game and hits less than a third of them.  For his career, he averages well below 33% on three pointers.

Despite this, I maintain my belief that it is a good thing that he is willing to take those shots.  Because sometimes he makes those shots, not just once in a while, but a lot.

Over the last 5 games as of posting, Smart is shooting 40% on 4 attempts per game.

Small sample size?  Of course.  But Smart has done this a lot over his career.  One month he'll be a Tony Allen type shooter.  The next month, he's Courtney Lee with better handling and passing.

Part of it is the type of shots Marcus takes.  He's shooting 50% on corner threes this year, which is great.  His rookie year, he shot just under 40%.  Last year, he couldn't hit corner threes, but overall, he's good at them.

Most of his threes aren't from the corner.

Marcus isn't alone in this category.  J.R. Smith comes to mind as another volatile shooter who is much more dangerous than his shooting percentages suggest.  Carmelo Anthony and Kobe were never very good three point shooters, but they were always dangerous. 

Some guys are just streaky.


So how do we quantify that?  Smart will probably never be a "good" scorer in the sense of being efficient, but I think if we could find a better way to explain what he can do offensively than basic field goal percentages, it would help illustrate his value as a player to people who look at those standard box scores numbers and assume he's got to be awful.

[kozlodoev]

https://en.wikipedia.org/wiki/Variance

[PhoSita]

https://en.wikipedia.org/wiki/Variance

Yes, but is this recorded anywhere with regard to NBA shooters?

[kozlodoev]

https://en.wikipedia.org/wiki/Variance

Yes, but is this recorded anywhere with regard to NBA shooters?

I don't think so, but it's fairly trivial to calculate for per-game stats such as ppg, rpg, etc. Perhaps a little harder for percentages.

[saltlover]

https://en.wikipedia.org/wiki/Variance

Yes, but is this recorded anywhere with regard to NBA shooters?

I don't think so, but it's fairly trivial to calculate for per-game stats such as ppg, rpg, etc. Perhaps a little harder for percentages.

I once calculated it (several years ago) for points because Jeff Green seemed maddeningly inconsistent.  I don't remember the results other than they weren't interesting enough after a first pass to continue to look into.

[Denis998]

If making a stat from scratch to quantify something like this I'd probably do a linear regression plotting FG range vs. individual game FG℅ from various FG range. From there you would get a r² (correlation coefficient) which ranges from -1 to 1. Where the value of +/-1 signifies perfect predictive correlation, and where 0 indicates no correlation at all.

For a consistent shooter (consistently bad or good) you would get a value closer towards the direction of +/- 1, while for an inconsistent "streaky" shooter you would get a value closer to the direction of 0.

[Fan from VT]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

[positivitize]

If you do go all Beautiful Minds on us, it would be cool for THE STAT to incorporate FT% and Clutch shots (shots with the game +-5 with under 2 min to go)

I understand why you need this stat though... When Smart takes his 3s within the flow of the offense they hardly ever feel like poor shots to me. He seems to make them more than he misses them in that context.

[positivitize]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

if the .750 % comes at a more opportune time (eg. the end of a tight game), I'd say that that variance is more valuable.

Think about Evan Turn(ov)er's quote "I may be a 25% 3 point shooter, but its a BIG 25%"

[Cman]

I tried to do this once long ago.
I computed (by hand) the variance of Paul Pierce's shooting when he was in games with a player, versus games when he was not with that player (bc that player was injured). I can't remember the other player. Walker, maybe? Anyway, I was convinced that Pierce was a less streaky shooter when he wasn't with the other player. But the stats analysis didn't bear it out (it was just super noisy).

[PhoSita]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

It seems to me that variance in shot-making means a higher ceiling in terms of points contribution.  That being the case, a guy who shoots 30% overall but occasionally nails 6 threes in a row has a greater chance of being the deciding factor in whether his team wins or loses.  Of course, depending on how much his team needs him, he might also contribute to losses.


Allow me to make an analogy to something non-basketball related ....

In a role playing game where the damage of an attack swing for a given weapon is calculated on a random dice roll, one weapon might have a damage range of 4-7, and another might have a range of 1-9.

The average damage of the first weapon is 5.5 per swing.  The damage of the second weapon is 5.

However, if the player character is attacking an enemy that negates all incoming damage below 7, the second weapon is going to be superior even if its average damage is worse, because occasionally it will get high enough on the damage roll to go beyond the damage reduction threshold.

My apologies for the geeky digression.


In basketball, the final score of the basketball game is like that damage threshold.  Sometimes, your team might get put over the top by the guy who nails 4/5 on threes, even if his average is pretty bad.

[hwangjini_1]

I have a challenge for any stat-heads out there -- we need a better way to quantify the relative badness of bad shooters.

By this I mean, we need a way beyond simply looking at overall shooting percentages to explain whether a guy is merely streaky and therefore unreliable but potentially dangerous as a shooter, versus somebody who is just a straight up bad shooter who should never take shots.

This is near and dear to my heart as a Celtics fan because one of the key young players on the team -- Marcus Smart -- is a guy who takes 4+ three pointers a game and hits less than a third of them.  For his career, he averages well below 33% on three pointers.

Despite this, I maintain my belief that it is a good thing that he is willing to take those shots.  Because sometimes he makes those shots, not just once in a while, but a lot.

Over the last 5 games as of posting, Smart is shooting 40% on 4 attempts per game.

Small sample size?  Of course.  But Smart has done this a lot over his career.  One month he'll be a Tony Allen type shooter.  The next month, he's Courtney Lee with better handling and passing.

Part of it is the type of shots Marcus takes.  He's shooting 50% on corner threes this year, which is great.  His rookie year, he shot just under 40%.  Last year, he couldn't hit corner threes, but overall, he's good at them.

Most of his threes aren't from the corner.

Marcus isn't alone in this category.  J.R. Smith comes to mind as another volatile shooter who is much more dangerous than his shooting percentages suggest.  Carmelo Anthony and Kobe were never very good three point shooters, but they were always dangerous. 

Some guys are just streaky.


So how do we quantify that?  Smart will probably never be a "good" scorer in the sense of being efficient, but I think if we could find a better way to explain what he can do offensively than basic field goal percentages, it would help illustrate his value as a player to people who look at those standard box scores numbers and assume he's got to be awful.

and, since december 23rd (22 games) smart is shooting three pointers at a very respectable rate. he is 30 for 79, or 38%.

is this a blip or a trend? we wont know for a while, but, as a sample size it is over a quarter of a full season.

[hwangjini_1]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

they actually did a similar analysis on this over on SoSH a bit ago, though it was for baseball hitters.

the general take away was that it did not make a big difference in terms of wins and loses. but everyone pretty much also said it is almost impossible to quantify with any dependability.

[Fan from VT]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

It seems to me that variance in shot-making means a higher ceiling in terms of points contribution.  That being the case, a guy who shoots 30% overall but occasionally nails 6 threes in a row has a greater chance of being the deciding factor in whether his team wins or loses.  Of course, depending on how much his team needs him, he might also contribute to losses.


Allow me to make an analogy to something non-basketball related ....

In a role playing game where the damage of an attack swing for a given weapon is calculated on a random dice roll, one weapon might have a damage range of 4-7, and another might have a range of 1-9.

The average damage of the first weapon is 5.5 per swing.  The damage of the second weapon is 5.

However, if the player character is attacking an enemy that negates all incoming damage below 7, the second weapon is going to be superior even if its average damage is worse, because occasionally it will get high enough on the damage roll to go beyond the damage reduction threshold.

My apologies for the geeky digression.


In basketball, the final score of the basketball game is like that damage threshold.  Sometimes, your team might get put over the top by the guy who nails 4/5 on threes, even if his average is pretty bad.

I think a lot of it might be a trick of memory too. If someone is the deciding factor in a good way by going 4/5 down the stretch in one game, but ends up at 30% shooting, it probably means he was the negative deciding factor in a few other games.

A lot like Kobe; people remember the successes, and there were a lot, but they forget the failures, of which there were ~ 3 times as many. So he buried the Lakers 3 times as much as he lifted them; they would have won many more close games over his career if he played differently.

[PhoSita]

Is there any data to suggest that a high variance shooter (ie shoots .750 in one game on 8 shots, then .250 per game on 8 shots over the next 4 games for a total of 35%) is any more or less valuable to winning than a player who just shoots 8 shots per game and makes 3 out of 8 for 4 games then 2 out of 8 in the 5th game for a total of 35%?

It seems to me that variance in shot-making means a higher ceiling in terms of points contribution.  That being the case, a guy who shoots 30% overall but occasionally nails 6 threes in a row has a greater chance of being the deciding factor in whether his team wins or loses.  Of course, depending on how much his team needs him, he might also contribute to losses.


Allow me to make an analogy to something non-basketball related ....

In a role playing game where the damage of an attack swing for a given weapon is calculated on a random dice roll, one weapon might have a damage range of 4-7, and another might have a range of 1-9.

The average damage of the first weapon is 5.5 per swing.  The damage of the second weapon is 5.

However, if the player character is attacking an enemy that negates all incoming damage below 7, the second weapon is going to be superior even if its average damage is worse, because occasionally it will get high enough on the damage roll to go beyond the damage reduction threshold.

My apologies for the geeky digression.


In basketball, the final score of the basketball game is like that damage threshold.  Sometimes, your team might get put over the top by the guy who nails 4/5 on threes, even if his average is pretty bad.

I think a lot of it might be a trick of memory too. If someone is the deciding factor in a good way by going 4/5 down the stretch in one game, but ends up at 30% shooting, it probably means he was the negative deciding factor in a few other games.

A lot like Kobe; people remember the successes, and there were a lot, but they forget the failures, of which there were ~ 3 times as many. So he buried the Lakers 3 times as much as he lifted them; they would have won many more close games over his career if he played differently.

It depends on how close the game is.

If you lose a game where you were down by 5 in the last minute, it would make a huge difference if a guy went 2-5 instead of 0-5.

If you lose a game where you were down by 10 in the last couple minutes, a guy hitting 2/5 instead of 0/5 wouldn't matter.

But that guy going 4/5 or 5/5 could have made the difference.


I think what you're saying matters a lot if the guy is a main part of the offense.  If you take a lot of shots, you can shoot your team out of the game.  But a role player who typically takes 5-10 shots a game at most probably won't shoot you out of it.  If he goes on a hot streak he might win you the game, though.

I guess my point is it matters whether you "expect" to get points from that guy or not.  Is your team built to win even if that guy is cold that night, or are you relying on that guy to hit his shots in order to keep up with the opponent?