Why don’t we measure TS% more precisely for the play-by-play era?

[lessthanjake]

The formula for True Shooting % multiplies the number of free throws taken by 0.44. This is because, on average, there are actually 0.44 possessions taken up per FT attempt. The reason that this is not 0.50 is because there are scenarios where FTs are taken where it’s not two FTs for a possession. These include and-one’s, fouls on three-pointers, and technical foul shots.

The thing is, though, that that 0.44 average is not necessarily descriptive for all players. Some players get more and-one’s than other players. Some players get fouled on three-pointers more than other players. TS% will actually underestimate the scoring efficiency of those players, and it’ll overestimate the scoring efficiency of players who very rarely have that happen. It seems to me that it’d be superior to actually measure the real TS% for each individual player, rather than just applying that 0.44 multiplier to everyone, when that 0.44 multiplier will often be meaningfully wrong.

Prior to the play-by-play era, I don’t think we can do that, because we don’t know how many and-one’s players got, or how many foul shots came off three-pointers, or how many technical foul shots they shot. But in the play-by-play era we do have this information. It seems to me that, for play-by-play era stats, it’d be superior to use a more precise, personalized TS% for each player. Unfortunately, I don’t think we can just look at basketball-reference and figure it out, because, while we do have stats for and-one’s, I don’t think we have readily-available stats for fouls on three-pointers or for technical foul shots. That data does exist though (since it is part of the play-by-play info), and it seems to me that it’d be better if it were systematically run. Perhaps it’s just something that no one at basketball-reference or elsewhere has deemed worth the time it would take to do it (which is fair), but it does seem like an obvious improvement that could be made in data we have.

And I’ll note that this applies not just to TS% but to anything that is derivative of TS%. For instance, BPM uses a formula that applies a 0.44 multiplier on FTs. Presumably, the BPM stat could be slightly improved by more accurately measuring possessions each individual player used on FTs, rather than just applying the 0.44 multiplier across the board.

EDIT: Others have very helpfully dug up versions of TS% that are a more precise, personalized TS%. Specifically, PBPstats and dunksandthrees seem to both measure the real TS% for players, with the difference between the two being that PBPstats seems to take technical foul shots out of the equation while dunksandthrees does not. So, one of those is the best measure for TS% IMO, with the preference between the two just depending on how you feel about technical foul shots counting.

[Colbinii]

Because the point of a statistic is to capture a small part of the game and TS% does an excellent job at capturing scoring efficiency within a 95% accuracy in 99.9% of discussions.

Nobody is going to say "Player A is better than Player B because 60.8 TS% > 60.4 TS%"

[lessthanjake]

Because the point of a statistic is to capture a small part of the game and TS% does an excellent job at capturing scoring efficiency within a 95% accuracy in 99.9% of discussions.

Nobody is going to say "Player A is better than Player B because 60.8 TS% > 60.4 TS%"

Yeah, it’s not likely to change much, but it just seems like an obvious way to improve the accuracy of stats we have, and surely improving stats is good since accuracy is the whole point of statistical analysis. And it’s not like something that can change things on the order of up to like 0.5% TS% is completely de minimus. It’s not going to fundamentally change our views of players, but it’s not completely meaningless either.

[Djoker]

I thought about this in the past as well. Probably the main reason it's not done is it would be very time consuming. Some stats as you said aren't even readily available for reference so it would be a monumental task to calculate. While it probably wouldn't impact player efficiencies by much, I'm not sure who little or how much it could make a difference to be honest. For some players, it could be significant for all we know.

[Colbinii]

I thought about this in the past as well. Probably the main reason it's not done is it would be very time consuming. Some stats as you said aren't even readily available for reference so it would be a monumental task to calculate. While it probably wouldn't impact player efficiencies by much, I'm not sure who little or how much it could make a difference to be honest. For some players, it could be significant for all we know.

It's fairly obvious who it helps and hurts.

It helps Jump Shooters by giving them an inflated FTR. It hurts High FTR players like Harden.

[Doctor MJ]

The formula for True Shooting % multiplies the number of free throws taken by 0.44. This is because, on average, there are actually 0.44 possessions taken up per FT attempt. The reason that this is not 0.50 is because there are scenarios where FTs are taken where it’s not two FTs for a possession. These include and-one’s, fouls on three-pointers, and technical foul shots.

The thing is, though, that that 0.44 average is not necessarily descriptive for all players. Some players get more and-one’s than other players. Some players get fouled on three-pointers more than other players. TS% will actually underestimate the scoring efficiency of those players, and it’ll overestimate the scoring efficiency of players who very rarely have that happen. It seems to me that it’d be superior to actually measure the real TS% for each individual player, rather than just applying that 0.44 multiplier to everyone, when that 0.44 multiplier will often be meaningfully wrong.

Prior to the play-by-play era, I don’t think we can do that, because we don’t know how many and-one’s players got, or how many foul shots came off three-pointers, or how many technical foul shots they shot. But in the play-by-play era we do have this information. It seems to me that, for play-by-play era stats, it’d be superior to use a more precise, personalized TS% for each player. Unfortunately, I don’t think we can just look at basketball-reference and figure it out, because, while we do have stats for and-one’s, I don’t think we have readily-available stats for fouls on three-pointers or for technical foul shots. That data does exist though (since it is part of the play-by-play info), and it seems to me that it’d be better if it were systematically run. Perhaps it’s just something that no one at basketball-reference or elsewhere has deemed worth the time it would take to do it (which is fair), but it does seem like an obvious improvement that could be made in data we have.

And I’ll note that this applies not just to TS% but to anything that is derivative of TS%. For instance, BPM uses a formula that applies a 0.44 multiplier on FTs. Presumably, the BPM stat could be slightly improved by more accurately measuring possessions each individual player used on FTs, rather than just applying the 0.44 multiplier across the board.

I wish we that data were handy, I'd certainly rather be using precisely correct data when comparing modern players.

At the same time, I appreciate having data from a consistent technique when doing historical analysis.

[Doctor MJ]

I thought about this in the past as well. Probably the main reason it's not done is it would be very time consuming. Some stats as you said aren't even readily available for reference so it would be a monumental task to calculate. While it probably wouldn't impact player efficiencies by much, I'm not sure who little or how much it could make a difference to be honest. For some players, it could be significant for all we know.

It's fairly obvious who it helps and hurts.

It helps Jump Shooters by giving them an inflated FTR. It hurts High FTR players like Harden.

Hmm, I'm not sure I follow there.

In a nutshell, TS% is going to underrate players who get their free throws disproportionately on And-1's and overrates those who get their free throws disproportionately NOT with And-1's, right?

We use a weighting of .44 FTAs = 1 FGA.
A player who only shoots FTs off And-1's should have a factor of 0 instead of .44.
A player who only shoots FTs off missed 2's should have a factor of .50 instead of .44.

With Harden, my guess would be that his true TS would be worse than his estimated TS because of this, though it's murky because of 3's.

Just because I can see it simply, here's how Harden stacks up by And-1's in the 7 years where he led the league in FTAs, along with the And-1 leader:

'12-13: 1st (Harden)
'14-15: 5th (LeBron)
'15-16: 3rd (LeBron)
'16-17: 48th (Cousins)
'17-18: 7th (LeBron)
'18-19: 2nd (Giannis)
'19-20: 3rd (Giannis)

So my guess would be that at least in '16-17, his true TS would be worse than his estimated TS.

[penbeast0]

What we should have been doing since the dawn of the statistical era is counting a missed shot where there was a foul as a missed shot. Then, you just divide points by shots for scoring efficiency (points/shot). Instead we've had these kludges like ts% which is a decent stat but yes, could be more accurate.

[f4p]

if they ever figure it out, i would also remove technical free throws from the scoring (edit: it doesn't affect the true shot attempts ). i realize being a good free throw shooter is how you get to shoot the technical and it adds some value, but you haven't done anything to actually create the opportunity and you are basically getting a free point with no possession used just because you are an 85% free throw shooter and your next best teammate is an 82% free throw shooter. at least the 0.44 multiple makes you use some fraction of a possession for the free point.

[OhayoKD]

if they ever figure it out, i would also remove technical free throws from the scoring (edit: it doesn't affect the true shot attempts ). i realize being a good free throw shooter is how you get to shoot the technical and it adds some value, but you haven't done anything to actually create the opportunity and you are basically getting a free point with no possession used just because you are an 85% free throw shooter and your next best teammate is an 82% free throw shooter. at least the 0.44 multiple makes you use some fraction of a possession for the free point.

Missing a technical hurts though. Maybe subtract the league average for techincal free-throw makes?

[jalengreen]

I believe that pbpstats uses exact TS%, and they provide data for where a player's free throws come from... though I'm failing to actually reproduce their values using that data so I'm not sure

Harden's pbpstats page: https://www.pbpstats.com/season-stats/nba?EntityType=Player&EntityId=201935

Switch Table Data from "Scoring" to "Free Throw Source"

Has his '16-17 RS TS% as 61.92%, basketball reference says 61.3% TS% so not being calculated same way

My attempt to try to reproduce that '16-17 RS TS%: 2356/(2*(777+756+(38+190-27+124-2+61))) = 61.45%, doesn't align with that 61.92%

{PTS / 2 * (2PA + 3PA + (adding up all free throw sources, subtracting and 1s))}

Remove five heaves and I get up to 61.6%, still doesn't align with the 61.92%

Probably doing something wrong here maybe someone can figure it out

[lessthanjake]

I believe that pbpstats uses exact TS%, and they provide data for where a player's free throws come from... though I'm failing to actually reproduce their values using that data so I'm not sure

Harden's pbpstats page: https://www.pbpstats.com/season-stats/nba?EntityType=Player&EntityId=201935

Switch Table Data from "Scoring" to "Free Throw Source"

Has his '16-17 RS TS% as 61.92%, basketball reference says 61.3% TS% so not being calculated same way

My attempt to try to reproduce that '16-17 RS TS%: 2356/(2*(777+756+(38+190-27+124-2+61))) = 61.45%, doesn't align with that 61.92%

{PTS / 2 * (2PA + 3PA + (adding up all free throw sources, subtracting and 1s))}

Remove five heaves and I get up to 61.6%, still doesn't align with the 61.92%

Probably doing something wrong here maybe someone can figure it out

This is basically exactly what I was hoping existed! This is great! It gives us data on the number of and-one’s, the number of fouls on threes, and the number of technical foul shots.

I’m also a bit confused by whether PBPstats is using this data to get their TS% number. Since it differs from BBREF’s TS%, I’d assume yes. But, using the Harden example, my calculation based on this doesn’t align with it (and also differs from your calculations too).

Here’s how I’d calculate it. Basically, we want to get the number of possessions Harden ended with shots or FTs. He had 1533 FGAs. He drew 190 two-point shooting fouls, but 27 of those were and-1’s (and therefore already are associated with a FGA). So that adds another 163 possessions ended. He drew 124 three-point shooting fouls, but 2 of those were and-1’s, so that adds another 122 possessions ended. And then we add the 61 non-shooting foul trips to the FT line. I don’t think the technical fouls should be added, since they don’t end a possession. That leaves the calculation as being 2356/(2*(1533+167+122+61)) = 62.56%. That’s even higher than the 61.92% TS% that PBPstats says for Harden elsewhere. Not sure where that 61.92% comes from. But I do think that this gives a good example of there being a fairly meaningful difference here between what we get with the 0.44 multiplier and what we get looking at a player’s actual FT sources, since Harden’s TS% using the 0.44 multiplier is only 61.33%.

[lessthanjake]

if they ever figure it out, i would also remove technical free throws from the scoring (edit: it doesn't affect the true shot attempts ). i realize being a good free throw shooter is how you get to shoot the technical and it adds some value, but you haven't done anything to actually create the opportunity and you are basically getting a free point with no possession used just because you are an 85% free throw shooter and your next best teammate is an 82% free throw shooter. at least the 0.44 multiple makes you use some fraction of a possession for the free point.

Yeah, technical foul shots juice peoples’ TS% up some. I think if we wanted to account for that, the best thing to do would probably be to take them out of the equation, while accounting for how well the person did on them compared to average (either on FT shots in general or on technical foul shots—I’d probably prefer the former). So, for instance, if league average on FTs was 76%, and someone shot 50 technical FTs and made 45 of them, then for TS% purposes we wouldn’t add those 45 points scored, but would instead add the 7 points they scored above league FT average. OhayoKD suggested a similar thing. It’s a bit of a controversial adjustment, and I doubt there’d be agreement on exactly what the best way to adjust for it is (for instance, OhayoKD suggested doing it based on league average on technical FTs, while I’d probably prefer basing it on league average on FTs in general). So I don’t think it’s something that the TS% stat can really adjust for in the first instance, but it is something we can try to account for as an additional layer on top of TS%.

[jalengreen]

I believe that pbpstats uses exact TS%, and they provide data for where a player's free throws come from... though I'm failing to actually reproduce their values using that data so I'm not sure

Harden's pbpstats page: https://www.pbpstats.com/season-stats/nba?EntityType=Player&EntityId=201935

Switch Table Data from "Scoring" to "Free Throw Source"

Has his '16-17 RS TS% as 61.92%, basketball reference says 61.3% TS% so not being calculated same way

My attempt to try to reproduce that '16-17 RS TS%: 2356/(2*(777+756+(38+190-27+124-2+61))) = 61.45%, doesn't align with that 61.92%

{PTS / 2 * (2PA + 3PA + (adding up all free throw sources, subtracting and 1s))}

Remove five heaves and I get up to 61.6%, still doesn't align with the 61.92%

Probably doing something wrong here maybe someone can figure it out

This is basically exactly what I was hoping existed! This is great! It gives us data on the number of and-one’s, the number of fouls on threes, and the number of technical foul shots.

I’m also a bit confused by whether PBPstats is using this data to get their TS% number. Since it differs from BBREF’s TS%, I’d assume yes. But, using the Harden example, my calculation based on this doesn’t align with it (and also differs from your calculations too).

Here’s how I’d calculate it. Basically, we want to get the number of possessions Harden ended with shots or FTs. He had 1533 FGAs. He drew 190 two-point shooting fouls, but 27 of those were and-1’s (and therefore already are associated with a FGA). So that adds another 163 possessions ended. He drew 124 three-point shooting fouls, but 2 of those were and-1’s, so that adds another 122 possessions ended. And then we add the 61 non-shooting foul trips to the FT line. I don’t think the technical fouls should be added, since they don’t end a possession. That leaves the calculation as being 2356/(2*(1533+167+122+61)) = 62.56%. That’s even higher than the 61.92% TS% that PBPstats says for Harden elsewhere. Not sure where that 61.92% comes from. But I do think that this gives a good example of there being a fairly meaningful difference here between what we get with the 0.44 multiplier and what we get looking at a player’s actual FT sources, since Harden’s TS% using the 0.44 multiplier is only 61.33%.

Going off of your result:

2356/(2*(1533+167+122+61)) = 62.56%

Think you meant to put 163 there rather than 167. And removing technicals from the denominator made sense, though it had me wondering if pbpstats just removes technicals entirely. I checked and Harden went 29/38 on technical FTs in 2017, so removing those 29 pts:

(2356-29)/(2*(1533+163+122+61)) = 61.92%; lines up with pbpstats.com's TS% for harden

And just to get another data point

2016 steph scored 2375 on 1598 FGA. 110 2pt shooting fouls minus 30 and1s, 21 3pt shooting fouls minus 2 and1s, plus 60 non-shooting fouls. So 159 additional possessions. And curry made 30/31 tech FTs (lmao), so removing those 30 pts:

(2375-30)/(2*(1598+159)) = 66.73%; again lines up with what pbpstats has for his TS%. basketball ref has 66.9% for reference

So yeah, seems like the conclusion is that pbpstats provides exact TS% but with technicals removed entirely. Those are points that count so that might feel a little odd, dunno how I feel about it. But now we know what we're working with

[lessthanjake]

I believe that pbpstats uses exact TS%, and they provide data for where a player's free throws come from... though I'm failing to actually reproduce their values using that data so I'm not sure

Harden's pbpstats page: https://www.pbpstats.com/season-stats/nba?EntityType=Player&EntityId=201935

Switch Table Data from "Scoring" to "Free Throw Source"

Has his '16-17 RS TS% as 61.92%, basketball reference says 61.3% TS% so not being calculated same way

My attempt to try to reproduce that '16-17 RS TS%: 2356/(2*(777+756+(38+190-27+124-2+61))) = 61.45%, doesn't align with that 61.92%

{PTS / 2 * (2PA + 3PA + (adding up all free throw sources, subtracting and 1s))}

Remove five heaves and I get up to 61.6%, still doesn't align with the 61.92%

Probably doing something wrong here maybe someone can figure it out

This is basically exactly what I was hoping existed! This is great! It gives us data on the number of and-one’s, the number of fouls on threes, and the number of technical foul shots.

I’m also a bit confused by whether PBPstats is using this data to get their TS% number. Since it differs from BBREF’s TS%, I’d assume yes. But, using the Harden example, my calculation based on this doesn’t align with it (and also differs from your calculations too).

Here’s how I’d calculate it. Basically, we want to get the number of possessions Harden ended with shots or FTs. He had 1533 FGAs. He drew 190 two-point shooting fouls, but 27 of those were and-1’s (and therefore already are associated with a FGA). So that adds another 163 possessions ended. He drew 124 three-point shooting fouls, but 2 of those were and-1’s, so that adds another 122 possessions ended. And then we add the 61 non-shooting foul trips to the FT line. I don’t think the technical fouls should be added, since they don’t end a possession. That leaves the calculation as being 2356/(2*(1533+167+122+61)) = 62.56%. That’s even higher than the 61.92% TS% that PBPstats says for Harden elsewhere. Not sure where that 61.92% comes from. But I do think that this gives a good example of there being a fairly meaningful difference here between what we get with the 0.44 multiplier and what we get looking at a player’s actual FT sources, since Harden’s TS% using the 0.44 multiplier is only 61.33%.

Going off of your result:

2356/(2*(1533+167+122+61)) = 62.56%

Think you meant to put 163 there rather than 167. And removing technicals from the denominator made sense, though it had me wondering if pbpstats just removes technicals entirely. I checked and Harden went 29/38 on technical FTs in 2017, so removing those 29 pts:

(2356-29)/(2*(1533+163+122+61)) = 61.92%; lines up with pbpstats.com's TS% for harden

And just to get another data point

2016 steph scored 2375 on 1598 FGA. 110 2pt shooting fouls minus 30 and1s, 21 3pt shooting fouls minus 2 and1s, plus 60 non-shooting fouls. So 159 additional possessions. And curry made 30/31 tech FTs (lmao), so removing those 30 pts:

(2375-30)/(2*(1598+159)) = 66.73%; again lines up with what pbpstats has for his TS%. basketball ref has 66.9% for reference

So yeah, seems like the conclusion is that pbpstats provides exact TS% but with technicals removed entirely. Those are points that count so that might feel a little odd, dunno how I feel about it. But now we know what we're working with

Excellent post! It seems you’ve figured out what’s going on there. I’m okay with technicals being taken out of the equation entirely, I suppose, since it is a bit of an unfair benefit to the person who takes them.

In any event, this basically means that PBPstats’s TS% is actually what I was looking for. Which, to me, means that it’s the better version of TS%.

Finally, to compare apples to apples here, if you took out technicals, the basketball-reference TS% method would give you 61.11%. So accounting for things more precisely would increase Harden’s TS% by almost a percentage point that season. It’s not a big deal, but it’s not nothing either IMO.

[Throwawaytheone]

.

[lessthanjake]

Just wanted to add to the convo, dunksandthrees does something similar to this. I don't know their exact formulas but they claim to " true shooting attempts (TSA) while bbref only estimates them. DunksAndThrees uses *true* true shooting percentage."

https://dunksandthrees.com/epm

You can see a disparity between their TS% values and BBRefs, for example Curry being 61.6% TS% this season on BBRef and 62.1% on Dunksandthrees.

Excellent find!

As far as I can tell, this also does what I was looking for. The difference between this and the PBPstats version of this seems to be that the PBPstats version takes technical foul shots out of the equation entirely, while the dunksandthrees version includes them.

So basically, I think we do actually have precise measures of TS%, and we even have options for whether we want that precise measure to include technical foul shots or not!