True Shot Attempts and TS% Exact Formulas

[EvanZ]

Also, its weird that they claim to be more exact in their calculations because they're based on play-by-play data rather than estimates, and yet they're still using the standard formula for TS%. In fact, the .44 coefficient is used in a number of their formulas.

I do the same thing. The problem with free throws is that you have to track what happens on the following play. I do have the data, but it's just a huge PITA to do all the parsing necessary to calculate this particular stat exactly.

All my other stats are exact though (such as % of teammate field goals assisted and rebounding %'s). And I assume NBA is doing things similarly to how I do it for my site.

All in all, this is a good thing for fans. Not that "advanced stats" needed to be legitimized, but it certainly can't hurt that the NBA itself now realizes the importance of metrics as basic (ironically) as TS% and eFG%. In fact, as most large organizations follow consumer sentiment, I would have to think this is more a reflection of the NBA realizing they needed to catch up, and not necessarily them trying to lead.

[deepak]

Also, its weird that they claim to be more exact in their calculations because they're based on play-by-play data rather than estimates, and yet they're still using the standard formula for TS%. In fact, the .44 coefficient is used in a number of their formulas.

I do the same thing. The problem with free throws is that you have to track what happens on the following play. I do have the data, but it's just a huge PITA to do all the parsing necessary to calculate this particular stat exactly.

I thought the point of the .44 coefficient is to eliminate free throw attempts due to and-1s and technicals. It seems this is readily available in the PBP, so what else would need to be accounted for?

[EvanZ]

Actually, I think it's even more important to account for the 10-15% of missed free throws that result in offensive rebounds, thus not ending a possession.

[deepak]

Actually, I think it's even more important to account for the 10-15% of missed free throws that result in offensive rebounds, thus not ending a possession.

What does this have to do with TS%, though? The possession being extended shouldn't affect the TS% of a player.

[EvanZ]

Actually, I think it's even more important to account for the 10-15% of missed free throws that result in offensive rebounds, thus not ending a possession.

What does this have to do with TS%, though? The possession being extended shouldn't affect the TS% of a player.

I'm just explaining what I thought the 0.44 represented, not whether it's appropriate for TS%. But if I'm right that it accounts for possessions than you're probably right that it doesn't make sense for TS%.

[deepak]

Actually, I think it's even more important to account for the 10-15% of missed free throws that result in offensive rebounds, thus not ending a possession.

What does this have to do with TS%, though? The possession being extended shouldn't affect the TS% of a player.

I'm just explaining what I thought the 0.44 represented, not whether it's appropriate for TS%. But if I'm right that it accounts for possessions than you're probably right that it doesn't make sense for TS%.

To me, 0.44*FTA represents a "true shot" by the player which is not accounted for in FGA. So, TS% means: "points scored per true shot. (divided by 2)."

3 FTA due to foul on 3-point attempt = 1 true shot
2 FTA due to foul on 2-point attempt or in-the-bonus foul = 1 true shot
1 FTA due to and-1 foul = 0 true shots
All FTA due to technicals, flagrant fouls, clear-path penalties = 0 true shots

If those events can be easily determined from the PBP, then a more exact figure for TS% or any formula that uses 0.44*FTA can be found. Ultimately, I don't think it makes much of a difference, but if the data is there then they might as well use it.

[EvanZ]

I tend to agree with you. Maybe I'll change the way I'm calculating TS%. Although I still would like to know what 0.44 actually represents, because it's used for stats other than TS% to represent possessions used by a player.

[deepak]

I tend to agree with you. Maybe I'll change the way I'm calculating TS%. Although I still would like to know what 0.44 actually represents, because it's used for stats other than TS% to represent possessions used by a player.

True. So take USG% for example, which you define as:

USG% = (FGM + DRB%*FGX + 0.44*FTA + TOV) / TmPoss

If I understand this correctly, you're intending to discount FGA and FTA which are offensive rebounded to determine what percentage of team possessions the individual was responsible for ending. So, if a player's miss is recovered by his team, then he didn't "use up" the possession.

Basketball-reference.com defines USG% in terms of percentage of plays ended by a player rather than possessions, where a play is essentially a sequence that ends in a "true shot" or turnover. A play is defined as:

play = FGA + 0.44*FTA + TOV

Note that they still use the 0.44 coefficient as you do, even though they aren't intending to discard FTA which are offensive rebounded. An offensive rebounded FTA is such a rare event that it probably doesn't make a huge difference, but still this is a discrepancy in the interpretation of 0.44*FTA.

[Kevin Pelton]

The .44 is strictly ratio of free throw plays to free throws. Nothing to do with offensive rebounds.

[EvanZ]

Good to know. At any rate (no pun intended), I just updated my site so it has actual true shooting attempts the way deepak defined them.

Thus, instead of 0.44*fta, I now have:

(1/2)*(fta2m+fta2x) + (1/3)*(fta3m+fta3x)

I track And1 and Technical free throws separately, and those are also listed on the site.

My USG definition now has "shooting fouls taken" (defined as above) instead of 0.44*fta as well.

[deepak]

The .44 is strictly ratio of free throw plays to free throws. Nothing to do with offensive rebounds.

This a short and sweet way of putting it. I'll have to remember that the next time the question comes up of what the heck the 0.44 coefficient means. To most people outside this community, its a mystery.

[deepak]

Good to know. At any rate (no pun intended), I just updated my site so it has actual true shooting attempts the way deepak defined them.

Thus, instead of 0.44*fta, I now have:

(1/2)*(fta2m+fta2x) + (1/3)*(fta3m+fta3x)

I track And1 and Technical free throws separately, and those are also listed on the site.

My USG definition now has "shooting fouls taken" (defined as above) instead of 0.44*fta as well.

Thanks for the quick update.

Out of curiosity, how close is your version to the 0.44 estimate?

[DSMok1]

Good to know. At any rate (no pun intended), I just updated my site so it has actual true shooting attempts the way deepak defined them.

Thus, instead of 0.44*fta, I now have:

(1/2)*(fta2m+fta2x) + (1/3)*(fta3m+fta3x)

I track And1 and Technical free throws separately, and those are also listed on the site.

My USG definition now has "shooting fouls taken" (defined as above) instead of 0.44*fta as well.

For TS%, you would get the points for the And1 free throws, but (obviously) the TSA is already accounted for in the FGA, right?

EDIT: I have split this string of posts off from the NBA PbP data thread, since it's pretty much a different subject.

[EvanZ]

Yes, that's right. The full formula:

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(1/2)*pts/tsa

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pts = 2*fgm2 + 3*fgm3 + and1 + ftm2 + ftm3

(where ftm2 & ftm3 are free throws made on 2-pt and 3-pt shooting fouls, respectively)

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tsa = fga + (1/2)*fta2 + (1/3)*fta3

(again where fta2 and fta3 are free throw attempts made on 2-pt and 3-pt shooting fouls)