Trueshooting / True Shooting Attempts calc, why no distinction between 3PA and 2PA?

[WestGOAT]

Current formulas below
True Shooting Attempts (TSA): FGA + 0.44 * FTA
True Shooting Percentage: PTS / (2 * TSA).

I am assuming that TSA is multiplied by 2 since a succesful FGA would normally lead to 2 points back in the day.
However, aren't three-pointers then not overaly rewarded? I think this would be a more better calculation:

Modified True Shooting Attempts: (FGA + 0.44 * FTA) - 3FGA
Modified True Shooting Percentage: PTS / (2 * Modified TSA + 3 * 3FGA).

I think that this way TS% shouldn't go above 100% and this should be a more fair way to calculate "efficiency". I mean >100% efficiency shouldn't be physically possible anyway.

Anyone feel like crunching some numbers to verify these thoughts ?

Reference: https://www.basketball-reference.com/about/glossary.html#:~:text=TS%25%20%2D%20True%20Shooting%20Percentage%3B,is%20FGA%20%2B%200.44%20*%20FTA.

[Squared2020]

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[WestGOAT]

Current formulas below
True Shooting Attempts (TSA): FGA + 0.44 * FTA
True Shooting Percentage: PTS / (2 * TSA).

I am assuming that TSA is multiplied by 2 since a succesful FGA would normally lead to 2 points back in the day.
However, aren't three-pointers then not overaly rewarded? I think this would be a more better calculation:

Modified True Shooting Attempts: (FGA + 0.44 * FTA) - 3FGA
Modified True Shooting Percentage: PTS / (2 * 2TSA + 3 * 3FGA).

I think that this way TS% shouldn't go above 100% and this should be a more fair way to calculate "efficiency". I mean >100% efficiency shouldn't be physically possible anyway.

Anyone feel like crunching some numbers to verify these thoughts ?

Reference: https://www.basketball-reference.com/about/glossary.html#:~:text=TS%25%20%2D%20True%20Shooting%20Percentage%3B,is%20FGA%20%2B%200.44%20*%20FTA.

I think if you're looking for a percentage, that's a good way to rework it. But what are we capturing here?

To put my question into context, this is what each of the shooting metrics are unbiased estimators for:

- Field Goal Percentage: Capturing the percentage of field goal attempts that a player takes. Unbiased for percentage making, biased for points scored on field goal attempts.

- Effective Field Goal "Percentage": Capturing the average number of points per field goal attempt. 2*eFG is unbiased for points scored on field goal attempts, biased for field goal percentage.

- True Shooting "Percentage": Capturing the average number of points per scoring chance. Assuming 0.44 is still an unbiased parameter for the percentage of chance-terminating free throws, then 2*TS is unbiased for points scored per chance but biased for scoring percentage per chance.

It looks like you're trying to estimate the percentage of scoring chances that result in points. Is 2TSA the modified true shooting attempts? Or is it 2*TSA? Or is it 2*modified true shooting attempts. Once I get clarity on that, I could identify what you're measuring specifically.

I guess you could say the true efficiency out of the total possible points (output).
I see that I forgot to edit my initial draft, 2TSA should be Modified TSA: (FGA + 0.44 * FTA) - 3FGA. Thanks for spotting that, I have adjusted that.

As an example let's take a look at Kyle Korver in this game:
https://www.basketball-reference.com/boxscores/201005080UTA.html

His total possible output in this game was 25 points. He obtained 23 points, so with this modified TS% that is 92%.

[Squared2020]

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