What's the right way to calculate Exact True shooting?

[Gibson22]

As most of you will know, the true shooting stat is "flawed" in the fact that, unlike efg% which is a precise, plain and simple method to weigh 3s and 2s, ts is an estimation, because it has to take into account free throws, and a given number of free throws doesn't translate to a precise number of possessions used, with that meaning that 10 free throws don't always equate to 5 possessions. So there's that 0.44 coefficient. Now the main problems are 2

- By nylon calculus, since 2005 the 0.44 coefficient has been higher than league average, and in 2017 it took a very big downward trend going from about 0.433 to about 0.426 (I mean the fta possessions/total fta ratio) because there are more and more 3 pt fouls season after season, and obviously 4 point plays. So, this creates a relevant error

-The most important thing (because the previous aspect, while most definitely an issue, still affects the players equally in a given season, just sets the comparison with previous seasons slightly off) is that, obviously, the fact that there is a coefficient penalizes players who get a lot of and-ones, and fouls on 3 point shots.

Now, as you know we have play by play data. My main question is this. What's the right way to calculate the possessions? I think it should be 2 * (FGA + 0.5 * FTA2 + 0.333 X FTA3), and obviously that would divide the total number of points. Technical free throws and flagrant free throws should not be counted in the possessions count as they don't spend possessions. Points from technical fouls free throws should be substracted from the total of the player, for two reasons - if we did, those points would go in the total points but those free throws don't affect the total possessions, therefore awarding more than any other shot, the most undeserving way to score a point - this would be the flaw of the formula, but it would be a negligible flaw. Most players don't shoot 20 technical free throws in a season. Now, let's say curry goes 20/20 from those free throws, and the second best free throw shooter on the lineup, or in another team is shaq who goes 8/20. That's 12 points. Not that much in a full season. Now, realistically speaking, players don't go 20/20, 18/20 is elite, but more importantly, no team has shaq as their designated free throw shooter, every team has at least an 80% free throw shooter on the court at all times, so an elite 19/20 would pruduce at the most 3 points over the average replacament shooter over the course of a season. All in all, it's pretty obvious how little of a difference tha makes over the course of the season.

Now, let's get back to the issue. For me, the play by play EXACT TRUE SHOOTING would be, as I said earlier, Points-Technical free throws points / 2 * (FGA + 0.5 * FTA2 + 0.333 X FTA3).

Now, everything that I said to this point has been said multiple times, my problem is that I found two formulas that I think that are different from this one.

NYLON CALCULUS:James Harden in 2015. Using data from NBAWOWY.com, he had 2217 points in the regular season with 1470 field goals and 824 free throws. Additionally, there were 52 and-1 attempts, 66 three-in-a-row free throw sets, and 38 technical/flagrant foul attempts. The traditional formula results in a TS% of 60.49% via the following: 100*2217/[2*(1470 + .44*824)]. This is very similar to the output received with the real proportions of free throws considered: 100*2217/[2*(1470 + .5*(824 – 52 – 66/3 – 38))] = 60.71% So this way counts the free throw possessions subtracting from the total the and-one attempts, technical and flagrants.

Then we got nba wowy: their formula is 2*2ptm+ 3*3ptm+fta2m+fta3m+and1m (so basically the total points without counting technical free throws) / 2*tsa. The TSA is calculated fga+ft2a+ ft3a

So let's get an example. A player has 900 points on on 450 shots and 350 free throws. 250/350 from two, 50/100 from 3, 250 from the line. These 350 free throws, 14 are from technicals, 10 from flagrants, 40 and-1, 190 from 2 point attempts, 96 from 3.

TS%: 900/ 2* (450* FGA + 0.44 * FTA) = 74,5.

Exact True shooting %: 900-14 (technical fts)= 886 / 2 * (450 + 0.5 * 190 + 0.333 * 96) = 76,78. The difference is in the fact that the number of possession used by the free throws is much smaller: 0.44 x fta 350 = 154. Real number of possessions= 95 + 32= 127. And it isn't much bigger because I subtracted the 14 free throws from the total points

NYLON CALCULUS: 900/ 2*(450+ 0.5 * (350- 14- 10-40 -96/3)=

Now nba wowy: 2* 250 + 3 * 50 + every free throw besides technicals= 886 (I didn't specify the free throws made, but obviously it's the same) ///////// 2*tsa. So.... Ok, I figured, it's the exact same... with ft2a and ft3a they mean the same as 0.5 * 2 free throw shouting fouls, and 0,333 x 3 free throws shouting fouls...right? Otherwise, it would be totally off.

So my questions are:
1) Is my formula right? 2) NBAwowy means what I just said with ft2a and ft3a, right? 4) Where can i find the data for past seasons? On nba wowy I can only find the free throw stats for this last 2 seasons and it also doesn't have flagrant fouls stats

[Gibson22]

So I guess nba wowy has everything covered... BUT stuff from before 2018-19 and I don't understand what they do exactly with flagrant foul free throws

[Gibson22]

Again, I don't understand...nbawowy has lebron's ts the exact same as the bb-ref ts, even tho their formula seems the same as mine, and applying that the result would be 58,63, not 58,2, pretty big difference.