Question about TS% and .44

[Dr Positivity]

How I’ve always interpret using .44 instead of .50 in the TS% equation, is that fouls on And-1s don’t waste a possession, and sometimes players get 3 shots on one foul, or take a fouls shot in a technical, flagrant, clear path situation. Therefore the number of possessions per free throw is lower than one half

Is the .44 also after accounting for how the field goal on an And-1 was a free shot for the player? On a continuation if it goes in it's a made field goal, if it doesn't, because they got fouled it's not a miss in the boxscore. Effectively the value of getting fouled vs a FG attempt grows when you add in how a foul can lead to a continuation with +1 FGM and +1 FGA or neither, thus it's either a possession used with 1.000 or 1.500 TS% (2 or 3), or 2 shots at the line to represent a possession. Is this taken into account?

[Dr Positivity]

Using Lebron as a test case. According to NBA Miner his 75 and-1s lead the league, he has 0 four point plays. His stats are 1416 FGA, 491 FTA, 1920 Pts and .588 TS%. 75 of those FGM are the FG on the and-1, and therefore 150 points. Removing this from both categories makes his new FGA total 1341, points 1770 and TS% .568. Finishing continuation 75 field goals at a TS% of 1.000 increased his overall TS% 0.020.

The natural response to this is so what. Lebron getting continuations makes him a more efficient scorer, and his TS% deserved to go up. Ok, but philosophically, does this get away from the goal of TS% tracking points per shot and a "shooting" statistic?

To give an example, Harden is 1st in the league by far with 837 FTA and 3rd in total and-1 or 4 point play opps at 59. Brook Lopez is 25th in the league 403 FTA and 4th in and-1 opps at 58. In terms of and-1 opportunities per FTA is at Lopez at 14.4%, Harden 7.0% (at 15.3% Lebron has an even better ratio than Lopez). So even though Lopez is presumably around twice as likely to convert an and-1 as Harden, Harden makes as many continuations as him, just by getting to the FT line more often. Are we sure that crediting a player who creates a high volume of and-1 opportunities the same as a player who finishes them at a higher rate, is something TS% should cover? Or would a revised TS% without the effect of its continuation FGMs on the player's total, be more reflective of the player's "efficiency" of FGM vs potential FG misses. Then again, you could argue that since Harden's TS% goes up because of how good he gets to the FT line, it was always about putting yourself in a position to take efficient shots more than anything else. The current TS% including continuations is likely to reflect who is the most valuable scorer, but is it fair to suggest a TS% without continuation FGMs would be less accurate to a player's value, but be chosen of the two because of categorical purity instead, and the idea that a shooting % stat should be one where the only things that influence it have both a make and a miss as an outcome?

[Shot Clock]

viewtopic.php?f=344&t=1434968

I have lots of concerns with the never changing .44 fudge factor.