Something seems to be wrong with the TS% equation. If you look at basketball reference, it lists Cederic Maxwell as #1 of all time. Cederic didn't shoot 3s, and ended his career with an overall FG% of 54.6% while shooting 78.4% from the line. Good numbers, but the best of all time? Contrast that to John Stockton, a guy who finishes 10th on that list. He was good at 2s and 3s and ended up with an overall eFG% of 54.6, exactly the same as Maxwell, but he shot 82% from the FT line. So how can a guy that shoots the ball from the field, at the same rate as another, but hits a higher percentage of FTs come out with a lower TS%? The answer seems to be, that in the TS% equation, they chose not to count the free throw as half a shot. but rather .44 of an attempt. Not sure what the deal with that was. So guys with a higher ration of FT to FGA come out ahead using this metric. Maxwell shot .73 FTS for every FGA Stockton only shot .42 FTs for every FGA. So that's how Cederic Maxwell comes out as the most efficient scorer in NBA history according to the TS% metric.
.44 has generally been the standard for free throws as a percentage of possessions (also used in the PER calculation) to account for the occasional and-1 or technical free throw. But regardless, the individual's free throw taste is much more significant than the formula. Apply the .5 you prefer, and I bet Maxwell still comes out ahead.
He does not come ahead with .5. Did you read my post? How he shoots the SAME percentage as Stockton and a LOWER FT percentage. A free throw is a free throw is a free throw. What does it matter if it's an and one or a technical?
I did read your post. Did you actually do the math, applying the .5 rate you prefer? Presume both took 100 FGA, with both having the free throw rates and percentages you listed. Maxwell would hit 54.8% of his FGA for 110 pts, and would take 73 FT, of which he would hit 57. So, he would score 167 points on 137.5 possessions, equivalent to 60.7% TS ([167/2]/137.5. Stockton would hit (the effective equivalent of) 54.8% of his FGA for 110 pts, and would take 42 FT, of which he would hit 34. So, he would score 144 points on 121 possessions, equivalent to 59.5% TS ([144/2]/121]. Maxwell's significantly higher free throw rate has a larger impact on TS% than Stockton's slightly higher FT% does, and altering the FT/possession ratio had virtually no impact at all.
The .5 does bring them closer, to within half a %, because it increases Maxwell's denominator proportionally higher while their numerators (career points) stay the same. Something seems silly to say player A shoots better from 3, 2 and FT line, but has a lower TS% because player B shot more FTs. Though I guess the same thing could happen to someone who makes a large volume of 3s. I still say .5 makes more sense in the equation that .44. A FT attempt is a FT attempt and they all count for 1 point.
With .44 if a guy goes to the line 100 times and makes 100 shots, his TS% would be 113%. Whereas if he had simply made 50 out of 50 2 pointers, his TS% would be 100%. So it's tilted for FTs.
The TS% calculation is essentially a per-possession scoring rate. The .44 ratio for free throws is apparently based on the idea that 88% of free throws are of the two-shot-foul variety, and the other 12% are not directly in replacement of a possession (tech, and-1, third FT after 3 pt shot foul). As much as .5 seems more intuitive, .44 fits in better with the intended purpose of the calculation.