I ran a simple linear regression model to estimate FTAs based on attempts in the restricted area, paint+non-restricted area, mid-range, and 3 pointers. Not surprisingly all of them have positive t-stat values, with Restricted Area having 18.14, Paint/Non-RA at 6.58, mid range at 10.79, but 3P at only 2.86 (2 is a general rule of thumb good indicator), but keep in mind that of course the more shots you take the more FTA you get, and I would expect the closer to the basket the more likely you will get FTs from them, which is why I am very surprised that not only does mid-range has a higher t-stat than paint/non-RA shots, but it has the highest coefficient amongst the 4 shot types. Part of the reason is because the league as a whole shoots much less mid-rangers than the other shot types. So far this season, there were only about 20K mid range shots, whereas there were close to 57K RA shots, 40K P/Non-RA shots, and 83K 3P shots, which means that the impact of each mid range shot will simply be magnified, assuming. more FGA leads to more FTA.
Now plugging the numbers back to each individual player by aligning the coefficients (I hard set the y-intercept as 0, because if you shoot 0 FGA, you should get 0 FTM), I ranked the players by raw number of FTA exceeding expectations.
Note that Shai isn't that ridiculous in terms of getting FTs, ranking #6, while Luka, Avdjia and Harden are just so far ahead of everybody else. This is also a function of how many times you shoot as well, of course. The more shots you shoot, the more magnified the variance. Play style also factors in, Castle, Zion, Giannis and Randle are known to play bully ball, so they get more fouls. This can be seen by their high % of RA and Paint FGAs.
What is interesting is that Shai has by far the most mid range shots amongst the group. Booker is the only person who shot mid rangers more than any other types of 2 points shots, but Shai's RA shots and mid range shots are almost the same, and he has significantly less non-RA paint shots. Back to the earlier point, mid range shots had a notable impact on the FTAs, because most people took so few of them.
Given the hypothesis is that Shai is getting so many FTs despite his shot diet, I removed Shai from the set, and ran the regression again, and coefficient for mid-range shots went from 0.534 to 0.491, which is rather significant given that he is just 1 of a sample of over 500 data lines.
All I can say is, perhaps he is getting more than his share of FTAs, but the league, as a whole, has been rewarding mid-range shooters with more FTs at that range.
Now for the true conspiracy theorists out there, the team with the most additional FTAs compared to expected FTAs using shot profile? Of course, the Lakers, with a rather staggering 54 more FTs than the 2nd placed Cavs, and overall 268 FTAs more than expected, that is more than 3.6 FTAs a game more than expected. Truly staggering.
EDIT: I couldn't cut and paste the table in for some reason.