Hollinger's Ratings

John Hollinger uses a true shooting percentage (TS%) in his player ratings. He claims "True Shooting Percentage calculates what a player's shooting percentage would be if we accounted for free throw and 3-pointers." He uses the following formula:

TS% = (Total points x 50) / (FGA + 0.44*FTA)

For the mathematically challenged out there (JB, I'm talking to you), I'll break this down a bit. The multiplication of the total points by 50 is, essentially, a multiplication by 100 to get a percentage and not a decimal value and a division by 2 because there are 2 points per regular FG made. That's as far as I'm going to explain it.

While I appreciate the attempt by Hollinger to adjust for 3-pointers and free throws, I don't think Hollinger does it correctly. I'll illustrate my concerns using a few easy examples.

1. A made 2-pointer: this is the baseline and an excruciatingly easy problem. If you make a 2-pointer, your shooting percentage on the shot and your TS% are both 100%. This makes sense.

TS% = (2 x 50) / (1 + 0.44*0)
TS% = 100 / 1
TS% = 100

2. Shooting 2 of 3 on 3-pointers: this also works out well ... the correction for 3-pointers is fine. If you make 2/3rds of your 3-point attempts, you score 6 points, which is like making 3 of 3 2-pointers ... so going 2 of 3 from 3 should nets a TS% of 100 as well. Check it out.

TS% = (6 x 50) / (3 + 0.44*0)
TS% = 300 / 3
TS% = 100

3. A 2-shot foul: here, we find a problem. If you get fouled on a shot and make both FT's, that's like making the shot (if you get 2 FT's, you've obviously missed the shot you were fouled on). So, your TS% should be 100. Let's see what we get. Remember, if you are fouled on the shot and don't make it, it doesn't count as a FGA.

TS% = (2 x 50) / (0 + 0.44*2)
TS% = 100 / 0.88
TS% = 114 (I rounded to the nearest whole number)

So, based on Hollinger's formula, you are a better player if you get fouled on all your shots and then just make your FT's, rather than just making shots. Weird.

4. An "And 1": this is another problem scenario. An "And 1" (an old-fashioned 3-point play) should result in the same TS% as a regular 3-pointer because you are getting 3 points on one possession. Both of them should yield a TS% of 150. Let's see if they do.

Regular 3-pointer
TS% = (3 x 50) / (1 + 0.44*0)
TS% = 150

"And 1" (you get one FGA and one FTA)
TS% = (3 x 50) / (1 + 0.44*1)
TS% = 150 / 1.44
TS% = 104

When you convert an "And 1", not only is your TS% not as good as if you'd scored the same number of points in the same number of possessions just nailing 3-pointers, your TS% (104) isn't even as good as your TS% if you miss the shot and make the two resulting FT's (114). This is, obviously, flawed. The formula says the better player is the one who makes two FT's when he's fouled on a shot, not the guy who makes the shot and his one additional FT. Yep, 2 points is definitely better than 3. Wait a second, no it's not.

I haven't read Hollinger's document on where his formulas come from. I think I know how he came up with the TS% formula. But, I think it's an oversimplification of a problem that really isn't that difficult. Information should be available on "And 1's" and "1-and-1's" which would allow Hollinger to accurately calculate the TS%.

Anyone out there want to tell me I'm wrong?