PPS rewards getting fouled more than taking shots. If you miss the FTs, you don't get penalized. If you make them, you increase your PPS faster than you make shots. I agree with dursava that is not an accurate measurement of efficiency simply because FTs aren't free. They take up possessions, unless those are technical fouls or flagrant fouls. The whole idea of the Hack-a-Shaq tactic is on this principle. If Shaq misses the FTs, his team loses a possession. But Shaq's PPS won't be affected. PPS rewards the style of play of guys like Wade and Francis, who throw their bodies around in the lane to draw fouls. Oh, and of course it rewards floppers like Nowitzki. But it does not rewards players like Hamilton who are good at getting open. My bottomline complaint about TS% is its inability to account for the ability to get AND1 fouls, which I think is significant for a player's efficiency. PPS rewards AND1 (but it rewards all FT shooting anyway). TS% doesn't.
I never said PPS was better than TS%; I'm saying you can't prove via math that one is better than the other. I don't really like, either. The (FTA * .44) in the denominator is an anchor on the formula. It creates drag or friction that prevents the result from going up or down as fast as PPS. Yes, PPS rewards made FTs more than TS%; thus essentially penalizing misses because you failed to raise your PPS vs the guy who made the FT. Conversely, it also penalizes missed FGAs more than TS%. It goes down faster on missed FGAs, plus it goes up faster on made FGAs. PPS goes up and down faster; but the slopes of growth and decay of the two formulas is nearly identically. That is: The deltas of change are very siimilar. Do the math.
They are similar only approximately. And while the slopes grow similarly for a player, they don't grow in the same rate. And the rate varies from player to player. The two systems clearly favors different styles of play. PPS favors getting fouled more than taking shots. Like I pointed out, this means it favors getting into the lane more than taking jump shots. And it doesn't penalize poor FT shooting. Players like Shaq would look better at PPS than at TS%. TS% favors good 3pt shooters. And the volume of shots has no effect on TS%. That's why Novak looks good at TS% but not as good at PPS. He doesn't get into the lane and get fouled. But he is accurate whenever he gets open on a 3pt shot, no matter how scare it is that he gets open. There is no inherent "good" or "bad" in either method. Neither is nearly complete in measuring efficiency. But they are not totally worthless either. It gives you an approximation of how efficient a guy is offensively.
I'd hesitate to say I can "prove" that one metric is "better" than another. I don't like that wording. But as measures of scoring efficiency, TS% is more theoretically sound than PPS. Scoring efficiency, by definition, refers to points scored per scoring attempt. The formula for TS% is providing an approximation for that. PPS is actually measuring something different (points scored per field goal attempt). But perhaps you're not interested in scoring efficiency of players. Instead, you want a metric that will better reflect how the player improves his team's offense. So, we have this is the question: I'm considering adding some player; does TS% or PPS give me a better idea of how much they'll improve his team's offense? If you just have those two measures and nothing else, I'm not sure which is better. But, when we assess a player's offensive value, you have to look at both efficiency AND usage. TS%, on its own, tells us little. Combining TS% and total scoring attempts tells us quite a lot. More, I would say, than combining PPS and total scoring attempts. I've shown examples where PPS very clearly fails at capturing efficiency. Since you've yet to respond to any of them, it looks like perhaps you're not interested in scoring efficiency. In which case, we've been talking about different things.
Let's define efficiency, so we're on the same page on what we're talking about. Scoring efficiency for an individual player, in my mind, is points scored per scoring attempt. PPS is points scored per field goal attempt. Clearly, two different things. Another way to put it, is that if we defined scoring attempts as: scoring attempts = FGA + free throw trips that aren't And-1s Then, TS% attempts to model this with: scoring attempts = FGA + FTA * 0.44 PPS, on the other hand, does the following: scoring attempts = FGA + FTA * 0 = FGA Which is more accurate here? TS% is attempting to approximate scoring attempts, but sure in some cases it may not be precise. Particularly for a short stretch of games. Let's look at a concrete example to see how off TS% might be. A few years back, 82games.com had the following article on And-1s: http://82games.com/andone.htm In 05/06, Shaq led the league in And-1 opportunities as a percentage of his total shot attempts -- 8.5%. Let's see how bad TS% screwed up with its approximation for the season. That year, Shaq attempted 800 field goals, and 471 free throws, and scored 1181 points. So: total_shot_attempts = 800 fga + trips_to_line - and_ones and_ones = total_shot_attempts*.085 trips_to_line = and_ones + (471 fta - and_ones)/2 Based on that, I get: total_shot_attempts = 800 + (471 - total_shot_attempts*.085) / 2 total_shot_attempts = 993 shot attempts So, if my math is right, the real value of his TS% should have been 0.5*1181/993 or .595 TS%. The approximated formula gives us, instead, .586 TS%. For Shaq in that season, instead of .44 for our coefficient, we should have used 0.41. And this is a particularly extreme example.
this is fun, but i'm wasting too much time on this. i gotta go. in summary, i contend that the ability to move up or down vs other players is negligible between the two formulas...no matter if you're shooting FTs, 2s or 3s. maybe this weekend i'll be bored and see if i can prove it to myself. both formulas rank Maggette over the league's top high-volume, pure shooters. I don't like that. i'll have no problem saying i'm wrong. In the end though, TS% is a stat that fluctuates through the years, since you have to keep readjusting it based on past facts and rules changes...largely in a subjective manner.
durvasa, i know you are a stat hound. When you look at scoring efficiency, isn't it much simpler, cleaner, and more sensical to simply look at points per shot attempt for a player like Novak? What difference does it make where his shots come from, whether they come from the 3 point line, the FT line, or inside the 3 point line? He is making 1.65 points every time he shoots the ball. That is extremely efficient scoring, no matter how it is done. I do not see the benefit of breaking down TS% when PPS is so simple and clean. This is why I don't care for TS%. When you can look at the number of shots compared to how many points he scores, that tells you how effective a scorer he is. Corey Maggette and Dwayne Wade do it an entirely different way. They get to the FT line at an ungodly clip. I'm not saying Novak is as good or a better player than maggette or Wade. What I am saying is his ability to score the basketball, at least for the limited minutes he plays and against the scrubs he is playing against and with, he is a very efficient scorer. I'm not even claiming he makes an offense better because of his shooting. (But I think he does because of his ability to spread the defense.)
PPS is great if you're talking about a specific type of shot. For instance, we can consider a players PPS separately for different spots on the court. We could consider a player's PPS on threes, twos, FTs, and then his distribution of shots. But if you want to summarize their total efficiency on all scoring attempts with a single number, TS% tells you more.
I'll add: you're right that Novak is a very efficient scorer. But that's exactly what his TS% tells us. For his career its .601 TS%. And that's including him shooting 33.3% on threes his rookie year. Now, suppose in addition to hitting all this three-pointers at such a high clip, somehow Novak got to the line 5 times a game. And, further, let's suppose that he sucked at shooting free throws -- 35%. Would you still consider him a very efficient scorer? PPS would tell us that he is. In fact, his efficiency would increase because PPS doesn't properly penalize bad free throw shooting. But you and I know, and his TS% would confirm it, that if this was the case Novak would be a less efficient scorer.
^^This is exactly what I proposed. Like I pointed out, the 0.44 factor is an approximation for all players. It does not account for individual player's rate, which is precisely what we want to measure. It's like if you want to know a player's foul per minute rate, you want to use the actual minutes the player plays, rather than the average minutes of all players. I'd say the difference between .586 and .595 is significant. Of course, I agree that Shaq is an extreme case because of his poor FT shooting and his ability to draw And-1 fouls. But shouldn't the measurement have the ability to pick out the specially bads and the specially goods?
If you want to summarize a player's total scoring efficiency on all scoring attempts WITH a single number, there is no clearer statistic than PPS. TS tell you more about where their efficiency comes but where their efficiency comes from really doesn't matter when you are evaluating overall scoring efficiency. Just because a player has a higher percentage from 2 doesn't mean he is the more efficient scorer. The most efficient scorer is the scorer that makes the most points out of the shots he gets. That is, by default, the statistical definition of efficiency.
Ideally, we'd have all the information out our disposal to calculate scoring efficiency precisely. But, like I said, we have to make due with the limited information available in the box score. TS% gives us a better idea of a player's scoring efficiency than FG% or even PPS. It's not completely precise, but it's still an improvement over more traditional efficiency stats, and it is relatively easy to calculate from the official stats. And the And-1 effect, in the grand scheme of things, doesn't make a big difference on scoring efficiency for individual players. Realistically, the coefficient will range somewhere between 0.4 and 0.5 for players over a significant stretch of games, with the majority close to 0.44. So we can take TS% and say it's +/- 1% or so, if we want to acknowledge the extent of imprecision. In my opinion, not that big a deal.
I agree. But PPS doesn't tell you that. PPS = point scored / FGA. FGA is not the same thing as "shots he gets". If a player takes a shot and he misses but is fouled, then that shot won't be recorded under FGA. So, if a player goes 1/1 from the field, and 0/8 from the line (on 4 shots, he got fouled and went to the line) -- PPS would tell us he's just as efficient as a player who went 5/5 from the field without going to the line. That's clearly wrong. TS% says that FGA + 0.44*FTA better captures "shots a player gets" than FGA. And that's absolutely true.
And what would be the case of the player who went 5/5 from the field (dunks) but went 0 for 10 from the FT line in comparison to a player that went 3 for 7 from the field (3 point shots) and 2 for 2 from the line?
5/5 from the field and 0 for 10 on FT: PPS = points / FGA = 2 points per shot TS% = .5 * points / (FGA + .44*FTA) = .53 TS% or 1.06 points per shot 3 for 7 from 3-pt and 2/2 on FT: PPS = points / FGA = 1.57 points per shot TS% = .70 TS% or 1.40 points per shot PPS says the first player was more efficient overall, and TS% says the second player was more efficient overall. As for PPS, the player could have missed 200 free throws and used up all his team's possessions throughout the entire game, and his efficiency wouldn't change at all so long as he made those 5/5 from the field.
You proved what I've been saying. PPT favors player#1 (the Shaq type) and TS% favors #2 (the Novak type). Is the Novak type more efficient than the Shaq type? I don't know. In general, getting fouled IS a much more efficient way of scoring than taking shots. As great a 3pt shooter as Novak, he would have been more efficient if he got to the line more than shot more 3pters. A great 3pt shooter would average about 40% from the arc. That amounts to 60% TS%, just slightly better than Shaq's FT%.
honestly guys, you're not really proving anything at small sample sizes. The (FTA * .44) drags on the result. The greater that expression is, the greater the denominator is and thus the smaller the TS% result. The more FTs you shoot, the less effect other shots will have on the result, because that part of the denominator gets biggers. Under TS%, a heavy shooting FT player will get less gain in their % by shooting 2s and 3s. It's right there in the formula. In fact, I've already proven that their TS% will go down with higher volume of 2s and 3s attempted. Under PPS, there is not to drag on 2s and 3s made. They all count the same independent of FTs. They count more that they do under TS%, because they are not effected by FTs. You guys are not proving anything using small samples. Besides, you are not even comparing samples correctly.
Going by what I though was an agreed definition of efficiency -- points per shot attempts -- TS% is more accurate. FGA + .44*FTA is a more accurate formula for shot attempts than FGA. There's no way around that. If you would like to define efficiency in another way, then maybe PPS makes more sense. But we need to settle on a common understanding of what efficiency is.
