Replacement efficiency thoughts
Posted: Thu Oct 11, 2012 9:24 pm
Hi, I recently wrote an article about average efficiency and "replacement" efficiency, due to a problem I see with calculating total TS%. (http://asubstituteforwar.com/2012/10/09 ... mparisons/)
In short, one problem with combining efficiency and volume is that you get situations where eg. In 2011, Tyson Chandler takes 7.26 shots (FGA+0.44*FTA) at .697 TS% and Derrick Rose takes 22.74 shots at .55 TS%, with the league average at .542. Now an obvious way to measure the "value" of this is to multiply their volume of shots by league average TS%, then at their efficiency, and calculate the difference. The "expected points" produced (average TS% + player's volume) of Chandler's season is 3.9 pts, while at his TS% he produces 5.1 pts, for a difference of +1.2. Rose using the same method, has an expected points of 12.3 and real points of 12.5, for only a +0.2 difference. Because he's only marginally above league average in TS% even his massive volume of shots doesn't amount to much. Likewise, Nene adds +1.27 pts using this method in 2011, while superstar scorers Melo does +0.35 and Bryant +0.14.
From this there's usually two ways to take it, to say Chandler/Nene are better scorers than Rose/Kobe/Melo (as WP does in their calculations and leading to conclusions like 2011 Matt Barnes is better than 2011 Kobe), or to protect high volume, average shooting percentage has a lot of value because it makes teammates better enough to outweigh this.
However looking deeper outlined where the problem is IMO. Using 2011 Rose as a test case and hoopdata, I isolated 3 areas of efficiency/volume
Shots at the rim or FT line - Combined 9.34 shots a game, .723 TS% (Great shots)
3pt shots - 4.8 attempts a game, .498 TS% (Slightly below average efficiency)
2pt jumpshots - 8.6 shots a game, .395 TS% (Bad shots)
Essentially what is happening here is this. Rose just counting his shots at the rim and FT line, is producing an even greater mix of efficency and volume than Chandler and Nene's total scoring package (Rose "produces" +1.86 pts using the same calculation as Nene and Chandler's, in this shot area) . The reason his TS% drops all the way down to .55, is that he has a number of slightly below average TS% 3pt shots, and way below average 2pt shots. If strictly comparing Rose to league average TS%, he is being "punished" for taking those shots. Meaning it counts them as hurting his team by taking them, assuming the "replacement for Rose's FGA" works out to league average TS% (.542), enough to cancel out a pretty high volume of excellent shots he creates at the rim and FT line. It basically says "Well this Rose guys creates a lot of efficient shots, but you pay a price for it by putting up with his < .40 TS% shots"
IMO this is where the problem is. Because as I see it, Rose being on the team actually decreases the number of bad, 2pt jumpshots his team has to take. You take Rose off the team and the offense becomes a lot easier to guard. The team would have more trouble getting points at the rim/FT line, not only because he is the best at getting them, but because plays would be defended more tightly without having to help on Rose. Likewise the 3pt shooters would be guarded more. As a result they would likely struggle to find offense, ending in a lot of plays with the only thing they can get, mid-range jumpers.
Thus there is a pretty significant difference between what the stats say and what is happening. The reliability of the TS% stat as a whole is based on Rose being responsible for every shot's %. That a great shot is because he's there and so is a bad one. Thus Rose not playing, removes his great shots and removes his bad ones, and replaces them with league average shots (.542), assuming that's what we're comparing it to. But IMO Rose is more responsible for the great shots he creates at the rim and FT line than he is for the bad 2pt shots he's forced to take. The Bulls won't take those 2pt shots because Rose is on the team, they take them because their offense isn't good enough to avoid taking them. They are a necessary evil from a team perspective, not an individual perspective. Every team HAS to take 2pt jumpers, even everyone knows now how less efficient they are than 3s or at the rim, because when you can't get a shot at the rim or from 3, you go to the next available option. If Rose hypothetically had a massive positive increase in his team's number of "great shots" but a neutral impact on his team's number of "bad shots", this is a very different result than what TS% says about his scoring efficiency, instead of average he should be significantly positive. The idea of CAUSE is very important here. If Rose does not equally cause all the different types of shots he makes, should his total TS% be treated as if he's the cause for it?
So my idea was to drop the comparative TS% much lower. Basically I now compare every shot to replacement efficiency, which I determine is basically a long 2pt jumpshot with a player's hand in his face, basically the type of shot you take when your offense hasn't created anything and you just have to take a shot. Since 2pt jumpshots are typically around 39% for league average including the open shots and Dirk/Durants of the world, dropping it to 30-33% or so for a replacement shot made sense. I believe this fixes the problem for a guy like Rose pretty well. When he takes a midrange shot that goes in 40% of the time, a shot that we determine is caused not by Rose individually but as a necessary evil by the team, he not only isn't punished for it, but gets a slight boost if he hits it at .40 TS% vs .33 TS%. When he takes a .70 TS% shots, that of course gives a massive boost to his efficiency. Essentially it's hypothesizing that if Rose was replaced by a replacement talent, the team would take 23 stanky midrange jumpers in place of his FGA, and that this is really the difference of his shots on the team - and Rose is credited with every shot above stanky jumper, while when he takes a stanky jumper, it's a "the Bulls take that shot without him too" scenario. This obviously isn't a perfect assumption, hypothetically freeing up possessions could help other players drive to the rim and pick up more great shots than if they were playing with Rose, thus replacing his shots at a cleaner clip than .33. But I feel in general, players are rarely going to be producing at a worse level offensively because they're beside a teammate. There may be cases such as your Dantley, Maggette, Tyrekes, but that's something we just have to look out for, such as the fact that most of us know Dantley and Maggette aren't as valuable as their high TS% with the way we look at it now
Anyways, here are the numbers I got for Chandler, Nene, Rose, Melo, Kobe using .33 instead of .54
Tyson Chandler – 7.26 shots converted at .33 TS% sets a replacement conversion for those shots, at 2.40 pts. At his TS% of .697 he creates 5.06 points, a difference of +2.66 from replacement conversion.
Nene – 11.1 shots, replacement rate of .33 TS% would score 3.66 points, while Nene’s TS% of .657 scores 7.29, a +3.63 margin
Derrick Rose – 22.74 shots, replacement rate of .33 TS% would score 7.5 pts, Rose’s efficiency of .55 TS% scores 12.5, a +5.0 rate
Carmelo Anthony – 22.98 shots, replacement rate of .33 TS% would score 7.58 pts, Melo’s efficiency of .557 TS% scores 12.80 pts, a +5.22 difference
Kobe Bryant – 23.1 shots, replacement rate of .33 TS% would score 7.62 pts, Bryant’s TS% of .548 scores 12.66, a gap of +5.04.
Although it's playing towards a pre conceived bias/wanting to find a stat that makes Rose, Melo and Kobe's scoring vs Chandler/Nene's "look right", I think these numbers come out very well. They also fit well with PW better than the other ones, with 2.7 Ws per point putting Rose, Melo, Bryant at 13+ and Chandler/Nene at 7-8+
I also pointed out at the end of the article how Miller 91 (17.4 shots at .65 TS%) still ends up more valuable than say 02 Iverson (32 shots .489 TS%), so players can still benefit a lot from efficiency at a much lower volume. The gap between Miller and Iverson is very close overall though throughout their careers, with Iverson 01 topping 91 Miller and I assume his other seasons. Iverson was likely creating almost exactly as many great shots as Miller, while taking like 15 more bad ones, which arguably would've been taken by other players anyways (Though Iverson is a candidate for someone who's ballhoggery plausibly increased his team's number of bad shots, though with their poor talent level, I somewhat doubt it. Maybe on very early Sixers or the Nuggets)
Any thoughts on this idea?
In short, one problem with combining efficiency and volume is that you get situations where eg. In 2011, Tyson Chandler takes 7.26 shots (FGA+0.44*FTA) at .697 TS% and Derrick Rose takes 22.74 shots at .55 TS%, with the league average at .542. Now an obvious way to measure the "value" of this is to multiply their volume of shots by league average TS%, then at their efficiency, and calculate the difference. The "expected points" produced (average TS% + player's volume) of Chandler's season is 3.9 pts, while at his TS% he produces 5.1 pts, for a difference of +1.2. Rose using the same method, has an expected points of 12.3 and real points of 12.5, for only a +0.2 difference. Because he's only marginally above league average in TS% even his massive volume of shots doesn't amount to much. Likewise, Nene adds +1.27 pts using this method in 2011, while superstar scorers Melo does +0.35 and Bryant +0.14.
From this there's usually two ways to take it, to say Chandler/Nene are better scorers than Rose/Kobe/Melo (as WP does in their calculations and leading to conclusions like 2011 Matt Barnes is better than 2011 Kobe), or to protect high volume, average shooting percentage has a lot of value because it makes teammates better enough to outweigh this.
However looking deeper outlined where the problem is IMO. Using 2011 Rose as a test case and hoopdata, I isolated 3 areas of efficiency/volume
Shots at the rim or FT line - Combined 9.34 shots a game, .723 TS% (Great shots)
3pt shots - 4.8 attempts a game, .498 TS% (Slightly below average efficiency)
2pt jumpshots - 8.6 shots a game, .395 TS% (Bad shots)
Essentially what is happening here is this. Rose just counting his shots at the rim and FT line, is producing an even greater mix of efficency and volume than Chandler and Nene's total scoring package (Rose "produces" +1.86 pts using the same calculation as Nene and Chandler's, in this shot area) . The reason his TS% drops all the way down to .55, is that he has a number of slightly below average TS% 3pt shots, and way below average 2pt shots. If strictly comparing Rose to league average TS%, he is being "punished" for taking those shots. Meaning it counts them as hurting his team by taking them, assuming the "replacement for Rose's FGA" works out to league average TS% (.542), enough to cancel out a pretty high volume of excellent shots he creates at the rim and FT line. It basically says "Well this Rose guys creates a lot of efficient shots, but you pay a price for it by putting up with his < .40 TS% shots"
IMO this is where the problem is. Because as I see it, Rose being on the team actually decreases the number of bad, 2pt jumpshots his team has to take. You take Rose off the team and the offense becomes a lot easier to guard. The team would have more trouble getting points at the rim/FT line, not only because he is the best at getting them, but because plays would be defended more tightly without having to help on Rose. Likewise the 3pt shooters would be guarded more. As a result they would likely struggle to find offense, ending in a lot of plays with the only thing they can get, mid-range jumpers.
Thus there is a pretty significant difference between what the stats say and what is happening. The reliability of the TS% stat as a whole is based on Rose being responsible for every shot's %. That a great shot is because he's there and so is a bad one. Thus Rose not playing, removes his great shots and removes his bad ones, and replaces them with league average shots (.542), assuming that's what we're comparing it to. But IMO Rose is more responsible for the great shots he creates at the rim and FT line than he is for the bad 2pt shots he's forced to take. The Bulls won't take those 2pt shots because Rose is on the team, they take them because their offense isn't good enough to avoid taking them. They are a necessary evil from a team perspective, not an individual perspective. Every team HAS to take 2pt jumpers, even everyone knows now how less efficient they are than 3s or at the rim, because when you can't get a shot at the rim or from 3, you go to the next available option. If Rose hypothetically had a massive positive increase in his team's number of "great shots" but a neutral impact on his team's number of "bad shots", this is a very different result than what TS% says about his scoring efficiency, instead of average he should be significantly positive. The idea of CAUSE is very important here. If Rose does not equally cause all the different types of shots he makes, should his total TS% be treated as if he's the cause for it?
So my idea was to drop the comparative TS% much lower. Basically I now compare every shot to replacement efficiency, which I determine is basically a long 2pt jumpshot with a player's hand in his face, basically the type of shot you take when your offense hasn't created anything and you just have to take a shot. Since 2pt jumpshots are typically around 39% for league average including the open shots and Dirk/Durants of the world, dropping it to 30-33% or so for a replacement shot made sense. I believe this fixes the problem for a guy like Rose pretty well. When he takes a midrange shot that goes in 40% of the time, a shot that we determine is caused not by Rose individually but as a necessary evil by the team, he not only isn't punished for it, but gets a slight boost if he hits it at .40 TS% vs .33 TS%. When he takes a .70 TS% shots, that of course gives a massive boost to his efficiency. Essentially it's hypothesizing that if Rose was replaced by a replacement talent, the team would take 23 stanky midrange jumpers in place of his FGA, and that this is really the difference of his shots on the team - and Rose is credited with every shot above stanky jumper, while when he takes a stanky jumper, it's a "the Bulls take that shot without him too" scenario. This obviously isn't a perfect assumption, hypothetically freeing up possessions could help other players drive to the rim and pick up more great shots than if they were playing with Rose, thus replacing his shots at a cleaner clip than .33. But I feel in general, players are rarely going to be producing at a worse level offensively because they're beside a teammate. There may be cases such as your Dantley, Maggette, Tyrekes, but that's something we just have to look out for, such as the fact that most of us know Dantley and Maggette aren't as valuable as their high TS% with the way we look at it now
Anyways, here are the numbers I got for Chandler, Nene, Rose, Melo, Kobe using .33 instead of .54
Tyson Chandler – 7.26 shots converted at .33 TS% sets a replacement conversion for those shots, at 2.40 pts. At his TS% of .697 he creates 5.06 points, a difference of +2.66 from replacement conversion.
Nene – 11.1 shots, replacement rate of .33 TS% would score 3.66 points, while Nene’s TS% of .657 scores 7.29, a +3.63 margin
Derrick Rose – 22.74 shots, replacement rate of .33 TS% would score 7.5 pts, Rose’s efficiency of .55 TS% scores 12.5, a +5.0 rate
Carmelo Anthony – 22.98 shots, replacement rate of .33 TS% would score 7.58 pts, Melo’s efficiency of .557 TS% scores 12.80 pts, a +5.22 difference
Kobe Bryant – 23.1 shots, replacement rate of .33 TS% would score 7.62 pts, Bryant’s TS% of .548 scores 12.66, a gap of +5.04.
Although it's playing towards a pre conceived bias/wanting to find a stat that makes Rose, Melo and Kobe's scoring vs Chandler/Nene's "look right", I think these numbers come out very well. They also fit well with PW better than the other ones, with 2.7 Ws per point putting Rose, Melo, Bryant at 13+ and Chandler/Nene at 7-8+
I also pointed out at the end of the article how Miller 91 (17.4 shots at .65 TS%) still ends up more valuable than say 02 Iverson (32 shots .489 TS%), so players can still benefit a lot from efficiency at a much lower volume. The gap between Miller and Iverson is very close overall though throughout their careers, with Iverson 01 topping 91 Miller and I assume his other seasons. Iverson was likely creating almost exactly as many great shots as Miller, while taking like 15 more bad ones, which arguably would've been taken by other players anyways (Though Iverson is a candidate for someone who's ballhoggery plausibly increased his team's number of bad shots, though with their poor talent level, I somewhat doubt it. Maybe on very early Sixers or the Nuggets)
Any thoughts on this idea?