A Substitute for War

Basketball philosophy

Stats Tuesday: Should “replacement efficiency” be used instead of league average efficiency, in NBA comparisons?

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Derrick Rose at a promotional appearance.

The value of Derrick Rose’s efficiency in his MVP season is questioned by the advanced stats community (Photo credit: Wikipedia)

A hot topic among basketball nerds is what to do with players who shoot either a league average efficiency or a below average one. Our instincts tell us a player who shoots an average shooting efficiency when he has teammates who’s efficiency is well above average, is a problem. Because it indicates the player could be passing the ball more to these more efficient players, thus raising his team’s efficiency. It indicates that if the team’s efficiency is above league average, that the credit for this should be relegated to the players taking above average shots in efficiency, not the one taking a ton of possession at an average efficiency that doesn’t move the meter.

To use an example, in the last non-lockout year (2010-2011) league average True Shooting Percentage/TS% (incorporating 3s and FTs, essentially creating a points per shot metric) was .542. The MVP, Derrick Rose, had a TS% of .550. Kobe Bryant’s score was .548, Carmelo Anthony’s .557. They are considered superstar scorers in this season because of their volume points per game. But using a strict model of comparing volume and efficiency can create some shocking results. Take the two examples of Tyson Chandler and Nene, both not known for scoring talent, but among the league leaders in efficiency in 2010-2011. Chandler takes 7.26 shots a game in the regular season on the Mavericks (using the calculation FGA + 0.44*FTA) at .697 TS%. Multiplying Chandler’s volume of shots (7.26) times league average efficiency for points per shot (.542 TS%) adds up to 3.94 points. At Chandler’s real efficiency (.697) he scores 5.06 points, for a margin of approximately +1.12 points from average. Nene likewise has 11.1 shots at .657 TS%, using the same calculation as with Chandler he ends up adding +1.27 points compared to what his shots taken at average efficiency would create. However look at what happens when the same calculation is done with Rose, Melo and Bryant. Rose, taking 22.74 shots would create 12.3 points if had shot at league average efficiency, while at his real efficiency of .55, creates 12.5 points, a whopping difference of +0.2 in the points column. Carmelo, using 22.98 shots a game at .557 TS%, using the same calculation ends up adding about +0.35 pts compared to if those shots had been taken at an league average level, while Bryant at 23.1 shots converted at .548 TS%, ends up adding a measly +.14 points compared to the average conversion of those shots. All 3 of Rose, Melo and Bryant’s scores not only trail Chandler and Nene’s numbers, but they’re not even in the same ballpark.

This is why statistical attempts to quantify scoring have met such difficulty. Because any comparison to the league average shooting efficiency, is going to run into results indicating high efficiency, low volume players having more value than high volume, average efficiency ones. A good example is the site Wages of Wins (specializing in “Wins Produced”) recently publishing an article saying the Lakers would be better with Matt Barnes instead of Kobe Bryant on their team, because Kobe’s league average scoring doesn’t have value in a pure statistical model using methods like the above comparisons between Chandler and scoring stars.

The most obvious retort to this is that players like Bryant, Rose and Carmelo make their teammates efficiency vastly better by drawing defensive attention and space to themselves and off of them. But is this a good enough explanation for the difference between what the stats say (that their scoring has negligible impact on the game) and what we want to believe (that it has a massive impact on the game in favor of their team)? It still doesn’t feel right to treat those PPG numbers as without value.

This brings us to Player Efficiency Rating (PER), which is interesting because it generally seems to pass the sniff test in regards to ranking players – Meaning the players who are obvious superstar talents are around 25 in the score, all-stars are around 20, average players around 15 and below average players at 10. Very few rank in places or groups they’re not supposed to. What’s interesting about PER is just how low the threshold player’s shooting % has to cross for it to raise his score. On 2pt shots it raises his score as long as he’s above about 30%, on 3pt shots about 21%. This seems bizarre with how we normally feel about shooting percentages. A player with a TS% of .35 should be the worst in the league, let alone his team efficiency wise, so how can we believe in a stat that says those shots are helping a team? It gives a player a higher score for almost any increase in volume of FGA, even if at a brutally low percentage?

Yet there might be more truth to using thresholds this low than meets the eye. An important thing to remember about TS% is that because it is points per shot, when you see .54 TS%, it means for a 2pt shot to break that threshold, it has to go in 54% of the time. This is quite high. According to Hoopdata.com, in 2010-2011 shots at the rim had an efficiency of .641, shots from 3-9 FT .390, shots from 10-15 FT .393, 16-23 FT .394, and from 3 .538. The best shots in the game are at the FT line, where the average is .763. But essentially, every jumpshot in the game has a league average conversion below league average TS% – Even 3s, albeit they are much much closer than any 2pt jumpshot.

The league knows 2pt jumpshots are less efficient than shots at the rim, FT line or from 3 by a massive margin. 2pt jumpshots are seen as an option you take when those other efficient shots aren’t available. Put it this way, all teams are trying to increase their volume of shots at the rim and from 3 at all times. But when the defensive team “wins out” on a play, they can prevent the offense from getting any of these shots clean off, thus forcing the team to take a 2pt shot.

That’s why it may be interesting to look at what a “replacement” shot is instead of an average shot. Let’s call a replacement shot generally the worst type of a shot a team is going to get in a game. While the conversion of these shots is already poor and around 39% according to the above hoopdata splits, that number includes open 2pt shots by great midrange shooters – In reality, the worst kind of 2pt shot is by a mediocre to weak shooter, who’s contested. Instead of 39% conversion rate, it makes sense to say this shot likely goes in 30-35% of the time.

Thus what if we measured a player’s shots vs these replacement levels instead of the average? For example, take Derrick Rose. Within his 22.74 shots a game in 2011, according to hoopdata 6.3 of his field goal attempts were at the rim, which he converted at 60%. He took 6.9 FTAs a game at 85.8%. Added together, this is about 9.34 shots a game at .723 TS%. This is essentially what Nene and Chandler are doing offensively. However, the reason Rose’s TS% drops all the way to .55 is his midrange shooting. He takes 2.4 shots from 3-9 FT at .397, 1.7 shots from 10-15 FT at .420, 4.5 shots from 16-23 FT at .380. In total, he takes 8.6 2pt jumpshots a game at .395 TS%. He also takes 4.8 3s at .498 TS%, a better percentage but still one far below his TS% at the rim and FT line and below league average. In comparison to Nene and Chandler, what happens is Rose is penalized for taking so many shots below league average in efficiency bringing him to an average number overall in efficiency.

This is where the problem is. Because this calculation indicates that Rose is increases his team’s number of “bad” shots, or essentially every type of jumpshot, but particularly 2s. It indicates that if Rose didn’t take those shots, all of his 2pt shots (.395 TS%) and 3pt shots (.498 TS%) would be replaced with league average ones (.54 TS%), thus increasing his team’s overall efficiency. This cancels out all of his “good” shots.

But this isn’t true. In reality, we can use logic to deduce that Rose actually decreases, not increases, the number of “bad” shots his team takes. Without Rose, the 2011 Bulls’ offense would find themselves “beat” on a lot more plays by the defense, meaning they’d have to settle for the best shot available, which on many cases would be a 2pt jumpshot by players like Luol Deng and Carlos Boozer. Missing a player to create good shots at the rim, or to penetrate and kick to open shooters, would decrease the volume of these good shots and increase the volume of 2pt jumpshots. Or put it another way: Rose is the individual cause of almost all the “good” shots he creates at the rim and FT line, as well as the shots he opens for teammates. He is not the cause for bad, 2pt jumpshots. The cause for bad 2pt jumpshots is just what happens to basketball teams when they don’t have enough talent to secure a great shot every time down the floor. Rose playing for the Bulls decreases how many bad shots they need to take. But penalizing Rose for taking a high amount of 2pt jumpshots at a sub .40 TS% level, would only  make sense if Rose taking those shots was increasing the amount of bad shots they took.

By using replacement efficiency instead of average efficiency, a lot of this can be fixed. Now when Rose takes a shot at a .70 TS% clip, he is rewarded for it by it raising his shooting percentage – But if he takes a shot that goes in 33% of the time, he is not penalized for it, because he is simply taking a shot that the Bulls would’ve surely been forced to take anyways, assuming taking Rose off the team decreases their number of good shots and increases their number of bad ones.

Fascinatingly, look at what using replacement efficiency does to the statistical comparison between Chandler, Nene, Melo, Bryant and Rose – the only difference between this and the previous calculations is using .33 TS% and not .54 TS% for what they are compared to:

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.

This indicates Chandler and Nene have offensive value to their scoring, but the superstar wings have more – especially considering this doesn’t take into account how they make their teammates better with the defensive attention they draw.

Does that mean high end efficiency isn’t value? Nope, it’s still extremely important. Take the examples of Reggie Miller and Allen Iverson. Iverson in 2002, averages 32.11 shots a game, which .33 TS% would normally create 10.60 pts with. Iverson’s brutal .489 TS% that year creates 15.70 pts, a difference of +5.1 over the replacement score. Reggie Miller in 1991 meanwhile only takes 17.4 shots a game, which with .33 TS% leads to 5.74 pts. His TS% however was an insane .650, which with his shots volume, leads to points created of 11.31, a +5.57 difference over the replacement value. This is an example where Reggie taking less shots but at a higher volume, does in fact check out better statistically against replacement value, than Iverson’s unconscious shot chucking. However, one could defend Iverson ranking at least close to Reggie in this year (and 2001 Iverson ranks above 1991 Miller in the stat) by saying this – That Iverson creates as many efficient shots as Miller, Iverson’s coming primarily at the rim and line and Miller’s from 3 or at the rim/FT line – it’s just Iverson takes far, far more of his team’s “bad shots”, meaning 2pt jumpshots, than Miller does. But if the Sixers were already going to take these bad shots with or without Iverson, what really matters is the good shots he added to the team, because he’s not responsible for the bad ones.

Of course, it is possible for a player to be so bent on taking bad 2pt shots that he increases his team’s volume of them while being on the court. However in the modern NBA it’s hard to imagine this player keeping favor with his coaches for doing this, unless he’s providing other offensive contributions like Iverson was to the Sixers. If the player is solely taking low percentage 2pt jumpshots, without counterbalancing it with efficient shots at the rim, FT line, or from 3? Well that should be reflected in his shooting stats matching his 2pt percentage in the mid 30s, thus proving his offensive production is no higher than replacement level.

Finally, I think a thing to take from all this is that it’s really hard to get a high percentage shot in the NBA. Many players if defended well enough, could not score at more than a 30-35% clip. It’s because of the stars and the attention they draw that the average TS% is as high as .54. On a random note, I remember the first time I went to a live hockey game (haven’t been to a basketball one yet) with seats near the ice and realizing “Wow, making offensive plays is REALLY hard for these players, they’re draped by defenders if they try to do anything”, which is not an impression I could get from TV. If we’re trying to compare a star’s production to replacement production, assuming that player can contribute points at .54 TS% is a high number – only great players can consistently create shots that efficiency. In a way, comparing players to replacement TS% instead of average TS%, more accurately reflects that it’s not a given to get anything more than a bad shot if a star had passed the ball to someone else on his team.

By Julien Rodger


Email: julienrodger@gmail.com (Send me a question, if I get enough I’ll answer them in a mailbag)

Written by jr.

October 9, 2012 at 10:32 am

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