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Early Returns on Expected Points Per Shot

US Presswire

US Presswire

This weekend I was finally able to pull together the first round of Expected Points Per Shot (XPPS) numbers for teams, team opponents’ and individual players. If this is your first time reading about XPPS you can find the full explanation at any of those pages linked above. The short explanation is that XPPS is a metric that measures the quality of a team’s shot selection using the expected value of shot attempts from different locations. Trips to the free throw line, shots at the rim and corner three-pointers generally have a higher expected value and so shots taken from those locations will increase XPPS, mid-range jumpers and shots in the paint, but not at the rim, will decrease XPPS. To fully capture how XPPS relates to a team or player’s offensive performance I also compare that number to Actual Points Per Shot and the difference between the two, what I call Shot-Making Difference.

With this first round of numbers in hand, here are a few of the interesting stories from the beginning of the season.

Houston and Denver

On the offensive end, the two biggest shot selection stories last year were the Houston Rockets and the Denver Nuggets. They had the two highest XPPS marks in the league last season, which also happened to be the two most efficient shot distributions since the 2000-2001 season (as far back as I’m able to assemble XPPS numbers). Although they had some stylistic differences – the Nuggets attacked the rim like no team in recent memory, while the Rockets relied more heavily on the three-pointer – they both avoided long two-pointers as much as possible. So far this year, new Head Coach Brian Shaw‘s inside-out offensive approach has had a slash and burn effect on the Nuggets’ shot distribution, dragging them down to an XPPS that is essentially at the league average. The Rockets though, have gone in the other direction:

Screen Shot 2013-11-20 at 10.43.10 AM

The results of Shaw’s new offensive framework in Denver have been discouraging to say the least. Although the idea is to pound the ball inside in order to create open shots on the perimeter, neither piece has really been working as planned. About 10% less of the Nuggets shot attempts have been coming at the rim this season and the percentage of their shots coming from behind the three-point line has stayed flat (although they are hitting a slightly higher percentage of those three-pointers). While the language of the new offense seems to emphasize location and efficiency extremes, in practice it has pushed the Nuggets into the inefficient land of the long two-pointer.

While the Nuggets shot selection has been faltering the Rockets have continued to push boundaries. The three areas of the floor which provide the most efficient scoring opportunities are the aforementioned free throws, shots at the rim and corner three-pointers. Last season 56% of the Rockets’ non-turnover possessions were used from one of those three locations. This season that percentage has climbed to 61%. That’s an absurdly high number which looks even more outrageous when you put it in context. Take a look at how the Rockets’ XPPS from this season compares to every other team going back to 2000-2001.

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The efficiency of the Rockets shot distribution this season is about as far from last year’s record-setting performance as last year’s was from the league average. In terms of efficient allocation of offensive opportunities, they’re not just setting the pace they’re threatening to lap the entire league.

The biggest difference for the Rockets been the increase in free throw attempts – a Free Throw Rate of 0.339, compared to last year’s 0.232. If that 0.339 mark holds up across the entire season it would be the highest Free Throw Rate by any team of the modern era. Most of the increase in free throws can be attributed to the addition of Dwight Howard, but even with his poor shooting for the line they’re still posting a positive Shot-Making Difference and a higher TS% than last year. The Rockets offense certainly looks a little more stagnant this year and their offensive efficiency has basically remained the same because their TO% has gone up alongside their XPPS and TS%.


One of the teams I was really curious to look at in this first batch of XPPS numbers was the Philadelphia 76ers. Last season they ranked dead last in XPPS, a reflection of their love affair with the mid-range jump shot. But a new coach and some fundamental organizational changes have completely flipped the script. So far this season the Sixers have an XPPS of 1.064, well above the league average and the 8th highest mark in the league. This season mid-range jump shots have accounted for just 19.2% of their non-turnover offensive possessions, down from 32.0% last season. As a team their shooting percentages from each location are essentially comparable to last year but they’ve been able to increase their team TS% from 50.9 to 52.4%, primarily by reallocating shots to more efficient locations.

A lot of the improvement has been driven by new faces with very efficient shot-selections, James Anderson and Tony Wroten in particular. But we’ve also seen huge changes in the offensive decision making of Evan Turner, who has increased his XPPS from 0.973 to 1.037, and Spencer Hawes, who has gone from 1.002 to 1.073. Turner’s transition, in particular, has been really important. 34.8% of his shot attempts have been mid-range jumpers this season. That’s the same portion of his shot attempts that are coming at the rim and a huge decline from last season where 46.1% of his shot attempts were long two-pointers. He’s also attempting 5.3 free throws per 36 minutes, double his previous career high. Having an offense that chases the specific spaces on the floor instead of the first space that becomes available is already paying enormous dividends in Philadelphia.


Taking the mantle of worst shot-selection from the Sixers has been the Cleveland Cavaliers. So far their offense has an XPPS of 1.012, worse than what the Sixers put up last season. As a unit they’ve been gradually migrating towards long two-pointers, which now make up 31.8% of their non-turnover offensive possessions. Blame for this migration can be shared among several players. New additions Anthony Bennett, Earl Clark and Jarrett Jack all have an XPPS below 1.000 (league average is about 1.047). Kyrie Irving continues to pull up from mid-range with impunity, posting an XPPS of 1.016, and Dion Waiters‘ XPPS has dropped from the respectable 1.058 he put up last year to 1.027 this season.

Laying the NBA’s SportVU data over the top of these XPPS numbers really helps to highlight the problems. Through November 17th, the Cavaliers had attempted more pull-ups than catch-and-shoot and jumpers, with pull-up jumpers making up 34.4% of their total shot attempts. Jarrett Jack, Dion Waiters and Kyrie Irving combine to average 21.9 pull-up jumpers per game, making those pull-ups at a collective eFG% of 39.0%. Those three are all competent mid-range shooters but that competency is decreased off the dribble and that’s simply far too many possessions to be used in such a fashion for the Cavaliers to be build an efficient offense around.


On the defensive side of the ball the best XPPS allowed belongs to the Orlando Magic. You probably haven’t had a chance to see much of their defense this year, but it ranks 8th in overall defensive efficiency and done quite a bit with the somewhat limited talent they have available. Without a threatening rim protector they’ve still held opponents to just 25 shot attempts per game at the rim, the 4th lowest total in the league. Even more impressive they’ve been able to accomplish that without making significant sacrifices on the perimeter, where their opponents average just 17.3 three-point attempts per game, also the 4th lowest total in the NBA.

Without a big man like Roy Hibbert or Joakim Noah to close off the paint and prevent the cascade of frantic rotations that lead to open shots the Magic have had to rely on length and quickness from the backcourt. They’ve done a terrific job of swarming penetration and still recovering, making their close-outs threatening enough to force misses or swing passes from shooters who looked open just a second before. There is still work to be done to make sure this effort can be sustained across the rest of the season, but it’s been a very impressive start for the Orlando Magic.

Jeremy Lin

We already talked a little about the Rockets shot selection, but it’s worth singling out Jeremy Lin. So far this season his XPPS is 1.114, sandwiched right in between the marks of Kevin Durant and LeBron James. That’s a fairly significant increase from last season, when his XPPS was 1.089. Three-point attempts are making up the highest percentage of his shot attempts since he’s been in the league and his free throws attempts have rebounded in dramatic fashion after bottoming out last season. He seems to feel much more comfortable with his offensive role and responsibilities this season and he’s turning that into a surplus of offensive aggression.

Turning again to the NBA’s SportVU stats we see that Lin is averaging 10.1 drives per game, the third highest average on the league (drives being defined as when a player has ball at least 20ft. from the basket and dribbles to within 10ft.). He’s shooting 64.4% on those drives, second to only Tony Parker and Evan Turner among players who average at least 7.0 drives per game. Looking at his shot chart for the season you can see how his shot distribution has split itself, in the extreme, into shots at the rim from his drives and the spot-up outside shots the Rockets offense creates for him.

Jeremy  Lin Shot Chart from

Jeremy Lin Shot Chart from

As impressive as his shot distribution has been, the rate at which he’s making shots has been equally impressive. To this point he’s averaging 0.213 more points per shot than the expected value of his shot selection, one of the highest marks on the league.

Rudy Gay and DeMar DeRozan

At the other end of the shot-making spectrum we find Rudy Gay and DeMar DeRozan. The Raptors wing duo have posted XPPS numbers of 1.012 and 0.996 respectively, the 6th and 4th lowest marks among the twenty players who have played at least 300 minutes this season with a Usage Rate of 25.0%+. But a low XPPS doesn’t not necessarily preclude a high-usage player from offensive efficiency, both Al Horford and LaMarcus Aldridge have comparable shot distribution patterns to Gay and DeRozan. The difference is that Horford and Aldridge are fantastic mid-range shooters and play in an offense that is balanced around their skill sets. The offensive ecosystem in Toronto is very different.

Gay and DeRozan attempt 35.2% and 48.3% of their shots in the mid-range, respectively, hitting with 35.3% and 32.9% accuracy. When all the numbers are crunched we find that they average 0.090 and 0.006 points less per shot, respectively, than the expected value of their shot selection. That means they are punishing their team with not just an inefficient distribution of shots but also with significant inaccuracy. Interestingly the problem here has much more to do with shot-making then shot selection. I recalculated each player’s TS% using their same exact field goal percentages from each location, but a league average shot distribution and found that it barely moved the needle. Even if they were taking better shots there would still be a tremendous amount of offensive inefficiency in each player’s scoring. Sorry optimistic Raptor fans!

  • Yu-Hsing Chen

    I think you just jinxed Lin there ;)

    But yeah , his season have been extremely good so far. last night non-withstanding.

    • Ian Levy

      Thanks. Can’t tell you how much we appreciate you reading and commenting so consistently. Sorry if it feels like you’re all alone in the comment section sometimes!

  • Andrew Sutton

    Heat are scary as usual. I know basketball is more than shooting but if a team with a high shot making difference/Off rating, then that team could be dangerous in the playoffs i.e. the 2010 Suns.

  • Yu-Hsing Chen

    As suggested by others on the Rockets board, doing this analysis on what team ALLOWS their opponents to do would be very interesting as well (though probably a lot less fun for Rocket fan :P)

    keep up the great work.

  • Dodgson

    Great article! I really love the stuff you guys are doing.

    • Ian Levy

      Thanks for reading and commenting!

  • john

    The Rockets XPPS improvement is the direct result of Daryl Morey’s vision as a GM. Implemented by McHale, I expect the Rockets PPS to lead by far the league as soon as their 3PFG% returns to their mean.

  • Andrew Sutton

    Hey Ian,
    Whats the highest XPPS number have you recorded in your database?
    Harden is my favorite player to watch because of his smart play on offense. Plays a lot like how I play on NBA 2k.

    • Ian Levy

      Just looking at highest XPPS is a little complicated, because you have to account for differences in minutes played, Usage, etc. The highest last season, of players with a 28.0+ Usage Rate, was Harden’s 1.128. The highest this season is Ramon Sessions at 1.145. Harden is second at 1.130. Unfortunately I only have player numbers for the last two seasons but I’m hoping to continue assembling historical numbers soon.

  • MDMH1787

    Do we have any idea why inefficient shot selection is the norm for some players? It seems clear that certain types of play produce better shots and yet the Raptors, for example, seem to refuse to play in the fashion necessary to exploit the math. Is it perhaps the case that defenses “give” more open long-two looks because the defensive players recognize (whether instinctually or otherwise) that “letting” the offense take inefficient shots is good defense? Thanks for all of your work on this site I really enjoy it.

    • Ian Levy

      I really appreciate you reading and commenting and I’m really glad to hear you’re enjoying all the hard work we’ve been putting into the site.

      As to your question, I think it really depends on context. The first thing to think about is that my XPPS numbers don’t paint a complete picture of what’s a good shot. For example, Dirk Nowitzki and Kevin Garnett look like poor decision makers by this metric because they take so many mid-range jumpers but historically those have been very good shot for both players and they come within the framework of the offense. Defenses definitely “give” teams mid-range jumpers and it certainly seems like of all the shots in basketball they require the least amount of effort from the offensive player to create. As to what’s going on in Toronto, I’m as confused as anyone. I think some of it seems to be stubbornness on Gay’s part. He here’s what everyone says about him and it seems like he’s determined to become an impact player on his own terms. As to why the coaching staff hasn’t been able to institute changes, I have no idea.

  • Andrew Sutton

    What other stats have a high correlation with XPPS? My first guess is FT/FGA.

    • Ian Levy

      Definitely FTA/FGA.

      Basically Corner 3s, Free Throws and shots at the rim drive XPPS up. Mid-Range jumpers and shots in the paint, but not at the rim drive it down. Above the Break threes have an expected value that’s essentially the same as the league average XPPS.

      • Andrew Sutton

        If I throw in the effect of a contested defense on the premium shots, is it still better to take those shots than the bad shots even if they are open?

        • Ian Levy

          It depends on player and game situation, but I would need to figure out how to quantify contested defense better to really say accurately.

          • Andrew Sutton

            Great work regardless. I was gonna do this type of work for wages of wins but you beat me to it. I wanted to do a greatest of all time scorers based on the differential.

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