Last week, I used Hardwood Paroxysm to the story of my own personal obsession with shot selection. I’m of the camp that the quality of shots is one of the biggest factors in a team’s offensive success, an opinion I mean to continue codifying and supporting with evidence. My first contribution to this march forward was the development of Expected Points Per Shot (XPPS), a metric for evaluating the quality of a player or team’s shot selection. XPPS is built on the understanding that not all shots are created equal. A layup is much more likely to go in than a long jump shot. A three-pointer is also less likely to go in than a layup, but if it does go in it earns an extra point. All these trade-offs can be measured numerically. I’ve looked at 13 seasons of NBA shot data and calculated the expected value for shots from different areas of the floor. To calculate XPPS, I take a player or team’s shot selection and overlay those expected values to arrive at an average measure of expected points per shot for that player or team.
I have a few disclaimers before we go any further. The first is that XPPS relies on league averages, which means I use the same expected value on a corner three-pointer by Ray Allen as I do for one by Charlie Villanueva. Obviously this lumps everyone together and doesn’t account for a player’s own innate abilities and tendencies. For that reason I usually compare XPPS to Actual Points Per Shot. This helps us see who is over or under-performing the expected value of their shot selection. Second, we are measuring shot selection only by the expected value of each shot’s location. This doesn’t account for defensive proximity or game situation. Although we will be referring to the quality of shots this way in the aggregate, a corner three-pointer well defended and forced at the end of the shot clock is not necessarily a good shot just because it comes from that location. By the same token, mid-range jumpers have the lowest expected value of any shot location, but may actually be a good shot when a wide open opportunity is created within the flow of a well-structured offense. Also, although I use the phrase ‘per shot’ I include shooting fouls and free throws in my calculations, so ‘per scoring opportunity’ may be a better way of thinking about it.
The numbers for both players and teams can be found at Hickory-High. For me these numbers feel like an important first step to some deeper understandings of offensive efficiency. Over the next few weeks here at Hardwood Paroxysm I’m going to be digging into the numbers, trying to parse out trends and some of those important understandings. One of the first things I thought would be interesting to look at in the context of these XPPS numbers, is the way certain players affect the shot selection and shot performance of their teammates.
Nate Silver, of political analytics fame, put together some research in 2011 that found significant added value from a player like Carmelo Anthony in the way his offensive gravity created easier shots for his teammates. Silver’s research found that most of Anthony’s teammates with the Nuggets posted a significantly higher TS% when they played with Anthony as opposed to when they were on the floor without him. Kevin Pelton of Basketball Prospectus did some more digging and found the shooting effect to be slightly smaller than Silver found, but that Anthony also decreased his teammates’ turnover rates quite a bit.
Using XPPS and Actual Points Per Shot we can further this discussion by looking at how the quality of a team’s shot selection and accuracy change with certain players on and off the floor. The first group of players to look at in this context are high-usage scorers, like Anthony. The prevailing wisdom seems to be that having a potent individual scorer, even one who isn’t particularly efficient, puts pressure on the defense, and creates more space for their teammates. To begin testing that idea, I collected the NBA’s top-20 in Usage Rate and calculated their team’s XPPS, Actual Points Per Shot, and Differential when they were on and off the floor. For the ‘on’ portion I subtracted the player’s own points and field goal attempts to focus the results on their teammates. Here is the raw data:
The table above is sorted by the difference in Team XPPS when a player is on the floor, versus when they are off the floor. I find it incredible that the two players in this group who seem to make the biggest difference in the quality of their team’s shot selection are Jamal Crawford and Raymond Felton, both of whom flamed out spectacularly in Portland last season. It is important to remember that these numbers are subject to all the statistical noise one usually finds in On/Off statistics and are heavily influenced by both the other players on the floor and the quality of backups. However, we aren’t using these numbers to judge the overall quality of a player’s production, but rather to look at what they mean to their team. If data tables aren’t your thing, I’ve also created some graphs to show the numbers above.
The chart below shows the On/Off split for each player in XPPS:
Although there definitely seems to be an effect, only a handful of players made a significant difference in the quality of their team’s shot selection. We could probably attribute many of the small differentials to the difference in quality between a starter and a reserve as opposed to a fundamental shift in offensive approach implemented by a specific player. Of course we also need to look at accuracy and the graph below shows each player’s On/Off split for Actual Points Per Shot:
When you look at the graphs, Felton’s importance becomes even more striking. Although he plays most of his minutes with Anthony, his On/Off XPPS split is +0.056, more than twice that of Anthony’s. That may not seem like a huge number, but again we’re looking at things on a per shot basis. Stretched out over 100 shots, the Knicks’ shot selection is nearly six points better with Felton on the floor.
We see the same thing when we look at accuracy, where the Knicks Actual Points Per Shot is +0.098 with Felton on the floor, nearly triple Anthony’s differential. Again, stretching that out over 100 shots that’s a difference of almost 10 points. In an effort to remove as much noise as possible, I also calculated Jason Kidd’s numbers, since he isn’t included in this high-usage group. The Knicks shot selection is slightly worse with Kidd on the floor compared to when he’s off the floor, a mark they are over-performing but not nearly as significantly as the differential for Anthony or Felton.
The Knicks success and overall offensive efficiency have been a huge surprise, at least to me, this season. I wrote in the summer that I was expecting more of the same from them this season, and that I thought Carmelo Anthony’s Olympic summer would actually reinforce his ball-stopping, product-over-process offensive ways. But Anthony is having a career season, especially with regards to his offensive efficiency. His Actual Points Per Shot is up to 1.194 this season, an increase of 0.145 over last season’s 1.049. Most of that bump is because of his three-point shooting. At this point in the season Anthony has made 42.8% of his 6.3 three-point attempts per 36 minutes, both career-highs by a wide margin. It’s possible that at some point in the season his long-range shooting will regress towards his career averages (see Mayo, O.J.), but his overall efficiency won’t drop too far because he has also significantly improved his shot selection this season. Anthony’s XPPS this season is 1.063, up from last season’s 1.045. When we look at his XPPS only when Felton is on the floor, it jumps to 1.072. That means even if Anthony’s shooting averages regress all the way to league averages, he’ll have improved his efficiency by 0.014 points per shot, or 1.4 points per 100 shots, just by improving his shot selection. There are a nearly infinite number of elements here at play, but clearly Felton is doing some positive things for the Knicks’ overall offensive well-being, helping lead the re-focused charge on efficient offensive choices.
One of the other interesting things that I noticed is that several of the players on this list who had a big effect on their team’s shot selection happened to be effective-passing guards and wings – Felton, Crawford, Nate Robinson, Kyrie Irving. Next week we’ll focus on a different group of players, those with high assist rates, and see if we can tease out their effect on the quality of team shot selection.