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More On Shot Selection

US Presswire

Last Thursday I put up a post unveiling a new way of evaluating shot selection. The system is called Expected Points Per Shot, and it uses the expected point value of shots from different locations to calculate an expected per shot average for each player. We know that three-pointers on average are more valuable than long two-pointers. We also know exactly how much more valuable on average; 0.280 points per shot. Using that kind of information we can grade each player’s shot selection by how many points they should score on average per shot. That post also has a handy Tableau visualization that lets you play around and explore.

Putting together the original post took so much time that I didn’t have much chance for analysis before putting it up. I promised I would dig into the numbers, so I’m back today with a few interesting observations.

Free Throws

One of the most striking things to rise to the surface of that work was how valuable free throw attempts are. I included free throws as a component of my points per shot numbers, using the standard modifier of 0.44, multiplied by free throw attempts to calculate the number of possessions that ended with a trip to the free throw line. I did the same to include points from made free throws. Although this is an estimate, it allows shooting fouls to be included on a level playing field with other kinds of shots. The expected value of a free throw attempt is 0.759 points (the league average FT% over the past few seasons). That means that the expected value of a trip to the free throw line is 1.518 points (0.759+0.759), much higher than the expected value of a shot attempt at the rim (1.208) or a three-point attempt (1.081).

This realization is particularly important in the context of all the Hack-A-Howard hoopla from the past few weeks. At this point Dwight Howard is shooting 47.7% from the free throw line this season. That means that on any given trip to the free throw line there is a 27.4% chance he scores no points, a 22.8% chance he scores two points and a 49.8% chance he scores one point. In a tight game, with the expiring game clock as a limiting factor it often makes sense for teams to play those odds. But over the course of many, many possessions those odds are not as strikingly stacked against the Lakers.

With the expected value of each of Howard’s free throw attempt being 0.477, a trip to the free throw line has an expected value of 0.954 points (0.477+0.477). That’s more points than the Washington Wizards average per possession this season and within .02 points per possession of the offenses of the Cavaliers, Pacers and Magic. That says a lot about the offensive futility of those four teams, but it also puts Howard’s struggles into a much more rational and reasonable context. Sending Howard to the free throw line may be a smart play in a close game because a team can guarantee a particular scenario where the outcome is somewhat in their favor. But looking at the entire season this is nowhere near the worst case scenario for the Lakers’ offense.

There are plenty of offensive outcomes for the Lakers which net fewer points on average than two free throws for Howard – for example any shot by Steve Blake (0.937 points per shot this season) or Pau Gasol (0.828 points per shot this season) or even Kobe Bryant in certain cases. Over the last two years Kobe has attempted 106 shots from beyond 10ft. with less than five minutes left in the game and neither side ahead by more than five. On those shots he has scored 78 points, or an average of 0.736 points per shot. Any defense familiar with those numbers and given a choice would be much smarter to choose a Kobe jumpshot in a close game than sending Howard to the line. The problem is that the defense is not given an equal choice between two scenarios. They are given the choice between sending Howard to the line and facing the unknown. That could be the relatively beneficial scenario of Kobe forcing a long jumpshot, or it could be a Gasol dunk, a three-pointer for Metta World Peace or sending Kobe to the line. In terms of efficiency, Howard shooting two free throws is actually somewhere in the middle of the Lakers’ menu of offensive outcomes. But it is one the defense can essentially pick and guarantee the odds. Therein lies the advantage.

Shot Selection As A Mechanism For Improvement

The Knicks’ offense has been one of the biggest surprises this year. They currently have the second best ORtg. in the league and the fifth best eFG% at 51.8%. This is a pretty impressive performance for a team that has featured big minutes for J.R. Smith, Raymond Felton and Jason Kidd, all who have career FG%s below 43.0%. One of the big driving forces for their offensive improvement has been their shot selection.

The three most efficient shooting options we’ve found are trips to the free throw line, shots at the rim and three-pointers. By my calculation 69.8% of the Knicks scoring opportunities have come from those three scenarios. Last season that number was just 58.6%. This improved shot selection has come from nearly the entire team. The Knicks have 9 players who have played at least 200 minutes this season. 6 of those 9 have an Expected Points Per Shot value of 0.950 or greater and everyone except Rasheed Wallace and Ronnie Brewer is actually outperforming their XPPS, scoring more points per shot than expected. Simply, the Knicks are making shots because they’re taking the right shots.

Intelligent Design

The Miami Heat are another team which is really using the talents of their players in an efficient shot selection array. The image below shows the placement of Heat players’ who have played more than 200 minutes, taken from last week’s visualization.

The Heat’s three highest usage players, Dwyane Wade, Chris Bosh and LeBron James all have relatively inefficient shot selections, with XPPS marks below 0.900. We can attribute this to the fact that none of the three is a prolific three-point shooter and all rely heavily on mid-range jumpshots, which have a lower expected value. However, each player is scoring at an actual per shot rate much higher than their expected rate. In fact, Bosh and LeBron both average over 1.00 points per shot. All three players shoot at average or better rates on those mid-range jumpers, and also generally outperform the league average at the rim and at the free throw line.

Having your three central players capable of such efficiency levels, without needing to have high-value offensive opportunities created for them, also has a terrific trickle down effect. The three marks along the top of that image represent Ray Allen, Rashard Lewis and Shane Battier. As complements to Wade, Bosh and LeBron each of those three is able to focus on very efficient shot selections, primarily three-pointers. Each is a very good shooter already, and the defensive attention given to the Big Three just makes it even easier for Allen, Lewis and Battier to outperform expectations. Each is averaging at least 1.100 points per shot.

There is still some more work to be done with these numbers. I’m hoping to keep them updated on a fairly regular basis throughout the season, and I’d also like to put some of the numbers together for teams as opposed to just individuals. Hopefully that work will be coming soon. If there’s anything else you’d like to see, or somewhere else you’d like me to take the numbers, just ask!

  • NW

    There are a couple of extra factors that I think affect the hack-a-Howard defensive shot preference over letting Kobe et al. shoot:

    First, sending Howard to the line achieves 3 things for the defensive team from a positional standpoint: (1) It puts the defensive bigs in perfect box-out position, between the offensive rebounders and the hoop. (2) It pretty effectively takes Dwight Howard (I’d assume the most potent offensive rebounding threat the Lakers have) out of the equation, and (3) It puts Kobe, Nash (when healthy) and any other drifting perimeter shooters in a known, relatively static position- the D can go and stand right next to them; the Lakers wings aren’t going to sneak to the corner for an open 3. If Kobe shoots, you’ve got Dwight hovering near the hoop for the putback, someone else slipping down for the open shot, etc. etc. (See this interesting article on the “Kobe Assist”:

    Second, fouls can control the clock. Dwight at the line means that the Lakers aren’t running down 20 seconds in the late game before putting up a shot.

    Finally, breaking up the rhythm and flow of an offense, and getting into Howard’s head a bit seems like a great idea. I’d be surprised if he was master of his emotions, and I could really see him getting down on himself after a few misses, and overthinking/overtrying with even worse results.

    Ultimately, I guess I’d ultimately argue that one would do well to employ some sort of super-complex adjusted metric for shot-selection in the context of a play, rather than simply shot selection as a value of point-scoring-likelihood in a vacuum. Interesting read, in any case.

    • Ian Levy

      Thanks for taking the time to read and comment.

      I didn’t touch on all those variables but I think you’re stating my point in a much more complete way. Hack-A-Howard allows the defense to control the context, and set a huge number of variables in their favor. My point was just that those controlling those variables provides at least as much value as the decrease in efficiency of Howard at the free throw line as compared to other options.

      People have the sense that Howard at the line is this catastrophic offensive action, when in the larger context it’s not nearly as bad as the perception.

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