Monthly Archives: August 2010

Shot Selection and Efficient Scoring

At the beginning of the summer I wrote two pieces about shot selection of several big time NBA scorers. The posts focused on the apparent habit of certain players to rely on specific types of shots to work themselves into a rhythm. The first piece covered the regular season and the second looked at the same players but over the course of this year’s playoffs.

Since writing these posts, I’ve spent quite a bit of time thinking about what the next step is in looking at this information, and what else can a player’s shot selection tell us about their ability to score efficiently.

An excellent series of posts from Albert Lyu at Think Blue Crew on the value of blocked shots, gave me another idea and another piece of data to factor in. For the second post in this series Lyu calculated the Expected Points Per Shot by location. This information gave me another way to examine a player’s shot selection. Another way to think of Expected Points Per Shot, is the average number of points scored on a shot attempt. For example, over the last 4 NBA seasons, factoring in makes and misses, a field goal attempt at the rim was worth an average of 1.208 points.

Using numbers from Hoopdata’s Shot Location Database, and the Expected Points Per Shot from Lyu’s post I was able to calculate what I am calling Expected Points per 40 Minutes (XPts/40). I began by calculating each players XPts/40 from each area of the floor. To do that I took each player’s per 40 minute field goal attempts from each area of the floor and multiplied it by the expected Points Per Shot for that location. Adding these categories together results in XPts/40. Another way to think about this is, given a player’s per 40 minute shot selection, how many points would he score, shooting the average percentage from each location. The numbers I borrowed from Lyu are below:

  • At Rim – 1.208
  • <10ft. – 0.856
  • 10-15ft. – 0.783
  • 16-23ft. – 0.801
  • 3PT – 1.081
  • I needed to include Free Throws, so I used 0.759 the league average for last season.

This first graph shows these numbers for the players we discussed in my previous posts. Just to recap these were the Top 20 players from last season in terms of field goal attempts per game. (A link to the numbers for the entire league is available at the end of the post.)

Looking at this first graph you can see how many points each player should be scoring for each area of the floor given their per 40 shot selection. Players who rely heavily on scoring from specific areas jump out. Dirk Nowitzki should be getting most of his points from mid-range. Tyreke Evans, Carmelo Anthony and Dwayne Wade should be scoring most of their points at the basket. Danny Granger, Kevin Durant and LeBron James all rely heavily on their 3PT shots to look for scoring.

This next table takes the XPts/40 of each player and compares it to their actual Pts/40 totals.

The Pts/40 Differential shown here gives you a sense of which players are scoring efficiently once their shot selection is accounted for. Dirk Nowitzki shoots a ton of mid-range and long jumpers, but he shoots them extremely well and therefore scores more than should be expected. Kevin Durant is an almost identical case.

On the flip side you can see players like Tyreke Evans and Stephen Jackson who are scoring less than is to be expected. Evans is a poor jump shooter, and despite taking most of his shots at the rim, where he scores at about an average rate, he’s leaving points on the table by not hitting 3PTs and long jumpers. Jackson’s case is the reverse as his scoring drops below the expected level largely because of struggles to finish at the rim.

The graph below combines all the categories we have been discussing into one. For each shot location you can see how many points each player should expect to score given their attempts, how many points they actually scored from that location, and the difference. (Click on the graph to enlarge).

The players we are viewing here don’t demonstrate the full depth of this information. This list is the Top 20 players in the league last season in terms of field goal attempts per game. They take lots of shots because, for the most part they are effective and efficient scorers. Of the 20, only 5 (Gay, Ellis, Evans, Jamison and Jackson) average fewer Pts/40 than should be expected.

Almost all of the players on this list have a clear weakness, an area of the floor where their scoring efficiency drops off. Most of the players also have an area where their scoring efficiency is much stronger than expected. For these players their strengths outweigh their weakness and they score more than should be expected. Gay, Ellis, Evans, Jamison and Jackson are roughly average from the other four zones, and therefore their lack of scoring efficiency in one area drags down their Pts/40 below their XPts/40.

Dirk Nowitzki deserves some credit as the only player on this list who scores more than is to be expected from every area of the floor. In addition, the largest portion of his attempts are on jumpers from 16-23ft., which also happens to be the area of the floor where he has the largest positive differential between his expected points and his actual points. This would appear to be a great indication of a player who understands and maximizes his abilities as a scorer.

When you look at the numbers for the entire league, and at players of more average skills, you can see plenty of individuals being dragged down by poor inefficiency from certain areas of the floor.

For example, Jonny Flynn scores almost 3/4 of a point (-0.7608) less than expected on his 5.1 FGA/40 at the rim. In terms of maximizing scoring efficiency, this information can be viewed in one of two ways: 1) Flynn needs to figure out a way to become a stronger finisher at the basket. Or 2) Flynn should decrease the number of shots he attempts at the rim and focus on areas of the floor where he is more efficient.

You can also see players sticking to areas where they are efficient, and overall scoring more than should be expected. Carlos Boozer has a positive overall point differential of 1.952, averaging 22.7 Pts/40, with an XPts/40 of only 20.7498. This can be attributed to the fact that most of his shot attempts come at the rim and on mid-range jumpers, two areas where scores at an above average rate.

There is obviously more to shot selection than merely a player’s choice of where to shoot from. Defensive matchups, offensive systems, a player’s teammates and a host of other factors influence where his attempts come from. It was even mentioned in the Michael Lewis New York Times article on Shane Battier that some teams are even using defensive scouting reports focused on forcing players to shoot from areas of the floor where they are very inefficient.

While there is much discussion of this at an organizational level, and among bloggers and media, I wonder how much of it is communicated or internalized by the player’s themselves. The common perception is that 3PT’s and shots at the rim are the most efficient ways to score, but does Jonny Flynn know he might be better off shooting jumpers from 10-15ft.? Does Carlos Arroyo know that his point differential on 16-23ft. jumpers is almost the same as on shots from inside 10ft?

If you have some time, sort through the numbers for the entire league. Check out your favorite team or player. Check out players who have certain reputations and see if they hold up. Budget yourself some time though, there’s a lot to see.

XPts Data Set for NBA 2009-2010 Season


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Changing Teams and Making the Hall

With Shaquille O’Neal signing with the Boston Celtics next season, his late-career pattern of transition continues. I have never been a huge fan of O’Neal’s, but have spent some time recently thinking about how this will affect his legacy. He is certainly not the first player to change teams in the twilight of his career chasing a ring, or in his case additional rings. O’Neal’s case does seem extreme as he is now joining his sixth NBA team, and has reportedly burned bridges in each of his previous stops. It’s difficult to remember another future or present Hall of Famer who may not have a single team interested in “claiming” him and his career. Bill Simmons discussed this in a column today, while guessing at some of O’Neal’s motivations entering this season. I decided to put some numbers together and look into it a little more.

I created a list of all current Hall of Famers and a few likely inductees who haven’t become eligible yet. (Gary Payton, Kobe Bryant, Tim Duncan, Kevin Garnett, Reggie Miller, Ray Allen, Paul Pierce, Alonzo Mourning, Dikembe Mutombo and Allen Iverson.) I only counted Hall of Famers who were inducted for their playing careers (No Larry Brown, Jerry Sloan or Phil Jackson). I counted the number of franchises each player had spent time with. If a player was with a team and then returned to that team later in their career, it was counted as only one. Here is what I found:

  • The average NBA Hall of Famer played with 2.61 franchises over the course of their career. This number is skewed by several players who played for a huge number of teams. The mode for my data set was 1, meaning most players spent their entire careers with only one team.
  • 31.07% of players played for 1 team in their career.
  • 25.24% of players played for 2 teams in their career.
  • 21.36% of players played for 3 teams in their career.
  • 9.71% of players played for 4 teams in their career.
  • 4.85% of players played for 5 teams in their career.
  • Totalling these up, we see that O’Neal will have played for more teams than 92.23% of current and likely future Hall of Famers.
  • Only 7 other players besides O’Neal will have played for 6 or more teams over the course of their careers: Dikembe Mutombo – 6, Rick Barry – 6, Elvin Hayes – 6, Walt Bellamy – 6, Adrian Dantley – 7, Bob McAdoo – 8, Moses Malone – 9.

Although O’Neal is not alone in the number of jerseys he has worn, he’s in the extreme minority. I’m too young for any personal knowledge of the careers of many of these players, which may make O’Neal stand out to me even more. Of recent Hall of Fame inductees, and ones who I have actually seen play, none have played for as many teams as O’Neal and none have soured as many relationships along the way as he has. Perhaps this year will be a chance for him to turn things around, but it seems just as likely that this will continue to chip away at parts of O’Neal’s considerable legacy.

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Brain Buster #1

I’ve been working on a couple projects but haven’t been able to get anything up in awhile. I found this Brain Buster last night and it piqued my interest.

A basketball player who makes 80% of his free throws goes to the foul line for two shots at the end of a very close game: His team trails by two points with just 1.7 seconds remaining. If he makes both of his foul shots, the game will go into overtime.

What is the probability that he will make only one of two?


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Site Update 8/6/2010

Things have obviously been slow around here the past few weeks. There have been a lot of big NBA stories, but I just haven’t felt I had anything to say that wasn’t already being said in a hundred different places.

I do have some exciting updates though. I have gone ahead and purchased a legitimate web domain for the site. So you can now reach Hickory High at either or at the brand new! (Don’t forget the hyphen.)

Although there haven’t been many new posts since the beginning of July, I have added a few pages to the Stats Glossary. Pure Point Rating and Basketball Reference’s Play Index have both been added. Check them out, and as always I would welcome any feedback you have!

Finally, I have begun experimenting with Twitter. You can check out my page on Twitter  (@Hickory High) or here on the widget at the main page. We’ll see how this goes for awhile and whether it’s worth the time and effort.

Stay tuned for the conclusion of my Trading for a Championship analysis (hopefully to be finished sometime next week) and some season previews as we move into September.


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