NBA HD: The Sustainability of Shooting

I get lost in shot location data.  And I mean that in a good way.

I have been amusing myself with the shot location tables at Hoopdata all season and yet, I feel as though I’ve barely played around with it.  It still has that new car smell.

For instance, I noticed yesterday that Beno Udrih is shooting 71.8 percent on layups this season.  That’s on par with Steve Nash as the best conversion rate among point guards and worlds better than the average point guard (56.8 FG%).  I mean, Beno’s mark is literally double that of Derek Fisher (34.4 FG%, worst in NBA) .  Did this come out of no where or has Beno always been automatic in the lane like this?  I ventured over to his player page and discovered that he was a 53.7 percent shooter in his previous three seasons from this same area.  Evidently, this is a new development for the Slovenian but the fact alone lacked context.  What I mean is, how often do point guards experience a surge in their ability to finish at the rim? Is a 55 percent finisher always a 55 percent finisher? Clearly not in the case of Mr. Udrih but what’s the going rate?  And aside from finishing at the rim, do long jumpers maintain their ability to shoot long jumpers year in and year out?

Armed with my finest excavating tools, I dug in.  At Hoopdata, we have four seasons worth of shot location information dating back to the 2006-07 season.  For the uninitiated, we separate the shooting repertoire into 5 zones: at rim (layups, dunks, and tip-ins), short (<10 feet), mid (10-15 feet), long (16-23 feet), and three-pointers.  Since I was interested in the shooting abilities, I wanted to track the year-to-year field goal percentages for players.  But we don’t want to expose ourselves to the dangers of small sample sizes so if a player wanted his season to be submitted into the study, I required him to shoot 50 attempts in the zone.  If he did that, he’s welcome to the party.

For this study, the statistic of choice is correlation, how strongly one number is related to another.  If a player shoots well from 3-pointers, we assume that they will tend to shoot well from 3-point land the following season, unless that player’s name is Jannero Pargo.  We’ve never dabbled in 2-point land since the box score doesn’t differentiate between a slam dunk and a 22-footer.  Luckily, by using play-by-play data we can begin to explore the uncharted area.  Welcome to the New World.

After breaking down the numbers, I found that shooters in this sample had a stronger year-to-year correlation in at rim shots than 3-point shots.  In other words, the ability to finish at the rim (as measured by at rim FG percentage) is more strongly linked year-to-year than 3-point field goal percentage.  In fact, the correlation coefficient for the 671 player season tandems in the sample was +.61 which, depending on which statistics resource you consult, is widely regarded as a strong relationship (stronger closer to +-1, weaker closer to 0).   Here’s a graph depicting the year-to-year relationship for at rim percentage:

We already knew there was a strong year-to-year correlation (r = +.610) but perhaps it helps to conceptualize this visually.  You can see how much an outlier Beno Udrih’s year is as it’s separated from the pack at the trendline.  It’s not quite the biggest difference year-to-year but it’s close.  I’ve provided the trendline equation as well as the r-squared value for those who are interested.

Putting Beno and his at-rim percentage, let’s move further away from the basket and look at the relationship of short shots (less than 10 feet but not including at rim shots).

This relationship isn’t nearly as closely knit as the layup version.  For this area, the correlation was just +.200 which is a pretty weak, although it isn’t a completely random association.  Judging by the r-squared value, a player’s short field goal percentage only explains about four percent of the variance in the next year’s success rate.

This shot location typically contains long hook shots, floaters, runners, and short jumpers which aren’t high percentage shots and success rates tend to vary due to the number of shot varieties.  Andrew Bogut takes by far the most short shots in the league (6.0 per game) and even he can only convert at 44.0 percent which is slightly below the league norm.  Perhaps we love a player with a great floater because of the high difficulty and general inconsistency.  Additionally, the more scattered distribution might be a result of the relatively low frequency of shots from this area.  Remember though, to be admitted into this highly exclusive study, the player must have shot 50 shots in the area in both years to be included.

How about those shots that are taken between 10 and 15 feet away from the hoop? Are they consistent year-to-year like layups? Let’s take a look.

If you have a sharp eye, you can tell that the mid range shot is more repeatable shot than those in the <10 feet range, but not quite as strongly linked as shots at the basket.  With a correlation coefficient of +.371, we can interpret this as a moderate positive relationship.  Few players excel at the mid range shot and most of the time, it’s secondary in preference.  You can see on the graph that a 50+ percent campaign isn’t a guarantee for an encore in the following year.  On the flipside, a poor year doesn’t mean the end of the world.  Consider that Ben Gordon has shot 60.3 percent this year from 10-15 feet despite shooting just 35.9 percent last year in Chicago.  You can see him all alone at the top straddling directly below the “FG” in the chart title.

So, the mid range isn’t as correlated year to year as at rim shots but it’s stronger than short shots.  What about the least efficient shot in the game, the long two?

Interestingly enough, the long two doesn’t show as much predictability as the mid-range or at rim shots.  With a correlation of .333, the long two is not only inefficient but it’s also inconsistent year-to-year when looking at this sample of 571 observations.  As Howard Beck of the New York Times noted earlier this year, David Lee improved his long jumper greatly since last year and currently, the Knicks center is shooting at an impressive 45.6 percent from 16-23 feet.

Let’s step behind the line and look at 3-pointers.  This study has probably already been done since 3-point data has long been available before but I’ll replicate it here for comparative purposes.

This chart illustrates the effective field goal percentage of 3-point shots, which isn’t the same measurement as the other shots (the data in the set were measured by eFG% for threes).  The correlation here was +.394 which stands as a moderate relationship.  General Managers would benefit from teasing out the true talents from 3-point range and avoid the wild fluctuations.  Remember Corey Maggette’s 57.6 eFG% from 3-point range in his contract year in Los Angeles? Yeah, he’s one of the outliers (he shot 38.0 eFG% in the following year in Golden State and 36.6 percent this year).  The 3-point shooter the Warriors thought they signed hasn’t arrived quite yet.

So why do this stuff? Projection systems have long used 2-point, 3-point inputs and historical similarity comparisons to predict field goal percentage and thus points per game for every player.  Dividing the inputs into smaller buckets can glean more information on true shot ability.  We observed a very weak correlation for short (<10 ft) shots in their year-to-year relationship so if a player enjoys a remarkable year from less than 10 feet, we can regress that more to the mean.  For example, Derrick Rose this year is shooting 58.2 percent (78-134) from short range, which is a massive improvement from his 47.0 percent mark last season.  Will he be able to repeat that performance next year?  Looking at the <10 feet graph above, there are plenty of players that regressed back to more normal levels in the following year.  That’s something to consider.  If we were to solely look at Derrick Rose’s two-point game, we would miss this important piece of information.

You might be wondering the relationships of different types of players. For example, since big men dunk more, wouldn’t they have a higher correlation than point guards who rely for the most part on runners and layups in traffic?  Returning to Derrick Rose, how do short shots correlate for point guards? Well, I’m glad you asked.  I broke down each shot location zone into 5 smaller parts: point guards, shooting guards, small forwards, power forwards, and centers.  I don’t normally like to limit myself to the traditional positions but it served as a way to analyze further into subsets.

Click your zone of choice below to see the five bite-sized graphs.

At RimShortMidLongThrees

If you just want the correlations, I’ve provided the table below for your perusal.

Seth Carstens