Adjusting (and projecting) Three Point Shooting Statistics
by Bill Goldblatt
Statistically, three point shooting is a tricky subject. According to sound logic, a player’s ability to shoot a given percentage is likely to be impacted by a variety of factors, perhaps none of which may be as important as the teammates he is expected to play alongside – a factor which clearly cannot be anticipated by statistics. Perhaps no one example better illustrates this conundrum than Joe Johnson – he is credited with consistency, yet was a 48% three point shooter with the Suns in ’04-05, and no better than a 38% three point shooter since being acquired by the Hawks.
So, can statistics be used to anticipate three point shooting? I was among those who asked myself this question when the Rockets asked interested members of the statistical community to come up with “a model that best predicts an NBA player’s three point percentage for all players who shot 100 or more 3s in any season from 2000-01 to 2007-08” back in late April. Even in the statistical community, I found that relatively little had been written about the broad subject of three point shooting, and armed with all of the spreadsheets I needed from sites like Dougstats and Basketball-Reference, I decided to dig in.
I came to the conclusion that if one were to assume a consistent set of teammates and other external circumstances – it would then be possible to predict a player’s three point shooting performance by measuring prior performance and applying anticipated trends. A large part of the solution I came up with involves adjusting three point shooting statistics based on a statistical estimate of the quality of a player’s three point shot attempts. By creating my new statistic – which I will call Adjusted Three Point Shooting Percentage (ATPSP) for the time being – we are given a more accurate view of a player’s pure three point shooting ability as exhibited during any given season.
Based on my assumptions, a successful formula involved taking into account the following factors: shot quantity – the more three point shots attempted, the tougher it is for a player to be selective in his shot attempts, and the tougher it is for a player to maintain a certain shooting percentage; minutes played - for example, a player averaging 20 minutes per game may only be given major minutes by his coach on nights he is “hot,” or he may only be given major minutes when a matchup is considered favorable, thereby skewing per-minute based and other percentage based stats in his favor; teammates and coaches – it is assumed that a player’s three point shooting percentage is benefited when a player is surrounded by other teammates who pass the ball well, present scoring threats to attract defensive attention, and play within a well designed offensive system; and shot selection – a player who is, overall, a more efficient offensive option than his teammates is more likely to attract increased defensive attention, making his shots more likely to be contested, while indirectly creating shot opportunities for his teammates (and vice versa).
I started with a base formula of (3PT% * (3PA/MP)), and then multiplied by (1 + (.0075 * MPG)). This was a quick and easy and seemingly effective way to account for a player’s shot quantity, and the minutes per game adjustment seemed reasonable. Working with an historical spreadsheet and ignoring players receiving less than 11 minutes per game, this formula resulted in a list where those at the top – Dee Brown, Dennis Scott, Ray Allen, and George McCloud – seemed like they could arguably belong there. Even among those playing less than 11 minutes per game, names included only Voshon Lenard and Trevor Ruffin – again, very reasonable, especially considering that I had yet to make any team based or otherwise logical adjustments.
Next, the objective was to adjust players’ scores based on their respective teams. To do this, I aimed to create a formula to rank teams based on: 25% perceived overall offensive ability; 25% perceived passing ability; 25% perceived inside scoring ability; and 25% perceived three point shooting ability. The formula I decided on scores teams on a proportional scale to league-wide top performance in the following categories: Points Scored, accounting for 9.5 points; ORTG, also accounting for 9.5 points; Points Allowed, 3 pts; DRTG, 3 pts; AST/FGM, 25 pts; 2 Pt Shooting Percentage, 25 pts (“Close Shot FG%,” as gathered from nbatop.com, was utilized for ’07-08 statistics); and (3PT% * 3PA/M), 25 pts.
Before determining exactly each team’s score would affect its players’ ATPSP, I aimed to come up with a measure of a player’s shot selection. After a lot of thought, I thought that one logical way to do this would be to compare a players TS% with his teammates’ TS%; theoretically, this would do a good job of determining the likelihood that a player’s shots came at the expense of more offensively efficient teammates. To prevent small sample sizes from skewing results, I ran the following formula - ((1 + (.005 * MPG)) * (1 + (GP / 820)) * TS%) – and then assigned each player a rank between 1 (lowest) and 10 (highest) based on where his adjusted TS% ranked among his teammates, and multiplied that number by a variable which represented each team’s overall offensive production (theoretically, a player who is the most efficient player on a very good offensive team is assumed to have had even better shot selection, or simply to have had more of an otherwise positive impact, than the most efficient player on a poor offensive team – and vice versa).
Then, to determine the exact degree of adjustments, I experimented a little. Once I got to a point where Joe Johnson’s three point shooting appeared to follow logical trends in recent years, and the old Antoine Walker appeared to be a relatively poor three point shooter, I stopped experimenting - after all I could always go back to experimenting if results didn’t look good. For team based adjustments, the top ranked team’s players were assigned a “multiplier” of 1.2, and calculations were made to assign other teams’ players a number in between 1.21 and about 2-2.4 based largely on how the team’s score compared to the best team’s score (and adjusted very slightly and consistently, subjectively, to account for potential year specific errors). This “team multiplier” was to be multiplied by a player’s existing ATPSP. For reference, the table below discloses the team multipliers I used for each NBA team over the past five seasons:
Next, I took each player’s “team efficiency rank” and multiplied it by a variable approximately in between .09 and .126 depending on the team a player played for. This resulted in a minimum multiplier of .09 and a maximum multiplier of 1.26 to be multiplied by the player’s existing ATPSP. For recent seasons, this is the step where players such as Mike Miller, Ray Allen, Reggie Miller, and Peja Stojakovic tend to rise to the top of the list. Not coincidentally, this is also the step where Antoine Walker goes from looking like a decent or good three point shooter to looking like a poor to average one at best instead.
Then, I punished players who played less than 20 minutes per game (between 1 and 40+ percent, proportionate to how few minutes they played) and to a much lesser extent also punished those with less than 100 total three point shooting attempts. This was deemed necessary to prevent flaky results based on particularly small sample sizes.
The last step: I adjusted ATPSP per season. Over the past five seasons, statistically, three point shooting was more prominent in the NBA in ’07-08 than in any of the four previous seasons. Utilizing my base formula, the league-wide quality of three point shooting was nearly 27% worse in ’03-04 than in ’07-08, with differing figures in between. I assumed that half of the driving cause for this was a decrease in league-wide three point shooting talent, but it was reasonable to believe other rule and officiating based factors had also intervened. So, I adjusted yearly scores proportionately on a scale of 0-14% to compensate for this.
To view the following tables in the proper context, please note that the following analysis generally applies when judging a player’s ATPSP: