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Which Offensive Rate Stats Stay the Most Consistent When a Player Changes Roles?

Posted by Neil Paine on August 18, 2010

Last October, Jason Lisk published two great studies at PFR about which passing stats are the most situation-independent, looking at the year-to-year correlations in rate stats for both QBs that changed teams & teams that changed QBs. (Chase Stuart followed this up with additional interception rate research in March.) His conclusions? Sacks per dropback and completion % were the most consistent, which implies that those are more under the control of the individual QB rather than the situation he's in. At the other end of the spectrum, interception % is actually the least consistent rate stat, indicating that interceptions (or lack thereof) are more due to luck and situation than actual player skill (a finding Chase reinforces in this Footballguys article). This also means that when evaluating QBs, we should regress their interception rates more to the mean than their sack or completion rates.

What does all of this have to do with basketball? Well, I decided to do the exact same study for NBA players, except instead of looking at players who changed teams, I looked for players whose offensive roles changed (as measured by possession usage %). I can certainly look at players who changed teams as well, but for basketball my hypothesis is that the player's role is as important as anything in determining certain rate stats. This goes back to the concept of "skill curves", or the idea that a player's efficiency is fundamentally a function of not only his own skill, but also his usage rate.

So here's the setup: I took every player since 1974 who was between 24 and 34 years old and played at least 1,000 minutes in back-to-back seasons. I then sorted those players by the absolute change in their possession usage %, and took the top quartile as my sample of players who definitely changed roles. For these 1,036 players, I ran correlation coefficients on their year-to-year performances in these offensive rate stats:

  • True shooting %  (PTS / (2 * (FGA + 0.44 * FTA)))
  • Assist Rate (% of teammate FG assisted when on the court)
  • Turnover Rate (TOV/Possessions used)
  • Free throw rate (FTA/FGA)
  • Offensive rebounding % (% of available OReb pulled down while on the court)

High correlations indicate that the stat is more likely to be representative of a player's skill independent of his role in the offense, while lower correlations mean the stat is more a product of the player's situation.

The results:

Stat Correlation
TS% 0.627
AsR 0.905
ToR 0.724
FTr 0.802
OR% 0.932

The first thing that strikes me is how large the correlations are in basketball, relative to their counterparts in football. Even at their least consistent, NBA players' stats appear to capture far more of their skill level than those of NFL quarterbacks.

As far as the correlations themselves go, offensive rebounding % and assist rate seem to be almost completely independent of a player's role -- i.e., if a player has a good assist rate at 15% possession usage, you can basically expect that to be retained even at 25% possession usage, etc. Perhaps it is because those two stats measure tendency as much as ability, although there's certainly skill being captured in each as well.

True shooting % is easily the least consistent stat when a player changes roles, which seems to back up the concept of skill curves. When a player has a high TS% and a low possession %, it may be that his efficiency is inflated by taking relatively easy shots, attempts that comprise a smaller proportion of his shot selection when he is asked to increase his usage. Along the same lines, turnover rate was the 2nd-least consistent offensive rate stat when changing roles, suggesting that not only is shooting % dependent on the player's usage, but the ability to avoid turnovers is as well.

Finally, free throw rate was in the middle of the pack in terms of correlations. I expected it to be high, alongside OR% and AsR, but it makes sense that it would be lower when you consider that it at least partially represents a player's ability to get shots close to the basket... Just like the ratio of high-percentage shots to low-percentage ones decreases when you take on a bigger role (as evidenced by TS%'s low correlation), it stands to reason that the ratio of close shots to longer ones also decreases with an increase in usage, albeit at a slower rate.

7 Responses to “Which Offensive Rate Stats Stay the Most Consistent When a Player Changes Roles?”

  1. Westy Says:

    Good stuff. Will you also be running this for defensive stats?

  2. Jason J Says:

    The only one of those that strikes me as odd, and I actually looked this up and found it myself in a few individuals where it held true, is that OReb% does not appear to be tied to Usage. You'd think there would be a pretty linear relationship. Fewer scoring opportunities should mean more rebounding opportunities, right?

  3. Greyberger Says:

    1: Run it with what? I don't see how Usage% could have an effect on defensive rebounds, steals, etc... unless the theory is that players become tired from too many touches on offense, or demotivated by getting too few.

    Great post, by the way. The results remind me of the table in the Berri book where yearly box-score stats are explained by the year before.

  4. Jason J Says:

    Do you think some of the reason for the overall lack of correlation between Usage and these other offensive rates might be that, as a general rule, the drop is Usage is often due to a drop in ability (injury / age – I imagine age is the most common factor) which would lead to an across the board drop in rates rather than a dip in usage accompanied by a spike somewhere else?

    I wonder if we could find a way to isolate players in their primes where usage dropped due to a situational shift – like Thunder Dan when Barkley joined the Suns. He went from being a third option to a spot up shooter (oddly less responsibility led to his first All-Star appearance). Usage slipped. OReb% dropped. TS% spiked. All of that follows. Barkley pushed him to the perimeter. He was out of position to rebound and wide open to take high value 3 pointers.

  5. taheati Says:

    Perhaps it is because those two stats measure tendency as much as ability, although there's certainly skill being captured in each as well.

    With assists, wouldn't TO-rate track AST-rate if correlation suggested "tendency" more than ability?

    I think both (AsR & OR%) may point to ability, learned or innate, in the context of spatial awareness, visual acuity, biomechanics/kinematics.

  6. taheati Says:

    It'd be interesting to see if highte AsR and OT% follow players regardless of position, i.e., high OT% bigs who also have highter AsR relative to big norms, likewise guards and OT%.

  7. Ed Says:

    I like to think of players as hauling an offensive load. Use games that are not blowouts or where the player played too few minutes. Calculate what percentage of the offense he scored. Rank against all players. One can then compare the "load" players carry in wins, losses, win streaks, losing streaks.

    A change in load should indicate a change in roles and also indicate how effective the player is in the new role.

    The load accounts for the team quality or the environment a player finds himself in.