APBRmetrics

jready

I'm new to posting here, but I've been reading about APBRmetrics for a while. I know a lot of work has already been done on the usage versus efficiency debate, but I have not seen it studied on a lineup basis. I was not able to find any significant negative correlation between usage and efficiency, but maybe something useful can be found in all of this.

All data used for this can be found by downloading my spreadsheet from http://www.4shared.com/file/210055863/8c750ce/Lineup_Efficiency_Usage.html

I used the play by play data from http://www.basketballgeek.com/data/ for the 2008-09 season. While enormously useful, it was missing a few games for each team, so season totals won’t add up to the numbers seen elsewhere, but I don’t think this should cause too much error.

First, for every lineup that played at least one possession, I found how many points were scored and how many possessions were used by each player in each lineup. I counted a possession as being used by a player if he turned it over, made or missed and field goal, or made or missed the last of two or three free throws. This sheet is called TeamLinStats.

Next, I organized the data by player, keeping lineups separate. (By this, I mean that each player has points scored, player possessions used, and team possessions used for each lineup in which the player played). I calculated the players “usage” as player possessions used divided by team possessions used, and “efficiency” as points scored divided by player possessions used. This “efficiency” is not Dean Oliver’s offensive efficiency, but rather something very similar to true shooting percentage. I think the only significant difference is that I include turnovers in the denominator. This is because I wanted player stats to sum up to team stats, and this allows player possessions to sum up to team possessions. Also, for the purposes of this study, a player who is relied on for more usage would likely see his turnover rate increase, and that should be reflected in the data. This sheet is called PlayerLinStats.

I then summed up all the stats for each player, creating season totals. This data is in PlayerTotalStats.

For each player-lineup in PlayerLinStats, I found a player’s “True” efficiency and usage by taking the season totals and subtracting out the data of the lineup in question. I did this to avoid having the same shots counted as both independent and dependent variables in the same regression.

I then did a multiple regression, using Player Lineup Efficiency (the player efficiency in a given lineup) as the dependent variable, and Lineup Usage, True Usage, and True Efficiency as the independent variables. The value I am most interested in is the coefficient for lineup usage. A negative coefficient for lineup usage would imply that, if a player is in a lineup where he is relied upon to shoot more than his usual amount (accounted for by True Usage), his efficiency goes down. A positive coefficient would be evidence that teams manage to get the ball to players in lineups where he has a better change of scoring. The full results can be found in the “Multiple Regression” sheet, but the equation I got is:

Player Lineup Efficiency=0.785+ .062*True Eff+ .167*True Usage- .019*Lineup Usage

This initially looks promising, but despite the 39,000 player-lineups, the p value of the coefficient for lineup usage is only .35. Considering that half of the data consisted of lineups with 11 total possessions or less, I don’t think this is a very reliable regression.

I next did a weighted least squares regression. I don’t know any automatic way to do this in Excel, so I used the Excel solver to minimize squared errors weighted by team possessions used. The equation I got for this is:

Player Lineup Efficiency=0.819+ .071*True Eff+ .047*True Usage+ .087*Lineup Usage

It appears this data does not provide any evidence that the amount of possessions a player uses in a lineup, relative to his normal usage rate, significantly affects his efficiency in that lineup.
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Jimmy Ready

schtevie · Joined: 18 Apr 2005 Posts: 411

jready, am I interpreting your results correctly? Looking at the second regression, if a given player, who in a given line-up uses one fifth of the "possessions" (0.2) doubles his usage in that line-up (to 0.4) the effect on his "efficiency" in that line-up is to increase it by 0.0174, or 1.74 points per 100 "possessions" (turnovers, shot attempts, and freethrows).

But continuing the example, what about the other player(s) whose cumulative usage decreased by 0.2? According to your specification, does their resulting decrease in efficiency perfectly offset the increase?

These points of clarification aside, how does your approach address the fundamental problem in identifying the effect of usage on efficiency: the mismatch issue? Basically, we expect players who have advantageous mismatches relative to their defenders to take and make more shots. This effect needs to be accounted for to address the underlying issue.

jready · Posted: Fri Jan 29, 2010 4:40 pm Post subject:

schtevie · Joined: 18 Apr 2005 Posts: 411

No, no problem with the terminology, the "quotes" were merely included to emphasize that the terminology was yours.

Regarding the positive coefficient in the preferred specification, I guess it should also be mentioned that it is not just unidentified (but anticipated) mismatches that contribute to it, but randomness as well. Players take the easy buckets when defensive errors allow them. (On the other hand, bad players will take hard shots into the teeth of the defense.)

Finally, regarding your Pau Gasol explanation, I am not sure that I get your point. I think that my prior is that mismatches are independent of base usage, e.g. Pau Gasol is apt to be better than his primary defender, whether or not KB is on the floor. Then what determines the division of to-be-dispensed possessions between these two (or other) players has to do primarily with choices on the part of the defense. But whatever the case, the positive correlation between "line-up usage" and "line-up efficiency" should be expected to remain, no?

jready · Posted: Fri Jan 29, 2010 6:46 pm Post subject:

IrishHand · Joined: 15 Jul 2009 Posts: 115

DLew · Joined: 13 Nov 2006 Posts: 224

How is this study different than the ones done by Ryan Parker and Eli Witus on this topic? Why are you getting different results?

jready · Posted: Sun Jan 31, 2010 3:28 pm Post subject:

jready · Posted: Sun Jan 31, 2010 3:37 pm Post subject:

Crow · Joined: 20 Jan 2009 Posts: 816

If you split the data are there are any subgroups (by usage or efficiency level, age, shot distribution mix or some other player "type" or combinations of these) that behave differently, in a more statistically significant way?

When you can't find a pattern that fits everybody consistently, rather than end there (not saying you have or would, just trying to kick the ball forward) I'd think a next step would be to look for subgroups who have a more patterned behavior.

jready · Posted: Mon Feb 01, 2010 6:02 pm Post subject:

Thanks for the input. That's a a good idea. Because I already have usage rates in my spreadsheet, I started by separating players by their level of season usage, and did the weighted regressions again. The results this time were much more interesting.

For players who have a true usage of greater than .2 (which is, of course, more than an 1/5 of the teams possessions):

Player Lineup Efficiency=0.661+ .231*True Eff+ .046*True Usage+ .138*Lineup Usage

For players with true usage of less than .2:

Player Lineup Efficiency=0.836+ .042*True Eff+ .201*True Usage-.0128*Lineup Usage

Next, I tested the more extreme cases. First, the approximately 10% of players with usage over .260:

Player Lineup Efficiency=0.857+ .012*True Eff+ .026*True Usage + .227*Lineup Usage

Then, the approximately 10% of players with usage less than .13:

Player Lineup Efficiency=0.595+ .153*True Eff+ 1.54*True Usage-.224*Lineup Usage

These results are more interesting than my original results, and intuitively make sense to me. For players who are used to being high usage players (usage > .26), being in a lineup in which they have to be even higher usage won't effect them negatively at all. These players are generally the first option in any lineup, so they already are taking the tough shots that someone has to take. Increasing their usage further is thus generally a result of mismatches or other factors that would similarly increase efficiency.
For players who are low usage players (usage < .13), the lineup usage value has a large negative coefficient. These players tend to be the fourth or fifth option on the court, normally only taking open shots or layups. When they are in a lineup where they have an increased usage, this either means they are in a lineup where they are getting more open shots and layups, or taking shots that are above the difficulty level of the shots they normally take. This is the effect that I have been trying to isolate all along, and I think here, I finally found some evidence of it, in the -.224 lineup usage coefficient.
_________________
Jimmy Ready

schtevie · Joined: 18 Apr 2005 Posts: 411

I just want to go way back here and revisit the premise of usage vs. efficiency, and perhaps someone can remind me if I get the story incorrect. The belief that efficiency declines with increased usage is predicated on a big ALL ELSE EQUAL (apologies for the gratuitous use of caps). And the theory, solid theory that, is that this result occurs because of the increasing predictability of the offense. If it is known that Player X is going to increase his offensive responsibility, then the defense can accordingly shift their attention and increase on help defense, decreasing the resulting efficiency. I think that that is it.

One can then begin relaxing the ALL ELSE EQUAL condition a bit and say that some players might need some shots before they warm up, thereby supposing a positive relationship on that account. Equivalently, one can argue the flip side and say that some players begin to get fatigued past a certain usage rate, resulting in another negative relationship.

Other than this tweaking, one really needs to control for ALL ELSE to have faith in the resulting empirical estimates. In particular, there are a few important factors that I think have never been taken into account in any of the estimates I have seen produced (and again, someone please correct me if I am wrong).

(1) Defense. Players/Line-ups face opposing line-ups of dramatically dissimilar strength. And it cannot be assumed that they even out over a season.

(2) Possession/Scoring Opportunity Origin. For example, a player can increase his usage by increasing the fraction of fast breaks vs. increasing the number of shots in the half court, this is comparing apples and oranges.

(3) Shot Clock. A player may increase his usage by taking more shots at the end of the shot clock. These are expected to be of lower "efficiency" than those taken earlier on. But is completely incorrect to say, in the context of this question, that these are more inefficient.

Crow · Joined: 20 Jan 2009 Posts: 816

Jready, your equations are digestable and show easy to see differences. I wonder how they would look for other subgroups or combos of subgroups as I mentioned before. Efficiency / usage sub groups, usage / age, usage for perimeter vs inside by position or style, etc. Up to you if you want to check more but I think there is more to understand about usage, efficiency, experience and style.

I also wonder if there could be things worth seeing and thinking about resulting from a comparison of what you found by this approach for various subgroups to 1) hoopnumbers.com's estimated Adjusted team eFG% impact for the sum of the same subsets of players timeweighted and 2) just the shooting / scoring components of Statistical +/- for the same group. How well to all 3 align in general and when they differ what does that say about players, lineups, play calls / shot distributions or about the metrics?

jready · Posted: Fri Feb 05, 2010 1:24 am Post subject:

I'm very busy this week, but I do plan to go further with this idea, and look for trends in the data in many of the ideas you have suggested, as soon as I can.

Could you explain what you mean in your second paragraph? The way I read it is that you are suggesting comparing the results if, instead of my current measure of efficiency, which is essentially points per possession, I try using different measures of efficiency instead. I'm not sure what this would accomplish, beyond what a basic comparison of different measures of efficiency would.
_________________
Jimmy Ready

Crow · Joined: 20 Jan 2009 Posts: 816

I am sometimes not that successful at explaining or re-explaining but,

Ultimately the efficiency of a player, using your definition, over how ever many shots they take while on the court in all lineups is worth plus x or minus y points for time played per game or per 48 minutes compared to league average efficiency.

At least the Adjusted eFG% factor could be converted to a points for time played per game or per 48 minutes basis for player and probably FT/FGA could be roughly too.

The shooting / scoring components of Statistical +/ could be too.

That would make them more easily comparable, for all lineups or potentially you could do this for the major "Player Lineups".

It would allow an estimate of how much of a player's Adjusted eFG% factor was direct- because of their individual shooting / scoring, identified by your method or the Statistical +/- approach - while presumably the residual would be their indirect "shot creation impact", or at least one way to estimate it.

Your findings and the findings of the shooting / scoring components of Statistical +/- should have the same distribution but the values will be different if the "value" of better or worse shooting /scoring, based on the regression using Adjusted +/- data, is worth more than the surface raw value.

If that isn't helpful, don't worry about it. That's about as much as I can think to say about the idea right now.

If there are these three different ways to look at shooting / scoring impact I'd think it might be helpful to compare them.