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Scoring Consistency Metric?

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Post#1 Scoring Consistency Metric?
Sun Sep 16, 2012 1:16 am by PG24

Basketball Masterminds,

Trying to determine a new way to analyze scoring output here. I'm a huge Wolves fan, and will argue the case for Kevin Love being the best in the biz as far as young PFs go, however I'll be the first to say the guy isn't yet the scorer some casual fans think he may be when they look at his statistical output this past year.

I'd like to intro this consistency measure by first starting off with a few known scoring stats and use them to compare Love and a couple other of the top flight up and coming power forwards in the NBA - LaMarcus Aldridge and Blake Griffin, who all 'get theirs' in vastly different ways.

P40PA - Points Per 40 Minutes Pace Adjusted
TS% - True Shooting Percentage

2011/12

Code: Select all
Player                   P40PA          TS%
LaMarcus Alrdidge        23.6           0.560
Blake Griffin            23.1           0.557
Kevin Love               25.8           0.568


First glance it seems as though Kevin Love takes the crown as the best young scoring power forward in the game fairly easily, being that he does lead Aldridge and Griffin in both points and efficiency.

But what about consistency?

The goal here is to come up with another metric to measure the top NBA scorers; that is, as mentioned, some sort of a scoring consistency measure. One can view consistency in what I realize as two different aspects:

(1) Does the player score the same amount of points each game? and,
(2) Does the player score those points at the same efficiency rate each game?

Now, for me, the second question above is most important. There are a multitude of different reasons why a player's actual scoring output may vary from his average: blowout, ejection, injury, etc. However, the manner in which those points are scored should always be consistent, - as long as they are of course efficient - right?

Don't get me wrong - I believe a top scorer should of course be consistent in terms of the amount of points scored each game. I don't jive with the Monte Ellis' and others of the like in the NBA that score so inconsistently. It's just that consistency in the efficiency in which the points are scored in my opinion is the best barometer of a successful scorer. In my opinion it is better to be consistent in efficient output - whether that be scoring a lot of points and/or getting teammates involved - rather than being consistent in just 'getting yours'. I won't detail in the consistency of player in terms of points scored in this particular post, but obviously - that's not to say it isn't important (just know that for this post, all of Aldridge/Grffin/Love were fairly equal in terms of points scored variance).

With that said, to measure consistency I took the game-by-game log for each player and looked at the metric that measures scoring efficiency (TS%), and calculated the season average to equate the standard deviation for each player during the 2011/12 season.

For this comparison, here are the results:

Code: Select all
Player                 Consistency (TS%)
LaMarcus Aldridge      0.187
Blake Griffin          0.176
Kevin Love             0.253


Looking at this measure - Kevin Love deviates from his above average efficiency much more often that does his counterparts in LaMarcus Aldridge and Blake Griffin (who both average similar rates of above average efficiency). Sure, he puts up better scoring numbers and holds a slight edge in TS% - but is it doing his team more harm that he's not scoring those points at the same level of efficient consistency as often as his competition are? Would his team not be more successful if he could sustain more consistent levels of efficiency, thus leaving it to the more inconsistent role players to determine the outcome of each game?

I calculated all of 2011/12 using this consistency metric, but also chose a few of my favorite all-time dominant scorers since I've been watching basketball and will include the results in this post (picking and choosing seasons).

Code: Select all
Player                      Year          TS%       Consistency (TS%)
Michael Jordan              1990-91       0.605     0.149
Shaquille O'Neal            1998-99       0.584     0.123
Kevin Durant                2009-10       0.607     0.182


Not even including LeBron, which I'm sure would own this metric.

So, what flaws do you see with using this metric as a measure of consistency amongst scorers? How can it be improved? Do you believe it, as currently calculated, is fair to be utilized to compare scorers of the same position with similar true shooting percentages?
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Post#2 Re: Scoring Consistency Metric?
Sun Sep 16, 2012 3:24 pm by Nivek

I did some studies on consistency a few years ago. The problem with using straight standard deviation is that guys with higher scores to start with are likely to have a higher deviation. To say it a different way, say we're looking at points per 36 minutes. Two guys have SDs of 5 points per 36 minutes. But, if one guy averages 20 points per 36 and the other averages 10...you get the point.

This issue is solved by using coefficient of variation -- standard deviation divided by mean.

So, in my example above, 20ptPlayer has a coefficient of variation of .25 (5/20) where 10ptPlayer has a COV of 0.5 (5/10). So in this way, it's clear that 20ptPlayer is more consistent than 10ptPlayer.

In your example, the conclusion wouldn't change much -- Love would still be the least consistent shooter of the 3. But overall, you'll have more robust results using coefficient of variation.

Kinda funny note on this coefficient of variation thing. I was working on a consistency study and tripped over the problem I described above. My math education is meh -- I took classes in school and all that, but that was awhile ago, and I wasn't all that interested in math to start with. Much of what I know is stuff I taught myself because of basketball stats. Anyway, I knew I needed to resolve this problem, and so I just "tried out" this method...thinking I'd invented something new. When I described what I'd done on one of the stat boards, Dan Rosenbaum (an economist) dropped the coefficient of variation term. So yeah, I'd basically reinvented the wheel. :)
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Post#3 Re: Scoring Consistency Metric?
Mon Sep 17, 2012 7:38 am by penbeast0

PG24 wrote:Basketball Masterminds,

Trying to determine a new way to analyze scoring output here. I'm a huge Wolves fan, and will argue the case for Kevin Love being the best in the biz as far as young PFs go, however I'll be the first to say the guy isn't yet the scorer some casual fans think he may be when they look at his statistical output this past year.

I'd like to intro this consistency measure by first starting off with a few known scoring stats and use them to compare Love and a couple other of the top flight up and coming power forwards in the NBA - LaMarcus Aldridge and Blake Griffin, who all 'get theirs' in vastly different ways.

P40PA - Points Per 40 Minutes Pace Adjusted
TS% - True Shooting Percentage

2011/12

Code: Select all
Player                   P40PA          TS%
LaMarcus Alrdidge        23.6           0.560
Blake Griffin            23.1           0.557
Kevin Love               25.8           0.568


First glance it seems as though Kevin Love takes the crown as the best young scoring power forward in the game fairly easily, being that he does lead Aldridge and Griffin in both points and efficiency.

But what about consistency?

The goal here is to come up with another metric to measure the top NBA scorers; that is, as mentioned, some sort of a scoring consistency measure. One can view consistency in what I realize as two different aspects:

(1) Does the player score the same amount of points each game? and,
(2) Does the player score those points at the same efficiency rate each game?

Now, for me, the second question above is most important. There are a multitude of different reasons why a player's actual scoring output may vary from his average: blowout, ejection, injury, etc. However, the manner in which those points are scored should always be consistent, - as long as they are of course efficient - right?

Don't get me wrong - I believe a top scorer should of course be consistent in terms of the amount of points scored each game. I don't jive with the Monte Ellis' and others of the like in the NBA that score so inconsistently. It's just that consistency in the efficiency in which the points are scored in my opinion is the best barometer of a successful scorer. In my opinion it is better to be consistent in efficient output - whether that be scoring a lot of points and/or getting teammates involved - rather than being consistent in just 'getting yours'. I won't detail in the consistency of player in terms of points scored in this particular post, but obviously - that's not to say it isn't important (just know that for this post, all of Aldridge/Grffin/Love were fairly equal in terms of points scored variance).

With that said, to measure consistency I took the game-by-game log for each player and looked at the metric that measures scoring efficiency (TS%), and calculated the season average to equate the standard deviation for each player during the 2011/12 season.

For this comparison, here are the results:

Code: Select all
Player                 Consistency (TS%)
LaMarcus Aldridge      0.187
Blake Griffin          0.176
Kevin Love             0.253


Looking at this measure - Kevin Love deviates from his above average efficiency much more often that does his counterparts in LaMarcus Aldridge and Blake Griffin (who both average similar rates of above average efficiency). Sure, he puts up better scoring numbers and holds a slight edge in TS% - but is it doing his team more harm that he's not scoring those points at the same level of efficient consistency as often as his competition are? Would his team not be more successful if he could sustain more consistent levels of efficiency, thus leaving it to the more inconsistent role players to determine the outcome of each game?

I calculated all of 2011/12 using this consistency metric, but also chose a few of my favorite all-time dominant scorers since I've been watching basketball and will include the results in this post (picking and choosing seasons).

Code: Select all
Player                      Year          TS%       Consistency (TS%)
Michael Jordan              1990-91       0.605     0.149
Shaquille O'Neal            1998-99       0.584     0.123
Kevin Durant                2009-10       0.607     0.182


Not even including LeBron, which I'm sure would own this metric.

So, what flaws do you see with using this metric as a measure of consistency amongst scorers? How can it be improved? Do you believe it, as currently calculated, is fair to be utilized to compare scorers of the same position with similar true shooting percentages?


Well, so far, the person who took the most outside shots is the least consistent in each metric which sort of takes some of the interest out of this. A jump shot is less consistent than a post score . . . the 3 point shot has pumped the efficiency of outside shooters but it's still a lot more inconsistent than the equivalent short shot with equal ts%. Not sure if this is consistent for your measure but something to look at.
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Post#4 Re: Scoring Consistency Metric?
Mon Sep 17, 2012 3:44 pm by PG24

Nivek - thanks for the clarification. Coefficient of variation is exactly the method behind the calculation, not just straight standard deviation as stated originally.

penbeast0 wrote:Well, so far, the person who took the most outside shots is the least consistent in each metric which sort of takes some of the interest out of this. A jump shot is less consistent than a post score . . . the 3 point shot has pumped the efficiency of outside shooters but it's still a lot more inconsistent than the equivalent short shot with equal ts%. Not sure if this is consistent for your measure but something to look at.


For the most part, yes, a jump shooter will be more inconsistent than players who get their shots closer to the basket. It just depends on the player. In the end, if the goal is to compare and rate the top scorers in the league, shouldn't the expectation be that the premier players be consistent in what they do, no matter the way they go about it?

For example, the below list includes the top 20 scorers from last season (in terms of PPG) and charts their consistency number as well as TS%, sorted by consistency.

Code: Select all
Player                   Consistency          TS%
LeBron James             0.174                0.605
Blake Griffin            0.176                0.557
LaMarcus Aldridge        0.187                0.560
David Lee                0.192                0.549
Kevin Durant             0.195                0.610
Kobe Bryant              0.210                0.527
Russell Westbrook        0.215                0.538
Deron Williams           0.226                0.527
Al Jefferson             0.227                0.520
Paul Pierce              0.236                0.567
Dirk Nowitzki            0.237                0.564
Joe Johnson              0.247                0.557
Chris Paul               0.247                0.581
Carmelo Anthony          0.248                0.525
Josh Smith               0.251                0.499
Kevin Love               0.253                0.568
Brandon Jennings         0.255                0.514
Rudy Gay                 0.264                0.521
Monta Ellis              0.277                0.509
Andrew Bynum             0.282                0.594


The consistency measurement of course needs to be compared relative to a player's TS%. For example, where Smith, Love, and Jennings all scored at a similarly consistent rate, Love did so at an above average efficiency level whereas Smith/Jennings did so at below average levels. Bynum had one of the higher TS% in the sample, but on a game by game basis was the most inconsistent player on the list. LeBron and Durant are the gold standards, boasting the two highest TS% on the list coupled with being two of the most consistent scorers in the league.

Back to the original example, I don't think it's unfair to expect Love to score his points at a similar rate of consistency as Griffin and Aldridge if the expectation is for his team to win lots of games with him as the #1 option. Dirk is probably the best comparison to Love as their playing styles are much more similar, and in his prime Dirk had consistency rates of 0.183, 0.179, 0.182, 0.180 in 4 out of 5 seasons between 2003 and 2007 to go along with his extremely high true shooting percentages. Love is by no means inconsistent relative to the rest of the league, but if we can put any stock into this measurement it seems as though he still has work to do to reach the consistency levels of the most premier scorers in the league.
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Post#5 Re: Scoring Consistency Metric?
Mon Sep 17, 2012 4:34 pm by Nivek

One of the other things I've found useful with consistency is to look at the expected range of a player's performance. The way I did this was something like this: Say we have a 20 point scorer who has a 5 point standard deviation. His average is 20, his expected high is 25, his expected low is 15. Take a 10 point scorer with the same SD, and his expected high is 15 and expected low is 5.
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Post#6 Re: Scoring Consistency Metric?
Tue Sep 18, 2012 7:34 am by blabla

It's important to note that you want your players on bad teams being inconsistent and players on good teams consistent. You don't want everyone consistent. If everyone always exactly score their average, the bad teams would not win a single game. So for Love being inconsistent is actually a good thing because he's playing for a below average team
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Post#7 Re: Scoring Consistency Metric?
Tue Sep 18, 2012 8:11 pm by Dr Positivity

I would love to see a stat ranking consistency using Gamescore. I even sent an email to John Hollinger once telling him to use one for ESPN
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Post#8 Re: Scoring Consistency Metric?
Wed Sep 19, 2012 12:56 pm by Nivek

Dr Positivity wrote:I would love to see a stat ranking consistency using Gamescore. I even sent an email to John Hollinger once telling him to use one for ESPN


I've done this with my own measure, which (of course) is superior to Gamescore/PER. Results were interesting, but it took too long to get the data set up so I could analyze. I could use a programmer to automate my bright ideas. :)
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