Consistent Scorers

What is a consistent scorer? Some people seem to think it is someone with a good field goal percentage. I’m here to set the record straight, and to come up with a list of the most consistent elite scorers in the league.

So how would we define consistency when it comes to scoring in the NBA. One of the best ways is probably to look at how much a player’s scoring differs from his average on a game to game basis. This is called the variance, and we will explore this in this article.

The formula for what we will call PPG VARIANCE is as follows.

Where n is the number of games a player participates in during the season (n is always less than or equal to 82), i is an number between 1 and n, x_i is the player’s scoring output in the i^th game of the season, and X is the player’s scoring average for the 2010-2011 season. For those of you who don’t understand summation notation, this calculates the average squared distance between a player’s scoring in an individual game and their scoring average for the season.

Now it would be nice to be able to compute this for every player in the league, but unfortunately I don’t have nearly enough time to do that. So for this article we focus on elite scorers, which I will arbitrarily define to be players who averaged over 20 points per game this season. So our study will focus on the following 19 players.

Kevin Durant, Lebron James, Carmelo Anthony, Dwyane Wade, Kobe Bryant, Amare Stoudemire, Derrick Rose, Monta Ellis, Kevin Martin, Dirk Nowitzki, Blake Griffin, Russell Westbrook, Lamarcus Aldridge, Andrea Bargnani, Danny Granger, Brook Lopez, Kevin Love, and Zach Randolph.

I computed the PPG VARIANCE for the previous 19 players. Remember that if a player has a lower PPG VARIANCE than another player it means that on average that player’s per game scoring output is closer to his season average than the 2^nd player, which would imply that the first player is a more consistent scorer. Without further ado, here are the results (in order from smallest to largest).

Player	PPG VARIANCE	Player	PPG VARIANCE
Zach Randolph	39.86382	Lebron James	54.09966
Kevin Durant	41.46433	Kevin Martin	58.6725
Danny Granger	44.5528	Brook Lopez	59.31365
Dirk Nowitzki	46.30062	Kevin Love	60.17114
Russell Westbrook	47.26249	Lamarcus Aldridge	60.48041
Kobe Bryant	48.44438	Andrea Bargnani	63.78972
Amare Stoudemire	48.70957	Dwyane Wade	71.19581
Dwight Howard	52.39382	Carmelo Anthony	73.59352
Blake Griffin	53.10366	Monta Ellis	89.74984
Derrick Rose	53.78997

So from the above table, we see that by this measure Zach Randolph was the most consistent elite scorer in the league, and Monta Ellis was by far the least consistent.

However, is this an accurate measure of consistency? If a player averages 25 points per game, and gets 25 points on 10 shots one night and 25 points on 25 shots the next night, is he being consistently productive? By the previous measure, he would be considered consistent, but I don’t think that’s really true. Which is why another calculation needs to be done.

We will now define TS% VARIANCE as

Note that this is the exact same as the PPG VARIANCE formula, except we replace scoring average by season TS% (Y), and game by game scoring with game by game TS% (y_i). As with PPG VARIANCE a lower TS%% VARIANCE implies more consistent scoring.

The reason we use TS% instead of regular FG% is that TS% takes into account both the additional value of 3 pointers and free throws, where FG% counts regular field goals and 3 pointers the same amount, and completely disregards free throws. For any who don’t know, the formula for True Shooting Percentage is

Points/(2*(FGA + .44*FTA))

Doing the TS% VARIANCE calculation for the same 19 players yielded the following results.

Player	TS% Variance	Player	TS% Variance
Kobe Bryant	.009744	Zach Randolph	.015197
Lebron James	.010283	Kevin Martin	.015922
Russell Westbrook	.011181	Carmelo Anthony	.017120
Dwight Howard	.011262	Dwyane Wade	.017304
Brook Lopez	.012255	Monta Ellis	.018556
Blake Griffin	.012311	Danny Granger	.019819
Amare Stoudemire	.012812	Dirk Nowitzki	.020285
Kevin Durant	.012942	Andrea Bargnani	.021580
Lamarcus Aldridge	.014153	Kevin Love	.026834
Derrick Rose	.014248

So by this measure, Kobe and Lebron are the most consistent shooters, and Love is by far the least consistent.

So finally, to determine which of these elite scorers are the most consistent, we must combine these two measures.

The first way we might do this would be to simply look at how each player ranked in each measure, add the two numbers together, and then rank the players accordingly. This would be alright, but it probably isn’t the perfect measure. Why is that? If you look at the TS% VARIANCE table, you see that Griffin is only the tiniest bit behind Lopez, and is thus one spot behind. However, Love is in 20th and is extremely far behind Bargnani, who is one spot ahead of him. If we were to just add the rankings, Love would be penalized the same amount (one point) for how far behind Bargnani he is as Blake would be penalized for being behind Lopez. However, Blake and Lopez are essentially tied, while Love is clearly getting destroyed. Also, our final table would do nothing to show the differences in consistencies between 2 players, it would only show the rank. This would not accurately represent a combination of the 2 measures, so we need a better one.

We want to be able to just add the numbers together. However, since the numbers for FG% VARIANCE are as high as 80, but TS% VARIANCE numbers are not even remotely close to 1, we need to introduce a scale factor. Define the Scale Factor (Q) as

So for our sample, the average PPG VARIANCE is 56.155, and the average TS% Variance is .01546. We then calculate Q to be 3631.459 for our sample.

We then multiply each player’s TS% VARIANCE by this scale factor to get Adjusted TS% Variance. The results are shown in the following table.

Player	Adjusted TS% VARIANCE	Player	Adjusted TS% VARIANCE
Kobe Bryant	35.38493	Zach Randolph	55.18728
Lebron James	37.34229	Kevin Martin	57.82009
Russell Westbrook	40.60334	Carmelo Anthony	62.17058
Dwight Howard	40.89749	Dwyane Wade	62.83876
Brook Lopez	44.50353	Monta Ellis	67.38535
Blake Griffin	44.70689	Danny Granger	71.97187
Amare Stoudemire	46.52625	Dirk Nowitzki	73.66415
Kevin Durant	46.99834	Andrea Bargnani	78.36689
Lamarcus Aldridge	51.39604	Kevin Love	97.44657
Derrick Rose	51.74103

That looks better, those numbers have the same average size as those for PPG VARIANCE. We can now finally define what I will call a consistency value. The formula is simply.

Consistency Value= PPG VARIANCE + Adjusted TS% VARIANCE

Or alternatively

Consistency Value= PPG Variance + Q*TS% VARIANCE

So our final results are as follows

Player	Consistency Value	Player	Consistency Value
Kobe Bryant	83.82932	Lamarcus Aldridge	111.8764
Russell Westbrook	87.86763	Kevin Martin	116.4926
Kevin Durant	88.46267	Danny Granger	116.5247
Lebron James	91.44395	Dirk Nowitzki	119.9648
Dwight Howard	93.29131	Dwyane Wade	134.0346
Zach Randolph	95.0511	Carmelo Anthony	135.7641
Amare Stoudemire	95.2361	Andrea Bargnani	142.1566
Blake Griffin	97.81055	Monta Ellis	157.1352
Brook Lopez	103.8172	Kevin Love	157.6177
Derrick Rose	105.531

So the winner is... Kobe? That’s surprising, at least to me, since his game is based mostly around mid range jump shots which I would generally think are more inconsistent. After him you have Westbrook, which makes sense due to his high number of free throw attempts and fast break buckets. Durant also makes sense due to his extremely high free throw attempts at a consistently high percentage. After that you have Lebron, and then 5 big men in a row.

The biggest surprise is probably how low Wade is. As a player who draws a large number of free throws and attacks the rim a lot, he would seem to be a consistent player. Apparently that is not the case. Love finished lower than expected simply because he had BY FAR the worst TS% variance. After adjustment he was almost 20 points behind 19^th place. Ellis had a similar problem with PPG Variance.

Some final notes: This is not a perfect measure of consistency. For one it doesn’t do anything to account for minutes played. If Dwight plays only 20 minutes in a game because his team is up 30, that hurts his PPG VARIANCE. However, over the course of a season the effect isn’t that large. It also ignores other stats like turnovers that could be considered a part of being a consistent scorer.

Finally, and I cannot stress this enough... BEING A MORE CONSISTENT SCORER DOES NOT MEAN YOU ARE A BETTER SCORER! This is extremely important. Durant and Westbrook have nearly identical consistency by this measure, but would you rather have Durant scoring 28 points on a TS% of 59% or Westbrook scoring 22 on a TS% of 54%. It’s no contest. Being a more consistent scorer means we can better understand what to expect from that player on a day to day basis. Nothing more.

Hopefully you found this interesting. I appreciate any feedback and look out for future articles that may go into more detail with this stat.