Friday, 7 August 2015

How to compare NBA scorers (improved analysis)

(Originally posted on Monday, 18 July 2016)

This is an altered version of my previous post on this topic. My final calculations are slightly different (there is a difference when interpreting positive and negative extra values of shooting percentage) and they are based on the actual shooting percentage averages from the last 40 years. However, I left the previous examples, because they are very easy to calculate, even in memory.

Recently I had been toying with NBA statistics because I wanted to work out my own way of judging the value of different NBA drafts. The most important statistic are obviously total points scored (PTS) and points per game average (PPG), but I wanted to calculate the positive value of high percentage scorers and the negative value of low percentage scorers. Obviously a high-percentage scorer is better, but the question is how much better.

I used my formulas for calculating extra values for the NBA top 30 points per game (PPG) scorers. I used a current list (at the end of 2015-2016 season), but it will change it the future:
http://www.basketball-reference.com/leaders/pts_per_g_career.html

I decided to make separate calculations for 2-point shots, 3-pointers and free throws. In each case I had to assume a reference point for all the players. I decided that it would be best to calculate a league-wide average from the last 40 years. I based it on the league-wide team-averages of TOTAL numbers that I found on 40 such sites:
http://www.basketball-reference.com/leagues/NBA_2016.html

To be precise: from each such page I took the line “League Average” and summed them all.


1. Extra value of 2P%

This is a rather stable statistic, at least in the last 40 years. Currently the league-wide 2P% is 49.1 %, in 2006 (in the season 2005-2006) it was 47.8 %, in 1996 it was 48.6 %, in 1986 it was 49.5 % and in 1977 (the first season of the 40 seasons I analysed) it was 46.5 %.

An average 2P% from the last 40 years is exactly 48.3 %, but in the examples below I assumed a reference point of 45.0 %. The reference point of 45.0 % surprisingly makes the examples much easier to visualize and calculate in memory than any example with a reference point of 50.0% (not to mention the correct reference point of 48.3 %).

A player who attempted 2000 2-point shots (2PA) and made 1000 of these shots (2PM) (2P% = 50.0 %) during 100 games is worth for an average team 2.0 extra points per game. He scored on average 20.0 points per game (2000*50.0%*2/100) and the team would score only 18.0 PPG without him (without him the team would have to attempt all his shots: 2000*45.0%*2/100 = 2*1000*90.0%/100=2*900/100=2*9).

On the other hand a player with 3000 2PA and 1000 2PM (2P% = 1/3) during 100 games is “worth” for an average team -7.0 “extra” points per game (he took away these points from his team). He scored on average 20.0 points per game (3000*1/3*2/100), but the team would score 27.0 PPG without him (3000*45.0*2/100= 3*1000*90.0%/100=3*900/100=3*9).

Please, notice again that the positive extra value of 2P% is a virtual value. The first scorer actually scored 20.0 PPG, so he was already credited for those extra 2.0 PPG in the box-score. However the second scorer wasted those 7.0 PPG irreversibly (assuming that there were no offensive rebounds), so the negative 2P%_E values should be directly used to judge the scorers. The same goes for 3P% and FT%.

The precise formula for total extra value of 2P% is like this:

2P%_E = 2PA*(2PM/2PA-0.483)*2

All my formulas are made for TOTAL values, but here I had to divide the results by the number of games played by the players.

The best 2P%_E scorers from the NBA top 30 PPG list are:
1. Shaquille O'Neal: 3.22
2. Kareem Abdul-Jabbar: 2.79
3. Wilt Chamberlain: 2.55
4. Charles Barkley: 2.49
5. Adrian Dantley: 1.84
6. LeBron James: 1.73
7. Bernard King: 1.31
8. Karl Malone: 1.26
9. George Gervin (NBA stats only): 1.23
10. Michael Jordan: 1.15

All the other players from the list have a value lower than 1.00 PPG. The worst 2P%_E scorer from the list is George Mikan (-3.18 PPG for his NBA stats only), but in his times the league-wide 2P% was much lower than 48.3 %. The worst 2P%_E scorer from the list from the more recent times is Allen Iverson: -1.25 PPG.


2. Extra value of 3P%

This is a less stable statistic than 2P%. Currently the league-wide 3P% is 35.3 %, in 2006 it was 35.9 %, in 1996 it was 36.7 %, in 1986 it was 28.1 % and in the years 1977-1979 there were no statistics for 3-pointers. What's worse the number of 3P attempts was varying greatly over time – it was as low as 166 in 1981 and as high as 1975 in 2016. This is almost 12 times more 3P attempts! Even worse, some teams and players relied on 3-pointers and some other ignored them almost completely. For these very reasons I decided to value the 3P% in reference to the league-wide 2P% (48.3 %).

I calculate the extra value of 3P% in a slightly different way to take into account the fact that the 3P shot is worth 3 points:

3P%_E = 3PA*((3PM/3PA)*3-0.483*2)

Let's analyse an example with the reference point of 45.0 % (incorrect reference point, but very easy to calculate in memory). For example a player with 1000 3PA and 300 3PM (3P% = 30.0 %) during 100 GP is worth exactly as much as a player with 1000 2PA and 450 2PM (2P% = 45.0 %) during 100 G:
1000*30.0%*3/100=9.0 PPG
1000*45.0%*2/100=9.0 PPG
In this example (incorrect reference point) a high-scoring 3P shooter is good for his team if he makes more than 30% of his 3P attempts and he is bad for his team if he makes less than 30% of his 3P attempts.

Calculations with the correct reference point of 48.3% show that a high-scoring 3P shooter is good for his team if he makes more than 32.2 % of his 3P attempts and he is bad for his team if he makes less than 32.2 % of his 3P attempts.

The best 3P%_E scorers from the NBA top 30 PPG list are:
1. Stephen Curry: 2.65
2. Kevin Durant: 0.81
3. Dirk Nowitzki: 0.59
4. Larry Bird: 0.31
5. Carmelo Anthony: 0.22
6. LeBron James: 0.21
7. Kobe Bryant: 0.09

As you can see Stephen Curry is a phenomenon (Stephenomenon Curry). All the other players from the list have a value lower than 0.03 PPG. The worst 3P%_E scorer from the list is Charles Barkley, but his 3P%_E is only -0.31 PPG.


3. Extra value of FT%

This is a very stable statistic. Currently the league-wide FT% is 75.7 %, in 2006 it was 74.5 %, in 1996 it was 74.0 %, in 1986 it was 75.6 % and in 1977 it was 75.1 %. An average for the last 40 years is exactly 75.3 %.

I calculate the extra value of FT% taking into account the fact that a free throw is worth 1 point:

FT%_E = FTA*(FTM/FTA-0.753)

The best FT%_E scorers from the NBA top 30 PPG list are:
1. Kevin Durant: 1.05
2. Rick Barry (NBA stats only): 0.78
3. Dirk Nowitzki: 0.75
4. Oscar Robertson: 0.75
5. Michael Jordan: 0.67
6. Larry Bird: 0.66
7. Kobe Bryant: 0.62
8. George Gervin (NBA stats only): 0.62
9. Jerry West: 0.57
10. Adrian Dantley: 0.57
11. Stephen Curry: 0.56

All the other players from the list have a value lower than 0.50 PPG. Stephen Curry may be the best player as far as FT% is concerned, but he attempts too little free throws per game and this is the reason why his FT%_E is not the highest one. In fact there are 10 players ahead of him in this regard.

Clearly the worst FT%_E scorers from the list are Wilt Chamberlain (-2.75 PPG) and Shaquille O'Neal (-2.10 PPG).


4. Overall value of scorers (PPG-S%_NE)

Overall value of scorers should take into account the negative extra values of 2P%, 3P% and FT% (negative extra value of shooting percentage = S%_NE). Negative extra value of FT% should NOT be compensated by positive extra value of 2P% for the reasons already mentioned – a good 2P% scorer was already credited for his extra points in the box-score, but any missed free throws mean that he wasted such points irreversibly.

PPG-S%_NE = PPG + 2P%_NE + 3P%_NE + FT%_NE

Before I give you my final list I have to say something in defence of the low % (“negative”) scorers on the list. We have to remember that their coaches for some reasons kept them quite long on the floor, so maybe their teammates would be even worse for the team if they had to play longer minutes or take more shots than they actually did?

The best PPG-S%_NE scorers from the NBA top 30 PPG list are:
1. Michael Jordan: 30.12     (30.12 PPG -0.00)
2. Kevin Durant: 27.4     (27.4 PPG -0.00)
3. Wilt Chamberlain: 27.31     (30.07 PPG -2.75)
4. LeBron James: 27.11     (27.19 PPG -0.08)
5. Jerry West: 26.65     (27.03 PPG -0.38)
6. George Gervin (NBA stats only): 26.16    (26.18 PPG -0.02)
7. Oscar Robertson: 25.68     (25.68 PPG -0.00)
8. Allen Iverson: 25.31     (26.66 PPG -1.35)
9. Karl Malone: 24.89     (25.02 PPG -0.13)
10. Elgin Baylor: 24.88     (27.36 PPG -2.48)
11. Kobe Bryant: 24.87     (24.99 PPG -0.12)
12. Carmelo Anthony: 24.69     (24.94 PPG -0.26)
13. Dominique Wilkins: 24.63     (24.83 PPG -0.20)
14. Kareem Abdul-Jabbar: 24.41     (24.61 PPG -0.20)
15. Bob Pettit: 24.34     (26.36 PPG -2.02)
16. Larry Bird: 24.29     (24.29 PPG -0.00)
17. Adrian Dantley: 24.25     (24.27 PPG -0.02)
18. Dwyane Wade: 23.47     (23.65 PPG -0.18)
19. Pete Maravich: 22.44     (24.24 PPG -1.79)
20. Stephen Curry: 22.4     (22.4 PPG -0.00)
21. Bernard King: 22.27     (22.49 PPG -0.21)
22. David Thompson (NBA stats only): 22.11    (22.13 PPG -0.02)
23. Bob McAdoo: 22.02     (22.05 PPG -0.03)
24. Dirk Nowitzki: 22.01     (22.01 PPG -0.00)
25. Julius Erving (NBA stats only): 21.93    (21.97 PPG -0.04)
26. Rick Barry (NBA stats only): 21.86     (23.17 PPG -1.31)
27. Charles Barkley: 21.68     (22.14 PPG -0.46)
28. Shaquille O'Neal: 21.57     (23.69 PPG -2.12)
29. Paul Arizin: 20.51     (22.81 PPG -2.31)
30. George Mikan (NBA stats only): 19.13    (22.32 PPG -3.19)

Please notice that in case of 6 players (Michael Jordan, Kevin Durant, Oscar Robertson, Larry Bird, Stephen Curry and Dirk Nowitzki) their overall scorer value is equal to their actual PPG average. That's because they were above-than-average shooters in 2P% and FT% categories AND they were at least good enough 3P shooters not to harm their team (Michael Jordan) or there were no statistics for 3P% in their time (Oscar Robertson).

This way of comparing NBA scorers can be used only for this very purpose. The overall scorers' values above CANNOT be used to judge the draft value of NBA players. More on that in my next post, but it boils down to the fact that not all of the points should be credited to the actual scorers – basketball is a team sport after all. Moreover, weak shooters are simply punishing themselves by not scoring some points that better shooters would score. Punishing them more because of their poor shooting would be an overkill.

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