Fantasy Basketball: NBA Z-Ratings
by Brandon Tower, 10/24/06
Every site has it's own pre-season player rankings, almost all of which are based off of someone's subjective analysis and opinons. They may look at some stats, but alot of big time scorers end up on top, even though scoring is much easier to come by than blocks or steals. And if there are many categories a team is competing for, aren't good numbers across the board better than someone who just scores?
There's a way to account for both of these things. A Z-score (X-Mean/Standard Deviation) will give us a number of how well a player performed relative to all other players in a group for that stat. The key though, is that it standardizes the score on a scale of about -3.5 to 3.5. This allows to you to do this for all stats and simply combine them to find a Total Z-Rating that shows how complete/valuable a player is based on their last season.
Because it encompasses most of the stats tracked in a fantasy league, I used the NBA Efficiency rating to determine my population. I took the top 50 players, and shamelessly added in my favorite player, Kirk Hinrich (#62 eff).
I used the 10 basic categories: PTS, REBS, ASTS, BLKS, STLS, 3PTM, 3PT%, FT%, FG%, and T/O.
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So after plugging in some data and doing quick calculations, (ok, it took me almost 8 hours to do the whole thing in excel, I need some programming help), you can get the Z-scores for all the top 51 players (okay, top 50 in NBA Efficiency and Hinrich).
For example, the Z-scores for players for the Points category looked like this:
Player |
Pts/Game |
Z-Score |
Kevin Garnett , MIN |
21.8 |
0.2837 |
LeBron James , CLE |
31.4 |
2.0069 |
Shawn Marion , PHX |
21.8 |
0.2837 |
Elton Brand , LAC |
24.7 |
0.8042 |
Kobe Bryant , LAL |
35.4 |
2.7249 |
Dirk Nowitzki , DAL |
26.6 |
1.1453 |
Dwyane Wade , MIA |
27.2 |
1.2530 |
Allen Iverson , PHI |
33.0 |
2.2941 |
Ming Yao , HOU |
22.3 |
0.3734 |
Chris Bosh , TOR |
22.4 |
0.3914 |
Paul Pierce , BOS |
26.8 |
1.1812 |
Gilbert Arenas , WAS |
29.3 |
1.6300 |
Steve Nash , PHX |
18.8 |
-0.2548 |
Pau Gasol , MEM |
20.4 |
0.0324 |
Tim Duncan , SAS |
18.6 |
-0.2907 |
Marcus Camby , DEN |
12.8 |
-1.3318 |
Andrei Kirilenko , UTA |
15.3 |
-0.8831 |
Jermaine O'Neal , IND |
20.1 |
-0.0215 |
Chris Webber , PHI |
20.2 |
-0.0035 |
Jason Kidd , NJN |
13.3 |
-1.2421 |
Lamar Odom , LAL |
14.8 |
-0.9728 |
Dwight Howard , ORL |
15.8 |
-0.7933 |
Chris Paul , NOK |
16.1 |
-0.7395 |
Ray Allen , SEA |
25.1 |
0.8760 |
Carmelo Anthony , DEN |
26.5 |
1.1274 |
Chauncey Billups , DET |
18.5 |
-0.3087 |
Vince Carter , NJN |
24.2 |
0.7145 |
Richard Jefferson , NJN |
19.5 |
-0.1292 |
Shaquille O'Neal , MIA |
20.0 |
-0.0394 |
Tracy McGrady , HOU |
24.4 |
0.7504 |
Brad Miller , SAC |
15.0 |
-0.9369 |
Michael Redd , MIL |
25.4 |
0.9299 |
Antawn Jamison , WAS |
20.5 |
0.0503 |
Mehmet Okur , UTA |
18.0 |
-0.3984 |
Gerald Wallace , CHA |
15.2 |
-0.9010 |
Boris Diaw , PHX |
13.3 |
-1.2421 |
Carlos Boozer , UTA |
16.3 |
-0.7036 |
Jason Richardson , GSW |
23.2 |
0.5350 |
Joe Johnson , ATL |
20.2 |
-0.0035 |
Mike James , TOR |
20.3 |
0.0144 |
Rashard Lewis , SEA |
20.1 |
-0.0215 |
Baron Davis , GSW |
17.9 |
-0.4164 |
David West , NOK |
17.1 |
-0.5600 |
Ben Wallace , DET |
7.3 |
-2.3191 |
Zydrunas Ilgauskas , CLE |
15.6 |
-0.8292 |
Tony Parker , SAS |
18.9 |
-0.2369 |
Mike Bibby , SAC |
21.1 |
0.1580 |
Rasheed Wallace , DET |
15.1 |
-0.9190 |
Troy Murphy , GSW |
14.0 |
-1.1164 |
Andre Miller , DEN |
13.7 |
-1.1703 |
Kirk Hinrich |
15.9 |
-0.7754 |
So if you're still confused, in a nut shell all a Z-score is, is a standarized, relative score. The scoring champion Kobe Bryant obviously has the highest Z-score for PTS, and Ben Wallace the lowest, because he had the lowest amount of PPG.
We convert to the Z-score so we can do the same for all other 9 stats and add them together. This statistical analysis gives you the following rankings based on last seasons play:
Combined 10-category Z-scores
(Based on last season's per game stats)
Rank |
Player |
Z-Score |
1 |
Shawn Marion , PHX |
7.1205 |
2 |
Dirk Nowitzki , DAL |
3.9213 |
3 |
Kevin Garnett , MIN |
3.8833 |
4 |
Kobe Bryant , LAL |
3.7346 |
5 |
Elton Brand , LAC |
3.6053 |
6 |
LeBron James , CLE |
3.1083 |
7 |
Ray Allen , SEA |
2.9438 |
8 |
Steve Nash , PHX |
2.2652 |
9 |
Gerald Wallace , CHA |
2.1130 |
10 |
Gilbert Arenas , WAS |
1.9895 |
11 |
Chauncey Billups , DET |
1.3717 |
12 |
Michael Redd , MIL |
1.2511 |
13 |
Rashard Lewis , SEA |
1.0966 |
14 |
Allen Iverson , PHI |
1.0804 |
15 |
Rasheed Wallace , DET |
0.9263 |
16 |
Marcus Camby , DEN |
0.7940 |
17 |
Chris Paul , NOK |
0.5680 |
18 |
Andrei Kirilenko , UTA |
0.5296 |
19 |
Antawn Jamison , WAS |
0.4733 |
20 |
Lamar Odom , LAL |
0.3690 |
21 |
Paul Pierce , BOS |
0.2154 |
22 |
Mike James , TOR |
0.1875 |
23 |
Dwyane Wade , MIA |
0.1115 |
24 |
Brad Miller , SAC |
-0.1114 |
25 |
Mike Bibby , SAC |
-0.1552 |
26 |
Jason Richardson , GSW |
-0.1601 |
27 |
Vince Carter , NJN |
-0.1741 |
28 |
Tim Duncan , SAS |
-0.1821 |
29 |
Jason Kidd , NJN |
-0.3176 |
30 |
David West , NOK |
-0.4502 |
31 |
Richard Jefferson , NJN |
-0.8376 |
32 |
Chris Webber , PHI |
-0.8962 |
33 |
Mehmet Okur , UTA |
-0.9767 |
34 |
Tracy McGrady , HOU |
-1.0683 |
35 |
Joe Johnson , ATL |
-1.1092 |
36 |
Pau Gasol , MEM |
-1.3180 |
37 |
Boris Diaw , PHX |
-1.4023 |
38 |
Ming Yao , HOU |
-1.4294 |
39 |
Kirk Hinrich |
-1.4987 |
40 |
Chris Bosh , TOR |
-1.6118 |
41 |
Carmelo Anthony , DEN |
-1.7262 |
42 |
Jermaine O'Neal , IND |
-2.1621 |
43 |
Troy Murphy , GSW |
-2.4320 |
44 |
Ben Wallace , DET |
-2.5922 |
45 |
Baron Davis , GSW |
-2.6065 |
46 |
Zydrunas Ilgauskas , CLE |
-3.1786 |
47 |
Tony Parker , SAS |
-3.2061 |
48 |
Carlos Boozer , UTA |
-3.3105 |
49 |
Dwight Howard , ORL |
-3.7768 |
50 |
Shaquille O'Neal , MIA |
-4.4651 |
51 |
Andre Miller , DEN |
-4.4780 |
Ha! You see Kirk Hinrich at 39?! I knew he belonged. (Yes, there are other's you could add in who would probably crack the top 50, but not many). Other than that, we do have alot of surprises. For one, it confirms my belief that Dwyane Wade is the most overrated fantasy player in basketball. If you think about it, it makes sense, he provides mostly scoring, which is readily available among many players. He gives you some assissts and a decent FG%, but he has nothing to offer as far as 3-pointers, and as a guard he's limited in blocks and other big men stats.
The fact that Gerald Wallace cracked the top 10 shows the importance of guys who can really get Blocks and Steals. Since the totals for those stats aren't nearly as hight as points or other stats, the few guys who can average 2 or 3 a night are so much more valuable because they are so few players who available to give you that. It's a completely objective way to judge a player's true value to your team in all stats relative to other players around them.
Of course no stat is perfect; because it's based all on the previous year's stats, there's no accounting for a player's improvement or the potential for a breakout season, or inversely, the chance that a player is on the decline or a one season wonder. It also doesn't account for a coaching change or change in basketball philosphy, i.e., are they reeling it in, or making like the Pistons are doing and planning on running? That knowledge could make Billups even more valuable than he appears to be. Finally, the last drawback is there's no way to compare a rookie against the guys already in the league, so that's another judgement call for the manager.
Summary:
For the most part, the players who will have the biggest impact on your team will be the star players on top of the game; the ones who are in their prime and whose numbers will be fairly consistent from year to year. Because this pattern generally holds up, you can standardize the numbers to find their relative value, and add them together to find their complete value for a fantasy team. While you may have to make some emergency overrides in special cases, like rookies, up and coming/aging players, a new coach, the Z Rating works exactly to the point of fantasy sports. There is no intangible value for a fantasy player, just numbers. The Z Rating is based off of those very numbers. Keep in mind, it is you're team, so have fun with it. Add your favorite player to the list, especially if that player is as great as, say, Kirk Hinrich.
Brandon Tower lives in New Jersey but roots passionately for his favorite team the Chicago Bulls.
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