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Fantasy Basketball: NBA Z-Ratings

NBA Statistical Analyst Brandon Tower


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.

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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