The numbers don't lie -- kind of

The Football Outsiders have a link to an SI.com article by Duane Cross on who is the best all-around RB in the NFL. The only problem is that Cross's method takes a lousy approach to identifying the best RB based on performance.

Let me explain. Cross, using the top 15 rushers from 2003, takes a bunch of offensive categories, ranks each player in each category from best to worst, and then sums up the total points for each player across all categories. The player with the most points is (according to Cross) the best all-around RB in the league.

I have one primary concern with using ranks to determine "the best." Rankings are arbitrary. They give us no insight into how much better a player ranked 3rd is than the player ranked 4th. To get around this problem, we can use z-scores. Z-scores are a way to standardize data in such a way that you can make comparisons about how much better Jamal Lewis was than Ahmed Green (instead of just saying that Lewis was 1st in rushing and Green was 2nd).

Anyway, Using the same 15 players Cross used (and the same categories), I converted all the ranks to z-scores and re-summed the totals (zscore TOT is the sum of all z-scores across statistical categories, zrank is the player rankings of z-scores, CBS TOT is the points totals used by Duane Cross, and cbsrank is the rankings of point totals).

Player	zscore TOT	zrank	CBS TOT	cbsrank
P. Holmes	14.8	1	224.5	2
L. Tomlinson	14.5	2	228.0	1
A. Green	13.3	3	207.5	3
J. Lewis	8.2	4	172.5	5
D. McAllister	6.0	5	162.5	6
R. Williams	2.5	6	135.5	9
F. Taylor	1.9	7	158.0	7
S. Alexander	1.7	8	180.5	4
T. Barber	-1.4	9	123.0	10
C. Portis	-4.1	10	149.0	8
T. Henry	-5.1	11	111.0	12
C. Martin	-5.3	12	94.5	13
E. James	-6.4	13	120.5	11
S. Davis	-10.5	14	93.5	14
D. Davis	-14.6	15	87.5	15
E. George	-15.5	16	64.0	16

Surprisingly, the findings are very similar. Cross had Tomlinson as the best all-around back and I had Priest Holmes -- but just barely. The fact that Holmes had 27 TDs last season was big (especially since the next highest total was 15 by Ahmed Green), but so too was the fact that Tomlinson had 100 receptions (Holmes had 74).

Looking at the lists, both seem to follow closely, with the only noticeable difference coming with Shaun Alexander. He's ranked 4th on Cross's list but 8th on my list. Why? In terms of z-scores, Alexander finished in the middle of the pack in most statistical categories, and as a result was unable to distinguish himself from the other average (among the top 15 rushers, anyway) backs. Using rankings as a measure can skew the results because (as I mentioned above) how much better one player is than another can't be quantified.

So even though using z-scores is a more accurate means of determining who the best all-around RB is (based on the categories Cross decided to use), in this case rankings work almost as well. That said, Cross had Tomlinson as his top back while I had Holmes (but only slightly edging Tomlinson).

This was a relatively simple exercise to compare methods based on easily available data. If you're interested, Football Outsiders have taken some in-depth (and I mean really deep) looks at measures that translate into success on the field (something more than just saying Tomlinson caught 100 passes -- how many of those receptions led to first downs?). Either way, I think it's hard to go wrong with Holmes or Tomlinson.