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Regression work: how does team spending by position translate to Wins?

We posted a couple of articles last season on salary cap correlations to wins, and you can find them here: Salary Cap research and the follow-on Top Paid player analysis.

The gist of those features was that Kickers, Running Backs, and Cornerbacks offered the best value in terms of high spending being connected to a good number of wins on the regular season, while many positions had minimal or even in the case of Linebackers and Defensive Tackles, negative correlations!

Now the correlations were weak in general, and as we pointed out though, what this perhaps means is that kickers and 'backs are more predictable in their performance such that you know what you're likely to get for the money, whereas at other positions there's higher risk in signings, etc. (not to mention that several teams have very high priced QB's sitting on the bench for one reason or another...)

This time round we have another season in the books to add to our data set, and we'll take a stab at running the regressions on how the positions interact, but first let's address the more obvious question: does spending more lead to more wins?

Correlation between total "Cap Value" spending and Wins

Since the salary cap number changes over time, we'll tackle this on a year by year basis...

Year
Correlation
95% CI
2000
.10
-.27 to .43
2001
.26
-.11 to .56
2002
.14
-.22 to .46
2003
.44
.11 to .69
Analysis: the simple answer is yes there's a connection between team spending on salaries and wins (not a big surprise) and this was seen clearly in the most recent season.

Team Total Spending by Position ("Cap Value")

Using the sum of cap value expenditures for the year by position and regressing for all the positions against the team's regular season wins that year produces the following values: (and no, we have not broken out kick returners, long snappers and other specialists)

Position
Coefficient
95% of CI
Intercept
4.08
-.28 to 8.45
K
1.70
.43 to 2.98
S
0.28
-.12 to .67
TE
0.22
-.30 to .75
RB
0.20
-.07 to .47
TE
0.22
-.30 to .75
OL
0.16
-.02 to .33
DE
0.13
-.09 to .35
LB
0.03
-.17 to .23
QB
0.01
-.18 to .20
CB
-0.02
-.23 to .20
WR
-0.08
-.36 to .19
DT
-0.11
-.37 to .14
P
-2.17
-3.89 to -.46
  R^2 = .17

Analysis: the 'intercept' starts at 4.0 wins, so to get less than that in the NFL might be deemed as doing really badly indeed!

The coefficients for positional spending reflect per million dollars of cap value accumulated, so in other words each million spend on a kicker is worth 1.7 Wins per year, whereas each million spent on a QB translates to roughly .01 additional wins. Go figure! Again what this really says is that if you spend on a kicker you know what you're going to get, whereas money put on Quarterbacks is a much more chancy investment (um, Ryan Leaf? Akili Smith? Any takers?), not that it can't pay off.

Amusingly, the kickers work out to be the most valuable, while the Punters represent horrible spending -- perhaps a team that allocates a lot of salary to a Punter is already in the mindset that it will be punting frequently, never a good sign!

The other key point to note is that the 95% confidence intervals are huge, meaning that the true ordering of these positions cannot be established with any strong degree of confidence.

Since what we seem to be measuring is not so much value of spending by position but risk of spending by position what we might find as a preferable gauge is to look at the change in spending from year to year rather than the absolute money expended.

Team Change in Spending by Position ("Cap Value")

Position
Total Spending
Correlation
Change in Spending
Correlation
K
0.27
0.27
QB
0.04
0.24
OL
0.08
0.19
WR
0.01
0.15
CB
0.23
0.14
DE
0.16
0.07
S
0.04
0.04
TE
0.17
0.01
RB
0.26
-0.01
LB
-0.02
-0.03
DT
-0.04
-0.09
P
0.04
-0.13

Analysis: Looking at the change in spending does show significant differences for a number of positions, although yes the K spot still comes out on top. Sliding into the second spot though is QB change in spending, which has led to a healthy connection to wins, but defensive tackles, linebackers and punters still can't get no love.

In terms of the biggest difference between the 'Total' and 'Change' you have QB +.20, WR +.14, OL +.11 as positive movers, and RB -.27, P -.17, and TE -.16 as negative ones.

Let's see what the regression run has to say on this subject:

Regression Values:
Change in spending to Wins
Position
Coefficient
95% of CI
Intercept
7.55
6.92 to 8.19
K
2.80
1.14 to 4.45
QB
.29
.04 to .54
CB
.21
-.03 to .46
DE
.14
-.09 to .38
WR
.12
-.16 to .40
OL
.10
-.11 to .31
RB
.06
-.25 to .37
S
.01
-.41 to .44
LB
-.13
-.34 to .07
DT
-.16
-.42 to .10
TE
-.17
-.68 to .33
P
-1.54
-3.63 to .54
  R^2 = .26



Analysis: A slightly better R-squared number of 0.26 suggests a better fit between our set and the wins than using straight spending. Quarterbacks jump up to #2 positionally in the positive impact on wins, and given that you can spend many millions more on a QB than a K, the truth can be that this is a good place to spend the money. Likewise CB, DE, WR and OL come in at double digit values.

Punters? You're better off putting the money somewhere else and going with a cheaper option, says the data on this recent span of years.

Ah, but another take on this is not to look at the pure regular season wins achieved by the team, but rather the change in spending correlated to the 'Change in Wins' from the prior season to this one. The main drawback is that of course you are governed by certain restrictions on team upside and downside -- a team coming off a 14 win season has little chance of bettering that record, regardless of the moves it makes, whereas a 2-14 team would have to fail completely again not to see an improvement.

'Change in Spending' correlated to 'Change in Season Wins'

Position
Change in Spending
95% CI
WR
.17
-.04 to +.36
K
.15
-.05 to +.35
TE
.14
-.06 to +.34
DE
.12
-.08 to +.32
OL
.10
-.10 to +.30
QB
.04
-.16 to +.24
RB
.02
-.18 to +.23
CB
.01
-.20 to +.21
LB
.01
-.19 to +.22
P
-.03
-.23 to +.17
DT
-.07
-.27 to +.13
S
-.12
-.31 to +.09

Analysis: The standard errors as reflected in the 95% confidence intervals means we can't state with any kind of authority that the ordering is correct. However, for what it is worth there are some more divergences from the general spending totals by position numbers.

Wide Receivers possibly offer the best bang for the buck in increased spending from one year to the next (good news for Philadelphia perhaps in 2004), and the linemen (with the usual exception we are seeing of DT's) are all valued for changing a team's fortunes.

Let's look at the regression values on this one as the finale for today:

Regression Values:
Change in spending to Change in Wins
Position
Coefficient
95% of CI
Intercept
-.38
-1.23 to .48
K
1.48
-.75 to 3.70
WR
.32
-.05 to .70
TE
.27
-.41 to .95
OL
.15
-.13 to .44
DE
.14
-.18 to .48
QB
.04
-.30 to .38
RB
.01
-.40 to .43
CB
.00
-.33 to .33
LB
-.04
-.32 to .24
P
-.09
-2.90 to 2.71
DT
-.10
-.46 to .25
S
-.35
-.91 to .22
  R^2 = .12

Analysis: Again, upping the spending on kickers has the most impact in bringing about a positive change in wins from one year to the next. With WR, TE, and the OL all coming in strong it's in agreement with some NFL GM's who value the passing game players above all else (and the DE's have of course a little to do with preventing the other team from passing well).

The curiosity is the Safety spot, which has seen every additional $1 Million spent lead to a -.35 win adjustment under this regression. The big money signings of safeties have not panned out in general of late then, but the 95%CI once more renders any clear cut judgement absurd.

Now, if we can dig up some salary data heading into 2004 (probably down the line a bit, when final cuts are announced), it could be fun to see what the regression formulas would predict in the three cases:

  • Total Spending by position --> Wins
  • Change in Spending by position --> Wins
  • Change in Spending by position --> Change in Wins
As for me, I'm going out and signing the highest priced kicker I can find!


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