Obviously 3 $1 kickers is better than 1 $3 kicker. With no $1 kickers, is 2 $2 kickers better than 1 $3 kicker factoring in the extra buck?
OK, so I dumped a bunch of data and ran some regressions.Let's start with kickers. Here's the plan: look at every team --- even the ones that have been eliminated --- and record the following pieces of information about them:
1. How many kickers they took
2. How much money they spent on kickers
3. How many total points they have scored (or would have scored, for eliminated teams) at the kicker position during the first five weeks of the season.
Figuring that anything more than five kickers is probably not a very serious entry, and knowing how outliers can skew regressions, I threw out all teams who took more than five kickers. Then I ran a regression of total points versus number and money. Here is the formula that came back:
Total Points per week = 6.04 + .183*(dollars spent on PK) + 1.23*(HaveExactly2PK) + 1.94*(HaveExactly3PK) + 2.20*(HaveExactly4PK) + 2.37*(HaveExactly5PK)
[for you regression wonks, all coefficients massively significant. R^2 = .28.]
So, for example, if you have one $3 kicker, you can expect 6.04 + .183*3 =~ 6.57 points per week. If you have three $1 kickers, you can expect about 6.04 + .183*3 + 1.94 =~ 8.51 points per week. Two $2 kickers =~ 8.00 PPG
NOTE: these results are very, very sensitive to the particular performances of particular kickers in 2009 and the particular tendencies of contest participants in 2009. If Stephen Gostkowski were on record FG pace or if Dan Carpenter had gotten injured, or whatever, these results could look very different. On my to-do list is to go back and run this for 2008, but I'm not too confident about getting that done anytime soon.
With that (rather huge) caveat, here are the implications:
If you have one kicker, then adding a second one (for $1) will add about 1.23 + .18 = 1.41 points per week.
If you have two kickers, then adding a third one (for $1) will add about 1.94 - 1.23 + .18 = .89 points per week.
If you have three kickers, then adding a fourth one (for $1) will add about 2.20 - 1.94 + .18 = .44 points per week.
If you have four kickers, then adding a fifth one (for $1) will add about 2.37 - 2.20 + .18 = .35 points per week.
This is exactly what we'd expect to see: diminishing marginal returns.
I'll let the nerds toss this around for a bit, then post the numbers for Team D and QB. [For RB, WR, and TE, it gets a little complicated because I'm not quite sure how to count the flex.]