I've decided to post my thesis on starters vs. relievers once and for all, so I have a URL to point to when people say that relievers don't help your ERA and WHIP.
Postulate: The top closers (and middle relievers) help your ERA and WHIP approximately as much as the top starters.
To prove this, I have created stats called ERA Imp and WHIP Imp. I have not seen anyone else use these stats, and as far as I know, they are my own invention. ERA Imp measures how much a player's ERA will affect the "average fantasy team", by taking into account both ERA and IP.
For purposes of this proof, I will consider the "average fantasy pitcher" to pitch 163 and 2/3 innings, and to have an ERA of 3.355. This is based on an (admittedly) abitrary sample of the top 100 pitchers, based on last year's stats. I think these were the top 100 point-getters on Sportsline. Something like that.
For purposes of comparing any two pitchers, your staff will consist of 7 pitchers. The first 6 pitchers will be John Mediocre, a hypothetical pitcher who throws 163.67 innings and has an ERA of 3.355. The 7th pitcher is Pitcher X, that is, whoever we are trying to determine the value of.
Let's take Gagne as an example. The 6 John Mediocres will pitch a total of 982.0 innings, and will give up 366 earned runs. Gagne, last year, gave up 11 ER in 82.33 inings. Adding him to your staff will give you an ERA of 3.19, an improvement of .165.
What about Prior? Prior gave up 57 ER in 211.33 innings. Adding him to your staff of John Mediocres will also give you an ERA of 3.19, the same improvement of .165.
I computed this number for all of the top 100 pitchers, and, surprise, the top relievers are very close to the same ERA Imp and WHIP Imp as the top starters. I will post the entire list in the next post.
I believe that this proves my point.
1) Most staffs have more than 7 pitchers, and you rotate in your starters to get better matchups out of them.
Answer: Yes, but your stud starters stay in for all matchups. And I am only trying to prove the relative value of stud starters versus stud closers. So this doesn't apply here.
2) My staff had a much better ERA than 3.19. OR My staff had a much worse ERA than 3.35.
Answer: The staff ERA is highly dependent on league size and pitching staff size (the bigger either one is, the higher your ERA will be, as you have to rely on worse starters). I have no data that suggests this makes a difference in relative value of closers or starters.
I will post results in the next post.