THE BOOK--Playing The Percentages In Baseball

I don’t think you can use the same replacement level for a starter and a closer.  Every team has at least a reasonably-competent reliever to which it can entrust high-leverage innings.  If we say a “replacement reliever” is 4.5 R/G, and assume Pabelbon gives you 72 IP (more realistic for pure closer), that’s 16 runs saved, X 2.0 LI, = 32 runs.  As a 3.40 starter over 207 IP, he gives you 60 runs, about twice as much.

I have no idea, of course, if he could deliver 3.40 over 207 IP on a regular basis.  But if so, he’d be worth much more as a starter.

4.5 RPG replacement reliever qualifies him for about a 5.4 RPG replacement level as a starter.

If that’s the comparsion level, then (5.4-3.4)/9*207 = +46

I also wouldn’t use the “reasonably-competent”, since you are using a higher quality baseline for your closer than for your starter.

I think Guy is right. This is what’s called “chaining” (I strongly recommend Patriot’s article on baselines, where chaining is explained, for anyone who hasn’t read it, and even for those who have as a re-read: http://gosu02.tripod.com/id77.html). Essentially, the idea is that when you lose a player, he gets replaced by the next-best available player to you, who is then replaced by some bum. So if you lose your first baseman, he gets replaced by your best pinch-hitter, who is in turn replaced by a spare part. Most of the lost at-bats are then going to go the pinch hitter and not the bum, making the correct replacement-level equal to playing time lost by the starter X the pinch hitter’s ability + the time lost by the pinch hitter X the bum’s ability. This is more correct than the general replacement-level approach which says replacement-level is equal to playing time lost by the starter X the bum’s ability.

Anyways, what happens here is that the starter is going to be replaced by a much lower quality pitcher than the closer, as you’re more likely to find a guy who can prevent runs than a guy who can prevent runs AND throw enough innings. This is really important specifically because of the leverage that is involved, as the drop-off from the closer to the replacement will not all occur in the closer’s high-leverage innings, but rather partially in high-leverage situations and partially in the setup man’s lower leverage situations.

So in fact it IS correct to use a higher-quality baseline for your closer than for your starter. And any analysis that does not adjust for chaining is doomed to fail because of this.

I meant to suggest a “replacement closer” might be around 4.50 R/G.  A replacement reliever is 5.10, if our assumption is a replacement starter = 6.0.  Then we need to adjust for the chaining issue, as DSG suggests.  I’m just guessing there, but if anything 4.50 is probably a generous assumption—4.0 might be closer to the mark. 

In any case, 3.40 as a starter is equivalent to an ERA+ of 147.  That would make Papelbon third in history, between Lefty Grove’s 148 and Walter Johnson’s 146.  To me, when your analysis tells you to convert Grove and Johnson into closers, it’s time to reevaluate your methodology.