I've been comparing the Steamer Projection valuations - as run through my formula - to the NFBC ADP over aseriesofposts, and today I want to add a new wrinkle: accounting for closer scarcity.

You don't have to roster closers among your nine active pitchers, but due to the nature of the NFBC virtually everyone does. That's because a significant portion of your entry fee goes toward the overall prize money, and you have no shot at the overall title if you tank saves. That artificially drives up the price of closers, and we need to account for it of we're going to price the pitching pool accurately.

To that end, I decided to imagine instead of needing nine pitchers of any kind on your NFBC roster as is technically the case, you actually had to have a couple closers. I settled on six starters, two closers and a flex (starter or closer). The flex meant half the teams have a closer in that spot and half have a starter. Accordingly, I multiplied 6.5 starter slots by 12 teams to get 78 total starting pitchers drafted before the reserve rounds, and 2.5 closers (30 total.) I then separated the Steamer projections lists into starters and closers, using the 78th-ish* starter and 30th-ish* closer as my rough replacement value baselines.

*(For starters, replacement value was the average projections of pitchers ranked 68 through 87, according to ADP. I use 20-pitcher sample around the No. 78 starter to smooth out wins, ERA, Ks and WHIP. For relievers, replacement value was relievers 25-36.)

I calculated the value over replacement (VORP) in each category for the starters vs. baseline starters and relievers vs. baseline relievers. Then I adjusted the ratios for innings pitched and figured out how many standard deviations (in the overall mixed starter/reliever list) each pitcher's VORP was above or below the baseline for his group in each category. I added those together to get a total value.

Once you have the total value, you still have to convert it into dollars, and to do that I needed to know what the total budget for starters and closers was in the NFBC. Luckily, I had already figured that out in a prior post (you can click and evaluate the method for yourself.) It turns out 34 percent of the total pick value (converted to dollars) is spent on pitching, $1060.64 of the total $3120 (based on $260 per team). Of that $1060.64, based on ADP, $293.36 is spent on closers.

Once you have that number, it's pretty easy to add up the total values for all the closers drafted, divide that sum into the amount of money to be spent ($293) and get a multiplier. That multiplier is then applied to the total values to generate a dollar value. Here are the results for the closers (in order of ADP and based on the Steamer projections):

Based on these numbers**, it's easy to see why the elite closers should fly off the board in the fourth round - or earlier. But that's not really what this is demonstrating because I used the NFBC's own total closer expenditures to generate the closer budget. Put differently, the only reason the closer budget is $293 and not $200 is because the NFBC drafters collectively made it that way. So this doesn't show whether it's right or wrong, only that when you do apportion that much money to it, and treat closers as a separate position to be filled, here's how much of that budget you should apportion to each, assuming he was going to perform according to his Steamer projection.

You can see there's big gap between the top two (Chapman and Jansen) and everyone else. And the takeaway is that so long as closers are necessary as they are in the NFBC, and so long as this necessity pushes them up to where they're being pushed in the NFBC, then you should spend much more on Chapman or Jansen than anyone else, assuming you believe the Steamer projections.

This is a weaker point than I'd hoped to make, but it also underlines something that's hard to escape when doing these exercises: the power of the market to influence value. If you must have saves, and everyone's drafting closers in Rounds 2-4 until there are none left, what do you do? If you punt, you'll have a monster team in the other categories, but even so, it's hard to contend in the overall contest without saves, no matter how good your first four picks were. So the best we can do to some extent is assign a budget based on the market's practices and figure out how to make the best use of it. This is also true on the bigger question of hitting/pitching split.

(**The reason there are so many closers at the bottom with a zero dollar value rather than negative, is I set up the formula that way. When you allow negative valuations, it apportions even more money to the guys at the top, but that makes no sense because in practice the negative relievers would be dropped long before that.)

Let's take a look at what happens to the starting pitchers when you apportion them 34 percent of the budget ($1,061) minus $293 (closer budget) = $768 for 6.5 slots and compare them only to other starters:

Oddly, while Kershaw is still on top and by a massive margin, his overall price ($43.32) is much less than it was ($48.41) when I did this while including closers. Even stranger, on the first pass, I made the hitting/pitching split 70/30 rather than the NFBC's 66/34 here. You'd think Kershaw would have even more value.

But three things cut against that - when you remove the closers, the ERA/WHIP baseline gets lower, meaning more starters have value in those categories than they did when closers were included. That means while Kershaw's even further above replacement than before, he has to split the ERA/WHIP money, so to speak, with more high-inning players than before. Second, for whatever reason, Steamer seems to have reduced Kershaw's projection - from .92 WHIP to .97 and 2.30 ERA to 2.37. (I'm not 100 percent positive of this, but I'm trusting my memory here.) Third, the first time I ran the numbers, closers were worth quite a bit less because they didn't get a scarcity boost, i.e., I didn't assign them $293 of the $1,060. In fact, under the original undifferentiated 70/30 split, pitchers got $936 total and closers $143.9. That left starters with $792.1, $24 more than they have here.

The same is true of Max Scherzer, also still an outlier and also cheaper than before, but the rest of the pitchers are more or less the same as before without the closers included.

Here are the top 120 pitchers with starters and closers re-integrated:

It's interesting to note Jansen is the No. 5 overall pitcher, while Chapman is No. 7, ahead of Corey Kluber Stephen Strasburg and Jon Lester.

Next post will take on the hitters, with catchers separated out the way the closers were here.