Fantasy baseball: understanding replacement level

I like fantasy baseball because it makes us work. The 21st Century baseball fan know rather a lot about the numbers. He knows what's predictive and what's not. He knows where to find high quality projections. He thinks he understands value.

But what happens when he, the self-assumed smartest guy in the room, actually has to step into an auction draft room with eleven others and test himself? If he's at all like me, he knows that he needs to take those projections and turn them into dollar figures. It should be an easy task for a bunch of savvy sabermetricians like we all are. Only it's not.

You could let someone else calculate auction values, but just once, give it a try on your own.

If you've never done it before, the first thing you'll do is calculate how many players will be owned in your league (let's call that x). Then you'll total the points projected for the top x players, and decide that by the total budget of all the teams. You'll get a ratio that you think is the average dollar value of a point. You will then use that to draft. So go away, do your draft, and then check back here.

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Now, evaluate your league looking for trades. The most valuable players are uninspiring starters or part-time players (Brayan Pena, Logan Morrison, Juan Uribe, for instance) who have been acquired for one dollar, right?

Wrong. You've ruined your season, but congratulations -- you've discovered replacement level!!!!!

Side note: Pardon the exclamation points, but I was pretty psyched when this happened to me. The great thing about discovering something that everybody -- including you yourself -- already knows is that you're certain you're right.

There's a baseline level of production that you don't have to pay for. These players should not be owned (at least not by mid-season) in your fantasy baseball league, and are freely available for anyone with one dollar to spend on them. That means that if replacement level is 400 fantasy points, then the first dollar buys you the first 400 points, and any calculations about value should ignore that. Every dollar above the first should buy an incremental number of points above that replacement level

It's an incredibly important concept that I think is easier to understand as a fantasy baseball player than it sometimes can be in real-life fandom.

★★★

So the obvious follow up question is, how do you set replacement level?

My non-DRB Ottoneu league draft is today, so I've been working through it, and this year, I've used a slightly different method than I have in the past. It's given some odd results, which I'm going to roll with. Either I've found an extra 2%, or I'm simply wrong, and will lose (bet on the latter). Here goes:

• Rather than using projections to figure replacement level, I'm using last year's production. There is more variability in real production than there is in projections, because what we're looking at in the projection is mean performance. Consider two players each projected to receive 300 plate appearances and to produce at a league average rate. As the season unfolds, one of them hits well, and because of an injury on his team, receives 600 PAs. The other picks up a minor wrist injury which saps his power, and after struggling for a time is demoted to triple-A. If you had gone by the projections, you'd have thought you could easily acquire either one of them for a small price. But as it turns out, only one of them would actually deliver points. Therefore, replacement level as defined by real production will be lower than replacement level as defined by projections. I think using the real production is correct for fantasy, but I just hope 2014 is a typical year, or else I could be wildly wrong for a few positions.
• I'm assuming perfectly efficient allocation of roster spots. This is of course not going to happen in real life, but my league is pretty good. The best players will be played in the right spots, mostly.
• I'm filling virtual roster spots from the top of the defensive spectrum down. That's a shortcut, but the right way to do it would be to make a recursive simulation, which is just kind of a lot more work than I want to do. So what this means is that I identified marked the top 24 catchers as starters. Then I identified the top 12 shortstops (that were not a starting catcher) as starters. Then I marked the top 12 second basemen (that were not a starting catcher or shortstop) as starters. I went through every position this way, and then added a number of players for depth at each position (never counting a player twice because of his multiple positional eligibility) too. At the end, I had identified all of the players who should be owned in a perfectly managed league.
• Finally, I averaged the production of the next 10 un-owned players at each position, and called it replacement level.