## Valuing Your Last Roster Spot

Fellow RotoGrapher Chad Young recently posted on the value of playing time as it pertains to weekly vs. daily leagues. The first commenter, Kris, asked a great (and difficult) question – “what is a roster spot worth?” Basically, how many dollars did an owner forgo to roster, say, Oscar Taveras last season?

The easy answer is, it depends. While I could sit here, reconstruct a standard league, make a handful of assumptions, and come away with a rough estimate as to the value of the last roster spot, such an analysis would miss too many factors. Instead, I will take the rest of this article to highlight some of the things you’ll want to consider when deciding how to deploy your final roster slot.

It doesn’t really matter if we’re talking about a redraft or keeper league since we’re only trying to estimate opportunity cost in Year 1. I’m going to tackle most of this article from the perspective of a points league, simply because the math is more intuitive. The same exercise can be performed for other league types, you just need to use a z-score method like that Zach Sanders uses with his player rankings.

Like with real baseball, positive performance becomes more valuable as the rest of your team improves. Consider the following real world Win Curve.

Imagine auction dollars on the y-axis and points on the x-axis. A large part of the graph is flat. That’s where gaining more stats doesn’t help you win anything valuable (even bragging rights). Almost all owners  who employ an actual draft strategy will live somewhere on the curved portion of the chart – at least to start the season. I consider the peak to be the number of points needed to be confident in winning the league 50 percent of the time.

Where you live on the curve is important as it greatly affects how valuable the marginal stats provided by your last player are to you. If, with perfect foresight, 300 points is the difference between fourth and first place, then you’ll want to eke every little bit of value you can out of your last player. If instead you need 1,400 points, not even a Jose Bautista quality waiver find can save you. Your last player isn’t important in that scenario.

This comes with a few assumptions. I already mentioned perfect foresight, which is to say that you have an accurate estimate of your team’s chances and understand the strengths and weaknesses of every roster in the league. For some of you that may even be true, but most owners don’t put in the time necessary to wrap their heads around that quantity of information. We’re also assuming that you can deploy your last roster spot in an optimal manner. Say you roster Rajai Davis so as to add about 20 marginal steals (you wouldn’t play him every time he starts), but then end up winning the category by 30 steals. Whoops, you just wasted your last roster spot (that may be simplistic since your large lead might have prevented a number of owners from chasing that stat…).

Since it’s nigh on impossible to know where you are on this win curve without huge error bars (for example, where do the Phillies think they are on the win curve?), the optimal strategy is to maximize stat accrual until such time as it becomes obvious that you’re either in or out of the race. At that point you can adjust your strategy accordingly.

Beyond knowing where you are on the fantasy version of the win curve, there are other considerations to keep in mind. A league with deep rosters like Ottoneu may never need to ponder this question. In fact, Ottoneu is designed specifically so that you can leave several roster spots fallow without leaving anything on the table in the current season. Conversely, owners in leagues with only a couple bench spots must make the absolute best use of those spots and can never consider using them on an inactive player.

Your roster also matters. If you have a bunch of flexible players like Ben Zobrist and Martin Prado, then you may need fewer players in order to cover every active roster spot most days. If most of those players are also everyday types, then you may not even need your last roster spot. However, it might be that you could pick up a platoon masher for free and enjoy a slight upgrade over one of your regulars 40 percent of the time. That’s up to you to honestly and accurately assess your roster and the talent in the waiver pool.

How you built your roster affects the viability of waiver additions. Some owners will draft a replacement level shortstop and/or catcher if they don’t get one of the good ones. In that case, there aren’t many platoon options on the waiver wire that would add much marginal value to your roster. However, I usually de-prioritize outfielders and starting pitchers in the draft knowing that I can find average or better talent for free at various points in the season. For example, my rotations were heavy on Patrick Corbin, Sonny Gray, Danny Salazar, Corey Kluber, Ivan Nova, Alex Wood, and Michael Wacha last season, most of whom I rostered for free or with FAAB money (I did draft Corbin with \$1/last round picks). That’s a little beyond today’s lesson, but you’re obviously better off if your last player is Kluber than Didi Gregorius.

Along a similar vein, your league’s replacement level matters. If it’s a deep league with a lot of active roster spots, the platoon options on the waiver wire might be guys like John Mayberry Jr. or Andres Torres. Given the choice between a part time scrub and a high upside prospect who may not play, I might prefer the prospect. The Torres’ of the world are only ever going to play when you don’t have another player active that day. Torres might add 100 points to your roster over a season, but a couple weeks from a top prospect could easily outdo a couple months of Torres. Of course, prospects are finicky beasts, for every example of one that gets called up and hits the ground running, there’s another that flops around and hurts his fantasy owners.

Your affinity for streaming comes into play here too. Those who know me know that I’m a huge proponent of streaming and the considerations in this article are a big reason why. With a dedicated stream slot, you are committing your last player to play every day of the fantasy season, thereby maximizing his value. For 5×5 leagues, you’re also accruing stats in 10 categories rather than five – although that’s only valuable if you make good, fortunate choices. A typical last player (position player or reliever) might play 60 games for your roster. Streaming essentially turns that one bench spot into three. This has frequently allowed me to pursue all of my marginal stats while ALSO rostering that Taveras quality prospect.

As for actually placing a value on that final roster spot, I prefer to use the economic concept of utility (aka happiness) and real dollars. For free leagues, the value of that marginal player is entirely utility based, which complicates the calculus. As a first level analysis, you can consider how much utility you would gain by finishing first rather than fourth. However, assuming a keeper league, you might be the type of person who would really enjoy waving a cheap Mike Trout over everybody’s head for foreseeable future. On the other hand, maybe you’re like me and would instead enjoy using Jonny Gomes and Adam Lind to beat a roster with considerably better players.

Money leagues have an actual dollar value that can be attached to the final roster spot. And depending where you are on that win curve, your final roster spot could be worth a very large portion of the purse. As such, I usually recommend an all hands on deck strategy for money leagues, at least until you master the format you’re playing.

Closing notes: One important consideration that was not addressed in this article was the value a prospect could provide once called up. Does a month and a half of Travis D’Arnaud outweigh four and a half months of waiting? Or six months of John Buck? I used D’Arnaud intentionally because he was quite bad last season. He’s a lesson that prospects can help as easily as harm your roster. Prospects are uncertain by nature, so while a couple months of Gray was great for fantasy owners, he could have also pitched like Kevin Gausman. My point is that unless you are very sure of the prospect (i.e. Stephen Strasburg), you’re using your last roster spot on an unknown quantity.

In general, this is an incredibly nuanced topic that could be discussed at chapter length. We can take that level of detail into the comments…

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