## 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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Brad is a former collegiate player who writes for FanGraphs, MLB Trade Rumors, The Hardball Times, RotoWorld, and The Fake Baseball. He's also the lead MLB editor for RotoBaller. Follow him on Twitter @BaseballATeam or email him here.

### 15 Responses to “Valuing Your Last Roster Spot”

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1. FeslenR says:

I think I often make the “mistake” of rostering the unknowns rather than the veteran guys. I love unearthing a Patrick Corbin, for instance. To me, that’s part of the fun of rotisserie fantasy baseball, especially, the free leagues.

If you’re playing for money, I can see why gambling on these lesser known guys might not be worth the crapshoot.

• Tak says:

On the flip side, taking a risk and maybe, maybe getting a breakout star (i.e. Trout his rookie year) with the last roster spot might be worth it when the alternative is a run of the mill Andres Torres-type guy. That might be the difference in winning a money league and not winning it.

2. David says:

Unless you’re in a league where bench scoring matters in some way, it’s impossible to put a dollar figure on a roster spot. As you explain, there is no one correct answer. It is entirely dependent on how you want to run your team.

There are many wrong answers though. Carrying replacement level players just to have “depth” is inefficient. Carrying non-scoring players (prospects, injured, etc…) at a cost of being unable to fill holes when a starter has a day off or short term injury is likewise bad. Also, IMHO, hoarding streaming-level starting pitchers is a wasteful tactic that I see a great many owners employing.

• The Stranger says:

“Carrying replacement level players just to have “depth” is inefficient.”

Depends on the scoring system and the roster spots available. In a points league, being able to fill holes and use all your available starts is a high priority – carrying a replacement-level guy makes sense there (though upside is always better than no upside). In a 5×5 league, it’s less defensible because missing a few starts hurts you less.

A side point on the idea of “replacement-level” players, or “streaming-level” starters: that sort of thing is a lot more obvious in retrospect. Going into this season, I would have guessed that Matt Carpenter was a replacement-level guy without a lot of upside. Ditto Juan Uribe, Alfonso Soriano, Will Venable, etc. But people who rostered those guys for “depth” wound up looking pretty smart. Whereas the guys who grabbed Jurickson Profar as a potential breakout star didn’t get any value from that roster spot (in redraft leagues, anyway).

• David says:

If I need to fill a roster hole for a day, I can grab a free agent. I don’t need to keep him on the roster otherwise.

Matt Carpenter was my starting 3B on day one :)

3. The Stranger says:

Good read, and it seems like there are a variety of viable strategies.

But here’s the real question: how much of fantasy baseball strategy is rendered irrelevant by luck, and our inability to predict the future? I can recall entire seasons where I constantly streamed the wrong guys, picked up promising players just before the bottom fell out, and gave up on struggling rookies a week before they became household names. As you say, Sonny Gray could just as easily have pitched like Kevin Gaussman, and if he does, you’re getting negative value from that last roster spot.

Which is to say, trying to maximize the value of your final roster spots by streaming, grabbing prospects, etc. is a high risk, high reward strategy, and I wonder whether any of us are really prescient enough to consistently beat the odds with it. In that case, it might be better to just fill that spot with a consistently mediocre player who can fill in as needed.

Of course, if the only goal is to have fun (or maximize utility), swing for the fences – you’ll remember the leagues you win and forget about the times you manage yourself out of contention, and it’s not at all satisfying to finish a solid third by playing it safe.

Luck plays as big a role in fantasy baseball as it does in real baseball if not more. And streaming starters in particular is fraught with risk – especially if your league mates roster too many pitchers (which is common). Besides blind luck, sometimes there are just better players around. Last year, I had guys like Corey Kluber, Ivan Nova, and John Lackey to stream with confidence, but the prior season was quite bleak.

• The Stranger says:

Clearly, the world needs a RotoGraphsGraphs site, where we apply sabermetrical analysis to fantasy teams, rather than actual baseball players, in order to separate the effects of luck from actual fantasy skill, identify the true talent levels of fantasy owners, and determine what strategies yield positive value.

That’s not actually a bad idea, an active Ottoneu league where a few of our best experts follow the season closely, report on the league, and invent stats for identifying luck/skill.

The key I think being that none of the writers should be in the actual league(s) being reported on.

And I know you meant it as a joke, but I do see some potential in it.

4. The Foils says:

“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.”

Wait, are you saying that prospects are uncertain by nature and usually an unknown quantity? We don’t take too kindly to that kind of talk round these parts.

5. Gee's Up, Hoes Down says:

I used roster spots in September to stash George Springer and Yordano Ventura for next season. This article makes me nervous. I hope their roles solidify early in spring training before our draft.

6. ncb says:

Enjoyed the read, but it is really sad that fangraphs continues to link Zach Sanders z-scores article as if it were the gospel. While I appreciate the attempt, numerous readers have pointed out so many flaws with it that it is pretty much useless.

Every approach has flaws because every league is different. Z-scores are definitely “good enough” and Sanders’ rankings have the advantage of being here on Fangraphs and freely available. I’m unaware of any freely available valuations that have a better, objective methodology. My own technique is league specific, very time intensive, just as error prone, and contains too many subjective elements to use here. At least without getting my head ripped off by you all.

The important part of any valuation system is that it gives you a rough idea of rank order and cost. Specific values aren’t necessary because there are too many factors that lie outside of statistics that needed to be manually adjusted for, and as I noted, too many leagues are non-standard, sometimes even if they have standard settings and rosters.

• Kris says:

There are lots of freely available rankings. I’m not sure if their methodology is any better though.

Personally, I just take the player pool and create Z-Scores from the entire gosh-darn thing. Then, adjust for position.

It works fine and isn’t terribly difficult. At this point, there’s no reason why every fantasy baseball player shouldn’t have MySQL installed on their computer. It makes everything so damn easy once you get over the learning hump.

I did enjoy the article though and I’m not sure if it’s correct, but over the last three years or so, any time I can’t get the value I want, I always just plug in relievers. Mainly because I’m risk adverse and they’re almost never going to hurt you (unless they’re Jake McGee during the first few months of last year…ugh, that guy)