The Mathematics of Fantasy Baseball: An Injured Fernando Tatis

The start of the 2021 Major League Baseball season has arrived notwithstanding adversity.

The entire Mets versus Nationals series was postponed due to a number of players who tested positive for COVID-19. Prior to the season’s start, there were a number of talented major leaguers who succumbed to injury.

Eloy Jimenez and Adalberto Mondesi were absent from their respective team’s opening day lineup. Jimenez is likely to miss the majority of the 2021 season, while Mondesi could potentially return sometime in May.

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Tatis' Status

Earlier this week, we learned of a major injury to San Diego Padres superstar Fernando Tatis Jr. that could shake up the fantasy landscape.

The full extent of Tatis’s injury and timetable is unclear to the public. This is typical. Here is what we know so far:

General manager A.J. Preller has told the media that Tatis will not need surgery for the time being. The injury has been classified as a shoulder subluxation, which is a partial dislocation of the shoulder resulting from movement beyond the normal range of the joint. Further exams later indicated a slight labrum tear.

Teams are not always completely forthcoming [to the public] on their medical knowledge of their players. If the Padres want to gain leverage in trade talks, it may not be in their best interest to fully disclose long-term injury details.

The day after the occurrence, my fantasy partner and RotoBaller injury expert, Reuven Guy posted this on Twitter, in comparison:

We also know that Tatis had experienced shoulder issues on two other occasions in the past few weeks. After Fernando produced just three defensive errors all of last season, Tatis committed five errors in the first five games of 2021 – two fielding and three throwing blunders. He clearly had been playing injured leading up to his unfortunate swing on Monday night.

Guy believes that Tatis will require corrective surgery at some point. Whether he may be able to hold off going under the knife until the offseason and is able to play through instability is unknown at this time. As for the timetable for Fernando's return to the field, it could range anywhere from the most optimistic estimates of 3 or 4 weeks to the real possibility of missing the entirety of the 2021 season.

I currently own exactly zero shares of Fernando Tatis in fantasy baseball. For snake drafts, my KDS preference of this draft season was to select in the middle portion of the order, or at the very top of drafts. With a top-two ADP, and in accordance with my preference of Mookie Betts & Jacob deGrom to others, Tatis was never an option that materialized for me. For auctions, his market price was set above my calculated cost. I valued Tatis at just over $40 in 15-team mixed leagues, whereas it typically costs $45 or sometimes more to roster him.

But for many of you, Tatis might lie as a crucial member of your fantasy squads. The question now is how to deal with his associated roster spot. As always, I prefer to look at the situation from a probabilistic / game theory point of view.

Value

Today, we will focus on the perspective of a redraft league. Keeper/dynasty league formats are far more complicated.

First, let’s assume that whenever Tatis returns, his skills will completely remain at his true talent level. That is likely a faulty assumption, but for now, let’s roll with it. Next, rather than coming up with an exact projected number of at-bats for Tatis – let’s perform a sensitivity test surrounding his possible 2021 playing time scenarios and assign some probabilities to those outcomes.

Above you will see the possible Fernando Tatis outcomes for 2021 with scaled statistics. There is no scenario where Tatis will amass 500+ AB in 2021. However, for each at-bat threshold thereafter, I assigned a probability point density. Again, I am not a medical expert – so these are rough likelihoods based on my understanding and knowledge of the situation. I tabulated a one-quarter chance that Tatis will miss the entire 2021 season.

You might find that my date of return distribution to be too conservative, or perhaps you find it not punitive enough. That may be. The idea in this article is to provide you with a methodology of looking at Tatis’s rest of season value and how to govern his roster spot.

To give a sense of the diminished values, above is the same analysis but with a replacement player’s stats supplemented for the time that Tatis will miss. I added in roughly the equivalent of Brandon Crawford’s stats - someone who approximately represents what one might find upon the waiver wire.

I also generated the associated full season 5x5 rotisserie values. To give you an idea at each playing time scenario of what Tatis would be worth according to the ATC Projections (for a 15-team mixed league), I listed an equivalently valued shortstop.

Taking the weighted average, I estimate that Fernando Tatis is now worth on the order of $17 on an expected basis. The projected value of holding onto Tatis is roughly comparable to playing Marcus Semien all season long.

If that sounds on the low side to you, citing “But this is TATIS!” – please remember that the above factors in a 25% chance that Fernando’s season is over – which could even be an under-estimation.

Risk

There is more to it than simply expected value. With the projected mid-level shortstop value expectation of Tatis, comes a greater amount of risk. The surrounding process risk is now larger from the sheer uncertainty of his return date, as well as his increased risk for re-injury. Plus, the longer he is out – the further away he will be from game action. He may require some extra minor league rehab time, further extending his absence.

The associated parameter risk is also elevated. We cannot be certain that his true talent will resemble that of an elite player upon return. Looking at the five games that he started in 2021 (playing through the shoulder injury), he batted a meager .167. The shoulder injury will be present all 2021 long. He might institute a [temporary] batting swing change, or may be instructed not to steal bases. The point is that the shape of his fantasy baseball profile is a large unknown, and is likely to be diminished.

The first principle of business is that a greater risk requires a greater return. In a vacuum, I would prefer a less risky, but similarly priced Marcus Semien over the now highly variable Fernando Tatis.

Trade Market

Now that we have a feel for Tatis’s value potential and associated risks, a few questions ensue.

If you own Tatis in a league:

• Should you seek out a trade?
• What should you look to exchange him for?
• What will the market offer for him?

If you do NOT own Tatis:

• What type of trade would be beneficial to your team?
• Will the Tatis owner be interested in such a trade?

To help us answer these questions, I enlisted my Twitter followers for the following two polls:

The results of the polls are fascinating. Both elicited a very wide range of responses. Almost a quarter of the field would trade Tatis for less than 20 cents on the dollar, while a third wouldn’t accept anything less than a small downgrade.

On the opposite end, a quarter of the respondents would only chance a trade for Tatis by exchanging a low-end shortstop. Forty percent of the crowd would trade their #1 SS for a stab at Tatis’s upside.

If you aggregate the results, the average seller will accept a 50% reduction in value from full price. The average buyer though, expects a 67% discount. The difference between the two is quite normal, and frankly, on the small side. Combining this small average departure of expectations with the large spread of perceived tendencies, it seems that the market should be primed for trade discovery. If you are risk-averse and own Tatis, I would expect that you could find a willing trade partner. If you are risk-seeking, you should at the very least approach your league’s Tatis owner to gauge his asking price. Uncertainty breeds differences of opinion, which ripens fruitful trade conditions.

Action

Onto the “What should you do?” question … let’s start with the seller’s point of view.

If you glance back at the playing time sensitivity chart, you will see that the upside of Tatis equates to some 75% of value. A trade for Xander Bogaerts or Bo Bichette is a slam dunk. You should be unquestionably willing to accept this. Treat the 25% value loss as a sunk cost from your perspective. But you should be able to accept a lower-valued player.

On the underside, a trade for Paul DeJong (of 15 cents on the dollar) leaves you with an automatic $35 value hole, which may be too great to overcome in order to compete for a league title. Unless the chances of a total Tatis season loss rises to over 50%, the probability of a first-place league finish remains higher with Tatis on your fantasy squad than by selling for marginal production over replacement.

My advice is to trade for roughly the expected value of Tatis’s scenarios, or slightly better. Trading for 50-60 cents on the dollar would be optimal, and it would decrease your team’s aggregate risk in the process. Gleyber Torres or Javier Baez would be on my target list. Perhaps make a similar (or more favorable offer) in your deeper mixed leagues, and even try asking simultaneously for a small pitcher upgrade.

On the buying side, there is no need to trade at all. Any acquisition should establish an increase in your chances of winning a league title. In order to evaluate whether the addition of Tatis to your roster makes sense, you’ll have to perform a risk/reward assessment. At par value, a trade would increase your team’s risk without a corresponding increase in team value. You would be foolish to trade Dansby Swanson or Carlos Correa away for an uncertain situation.

However, if you can trade a lower and more replaceable asset on your squad, it would be a risk worth taking. Paul DeJong’s profile can largely be replicated on the waiver wire, and is valued at half of Tatis’s expected ROS projection. I would take on some added risk for an expected doubling of the initial investment made on DeJong’s current roster slot.

On this week’s RotoWire podcast, Fred Zinkie discussed an idea for the buying side. He suggested to offer a starting pitcher for Tatis, if you have the depth. Depending upon your league size and format, middle to low-end pitchers can be more easily replaced on the waiver wire, and thus are more expendable. I will add that with exchanging a pitcher [for Tatis], the increase in aggregate team risk will not be as great, keeping the team’s risk/reward dynamic steadier.

Conclusion

I cannot think of a recent time in fantasy baseball where a consensus top-five player exhibited the possibility for a season-ending injury during the first week of the season. This is not a situation that we are used to.

Think probabilistically.

Think economically.

Account for both value and risk when making team decisions.

For the current situation, both on the selling side and on the buying side, the trade market is worth exploring. There is enough of a range of owner tendencies to allow for the possibility of an accretive purchase.

If you are in a non-trading league with injured list slots, the optimal play is simple. Insert Tatis in an IL slot, and pick up the best available replacement for your roster.

If you are in a non-trading league without injured list slots, with Tatis’s elite upside level of play, you would be wise to wait a few more weeks until more concrete information arises.

Many thanks to Reuven Guy of RotoBaller (@mlbinjuryguru) for lending his medical knowledge/opinion of the Tatis injury for this article. He also directed me to Tatis’s five defensive errors in 2021.

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