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Fat Tails and Baseball: Studying the Impact of the Improbable

Example made by Konstantin G. Aravossis.

The Problem

Ever since the beginning of the “Moneyball Revolution,” teams have been determined to project their success. They must know the future of their team before it happens, even if the projections are based on a wide range of assumptions. Due to such assumptions, teams are simply unable to produce precisely accurate models. The hard work of regressing performance rates and analyzing trilobites of data ultimately falls short. Despite this, these teams articulate their moves based primarily on projection data. Projection data fails to consider outliers, leading teams to miscalculate their risk.

Before I continue, I want to mention that the concept for this article was based on a theory popularized by Nassim Taleb. He suggests the idea of a Black Swan: a highly unpredictable event that can have severe consequences. Primarily using financial instances, he demonstrates how the failure of systems to consider extreme outlier risks and the effects that they can bring leads to companies miscalculating their bets. By not considering these instances, he argues that even the most conservative of investment portfolios is often one step away from total disaster. And while I am not in agreement with everything he states, this concept seems sound - all it takes is one instance of miscalculated risk to bring everything down.

I believe that this idea applies to professional baseball teams. Based on their decisions, I assume that the majority of teams consider such outliers non-factors. This leaves these franchises exposed to risks that they haven’t even thought about. Unexpected, negative exposure is the worst type of risk, and often the most lethal. Hence, I want to provide an analysis of the damage that these supposed “non-factors” bring, as well as how it is to be avoided.

In Major League Baseball, paying for the best talent is considered to be the most conservative way of ensuring that a winning ball club is put on the field. Projections show that success is likely, which motivates teams to pay for the big names. The data shows that these guys have produced over many years, and it almost seems definite that such production will repeat, justifying spending. By spending over $15 million on one player, a team is confirming these projections with certainty that continued success will indeed happen. They lack the will to speculate on a young prospect or a struggling hitter on another team to produce. So, they make the safe bet. Yet, that foolproof plan never seems to turn out that way. Rookies that are being paid the league minimum salary manage to outproduce the $20 Million/year catcher. The older outfielder that everyone thought was done adds more value to their team than the shiny, new acquisition. The most likely event fails to become reality. A Black Swan occurs. A team is both now out of contention and has a major portion of their payroll locked up for years in the future on a player that provides almost no value. The so-called “safe bet” failed. Despite being supposedly conservative with their roster, a team will now be in distress for the foreseeable future.

The projections never consider this. What are the odds that a player averaging three-ish fWAR per season would now only be able to produce less than one? Less than 5%, easily, and maybe even under the infamous 1% mark. Most teams amount a mistake like this to chance - they supposedly made the fundamentally right decision, but it just didn’t pan out. The thing they ultimately forget to question is how many times something like this happens. In the 2020 offseason (before the pandemic), 726 players were signed by free agency, contract extension, or avoiding arbitration. Several others were signed or traded during the season (although limited), leading to the sample of possible outliers being bigger than I can state confidently. For the sake of simple calculation, let’s say that 7 (1% of the 726) managed to significantly underproduce in comparison with what they were being paid. In this example, Player A was paid $16 million but produced -$3.4 million due to a foot injury that knocked him out for the majority of the season. Remember, unlike other sports, baseball’s contracts are guaranteed. The team ultimately missed the playoffs by two wins (the expected amount of value that the team thought Player A would produce). A 1% chance was the difference between a shot at a championship and watching October baseball from the couch. And thanks to their record being somewhat competitive, their draft pick will be in the lower teens. They now are worse off than they started. If they had not paid Player A, they would have a higher draft pick, about 15 million dollars (assuming a replacement was paid the league minimum), and the same results to show for it. It only took a minute chance to send the team into the oblivion of mediocrity.

Believe it or not, this example of performance happened in 2021. Mike Moustakas of the Cincinnati Reds produced -0.4 fWAR, failing to be worth even a fraction of what he was paid. I would consider this instance to be a Black Swan, as in highly unpredictable. Before going to the Reds, Moustakas last went on the IL (or DL at the time) in 2016 with the Royals. In stints there, he had injured a thumb and an ACL. This had nothing to do with his foot. He was seen as a relatively reliable player despite getting older. As the 2020 season went by, it became clear Moustakas was no longer that type of player. With the Reds that season, he went through a barrage of injuries that, despite having time to heal, continued into 2021. It was ultimately deemed he was suffering from plantar fasciitis, an injury that he had never had before. Something unlikely happened and the Reds paid dearly for it.

This may seem to be just one abstract example, but every year teams manage to overpay players due to the overall miscalculation of these risks. Eric Hosmer ($20M Earned) and Carlos Santana (7.25M Earned) were vastly overpaid in 2021 (among players with the qualified amount of PAs). When lowering that requirement to 0 PAs, to allow for injured players and other circumstances, Khris Davis ($16.75M Earned), Cody Bellinger ($16.1M Earned), Matt Carpenter ($18.5M Earned), and Marcell Ozuna ($14.3M Earned) stand out on a list that all produced less than negative 2 million dollars worth of value, meaning that they were clear liabilities to their team. While I wholeheartedly agree that teams have improved since the ancient, pre-Moneyball days, the fact that these examples exist proves that the data analysis that justified these contracts is far from perfect. Teams know much more than fans, but they don’t know everything, allowing for outlier risks to exploit them for tens of millions of dollars every year.

The critic of this proposed philosophy in baseball game theory and risk management states that there will always be winners and losers, deeming such risk countermeasures unnecessary. This counterpoint proposes no new changes in how teams deal with risk, maintaining the “if it ain’t broke, don’t fix it” logic. After all, many organizations are succeeding despite not visibly considering this. But in my general opinion, that way of viewing a team (or most matters in life) only leads to stagnating growth, which will eventually lead to failure. Teams are currently good - they can be great. If they can re-evaluate their risk profile to make those extremely negative outliers less impactful, then they can engage in an everflowing state of upside. Extreme downside risks, whether visible or not, pose the ultimate threat to a team’s wellbeing. Extreme upside takes, whether visible or not, allow for them to be champions. A given team is already utilizing this philosophy, avoiding the fallacy of allowing for an extreme downside, whether they know it or not. And through this practice, they are one of the best teams in Major League Baseball.

The Solution

As most baseball fans know, the Tampa Bay Rays are considered to be sabermetric geniuses. They consistently rank within the top five for the lowest dollar amount spent per win, being successful at an extremely efficient rate. In 2021, their total payroll was $70.8 million, ranking 26th in the MLB. They won 100 games that year, 8 more than the next AL East team. Tampa Bay is living proof that a team doesn’t need to spend big dollars to be successful, serving as a goal for many small-market teams. I believe that a big reason that they are so successful at this is through their exposure levels to Black Swans. To demonstrate this, I will dive into their 2021 payroll.

Payroll Data via Spotrac.

The big thing that I need to point out is their biggest salary payment - $11.7 million to outfielder Kevin Kiermaier. His contract accounted for 16.47% of their entire 2021 payroll, a percentage much lower than the biggest contract on other teams. While many clubs carry players that are worth north of 25% of the total payroll, the Rays steer away from any number of the sort. On top of that, the squad is only set to carry him through 2023, when he is set to become an unrestricted free agent. Tampa originally signed him to a six-year deal worth $53.5 million, which was on the higher end of their median contracts. That was the highest AAV obligation that they maintained last season, which made it the most worrying bet in regards to the possibility of a negative outlier that can’t be projected.

For this example, let’s say Kiermaier was subject to a freak accident. A minor hump of grass caused him to fall and hurt his knee, keeping him out for the season. Although the concept of anyone doing that is highly unlikely, it is still theoretically possible. Let it be known that I am by no means attempting to speak this unfortunate theoretical event into existence. If this event happened before 2021, the Rays would now be out $11.7 million with no probability of return. For some teams, this would be the difference-maker - their most expensive player out means that they will now not make the postseason. For Tampa Bay, it is a different story. Kiermaier only produced 2.5 fWAR (6th on positional team) that season, despite being the most expensive player. He was ranked 10th in offensive production and 2nd in defensive production on the team. Assuming that the Rays were only able to find a replacement player (this is unlikely), the Rays would stand somewhere between 97 and 98 wins. They would still be far ahead of the 92-win Red Sox in 2nd place. This unfortunate event did not happen, but even if it did, the Rays would be alright. Their exposure to the downside was abundantly low, which allowed them to mitigate their risks.

On the other side of the coin, their extreme exposure to low-risk, high upside outliers allowed them to be safely carried to the playoffs. Collectively, their Top 3 positional players of Brandon Lowe, Mike Zunino, and Randy Arozarena produced 13 fWAR on about $5.1 million worth of salary. The pitching was in a similar boat. Tyler Glasnow, Shane McClanahan, and Collin McHugh had 6.8 fWAR on roughly $6.3 million. The players they took a chance on, and used relatively little capital to do so, produced disproportionate returns. Those outliers carried this team. They produced the most value out of everyone while being some of the lowest-paid players. The fat tail of risk allowed them to succeed with relatively little investment, embracing the Moneyball-esque philosophy.

It is worth noting that this type of success with outliers is more than likely due to extensive research and investment into these types of opportunities. While I could unfortunately not find the Rays exact spending numbers on these tools, the consensus of the baseball community is that it is quite a bit. Most think they would rather spend money on analytic research versus players, which is likely accurate. They don’t need to be faulted for this, as they are clearly doing something correctly. Either way, low exposure to risk and high exposure to the upside has made this team the formidable force that it is in the AL East - they embraced the outliers, the Black Swans, the fat tails.

In defining a solution, I provide the Rays as a perfect example of low exposure to devastating risk and extreme exposure to high-upside bets. Teams need to get away from the safety net that is free agency blockbusters and conventional signings. Such transactions lack the efficiency to beat the competition and only provide a higher risk profile. Any traumatizing event to signings such as these can force a team into submission, something that no organization wants to deal with. In heeding this proposed solution, teams need to completely recalibrate their projections. Include variables to project the unlikely, plan for the worst-case scenarios, and be ready for anything. Projections themselves are only human nature, as we all have a desire to see the future. But in the words of Nassim Taleb, “I want to be broadly right rather than precisely wrong.” Aiming to predict these factors with precision will only bring one madness, but by allowing for many possibilities, one can go much farther than the competition.


In this examination, I have provided many examples of the benefit of embracing the unknown in baseball and letting go of the rigid structures of projection. And within this, I state a bold, concrete statement: teams will never be able to exactly predict their future (bidding that time travel is not invented). All they can hope for is the chance to be more accurate. This framework provides a way for teams, or even the modern fan, to evaluate their interaction with baseball differently. Outlier risks control our society, taking any major devastating event in history and thinking about whether it was likely beforehand (not in hindsight). To think baseball is different than the rest of the world would be madness - this is a game of people, not of structured chance. The sooner we begin looking at the game like that, the sooner the sport evolves.


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