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A Limited Guide to Baseball Contract Analysis


Red Sox 3B Rafael Devers; Photo via Keith Allison

In an era of long-term commitments and ever-expanding mega-deals in baseball, the ability to properly analyze the merit of a contract is extremely important. There are many different approaches to doing such a task, although lots of methodologies have several common themes. While analyzing Xander Bogaert’s recent signing with the Padres in-depth for Pitcher List (article linked here), I hinted at the thought processes and methodologies I use to differentiate between deals. While there is a place for such analysis, the primary goal of The Drummey Angle is to educate the reader so that they can conduct such analysis for themselves, using the axioms of sabermetrics to come to thoughtful conclusions. The difficult part lies in where to start. This article attempts to solve that issue by providing various frameworks to think about problems in contract analysis. The reader will hopefully be able to better understand and evaluate the massive contracts being handed out to stars across the MLB.


Defining the Objective


Understanding the key objective of a contract is crucial in deciding whether the deal can be considered successful. Different teams play to different standards, and such differentiation is necessary for an analysis of contracts. Is the team trying to win now or later? When teams are in different cycles of their building, different contracts are more justified than others based on their approach to winning. These approaches are oftentimes relevant to the extent of their probability of making the playoffs. Ergo, three team types will be established for these objectives - the shoo-ins, the fringes, and the lost causes. They are to be defined as follows:


Shoo-Ins - These teams are almost guaranteed to make the playoffs, regardless of any further signings. The acquisition of a player is only to enhance their already great odds, as well as possibly help establish a base for their future.


Fringes - These teams are not a guarantee to make the playoffs, although such a run is within their grasp. The right move could put them into the postseason. Thus, these teams are willing to sacrifice the future for gains in the present.


Lost Causes - These teams will likely not make the playoffs, even if they made a decent move. Any signing will likely be designated for their potential future success but serves to add little to no extra value now.


Different types of signings make sense for the different types of groups. Some make more sense than others, but the majority of teams aim to be optimal in their approach. Ergo, the need for an explanation regarding what types of deals suit what category.


In considering free agent contracts, the dynamics are somewhat straightforward. The Fringes group can face a potential windfall of cash if they do happen to make the playoffs. If the signing pushes them into October, then the team stands to inherently gain from that deal. Shoo-Ins wouldn’t gain as much, but peace of mind within a club is valuable. The knowledge that the playoffs are assured could yield a slight premium, but not quite as much from the Fringes that stand to gain the most. Lost Causes stand to gain almost nothing from these free agent deals, as the player is likely on the decline anyhow and such immediate extra value serves to almost no benefit to them. Hence, the order in which teams stand to gain from a potential free agent signing is as follows: Fringes, Shoo-Ins, and Lost Causes. Of course, this is solely in regard to free agent contracts - an early extension with consideration to the arbitration process is completely different.


Value of Free-Agent Signing to Team Types: 1. Fringes, 2. Shoo-Ins, and 3. Lost Causes


When extensions are signed, the player is generally up-and-coming and likely has not reached his peak yet. A team can take advantage of this and sign him for less than his free agent market value in exchange for the player’s future financial security in case something goes awry. It is therefore easy to come to the thought that such signings are future-oriented rather than present-oriented. So, how does this switch the value structure? While the value of a free-agent deal is the highest for Fringes, the value of a long-term extension is the lowest. Fringes are specifically focused on the now, and such a future-oriented transaction serves them little, as they are not specifically adding production now and likely locked up a bit of extra cash that could be otherwise spent on the free agent market. Next comes the Shoo-Ins, whose slightly increased view toward the future puts them above the Fringes. Shoo-Ins generally care about the present more than the future due to their current status, but they can afford to delegate some of their funds to secure success in later years. An extension will ensure that an up-and-coming player will continually add value to the team, leading to a better probability of making the playoffs in the case that the team breaks down to the Fringe level. Such a bet provides insurance - if the team can’t make the playoffs now, they still may be able to in the future. Out of everyone, Lost Causes stand to gain the most from the signing of an extension. Being completely future-oriented, an extension ensures a valuable player will be on their roster for years to come. As Lost Causes generally become Fringes in the future, adding value down the road will be tremendously beneficial when a competitive window opens up. The order of value to teams completely switches for extensions:


Value of Extension to Team Types: 1. Lost Causes, 2. Shoo-Ins, and 3. Fringes


Of course, there are other types of deals (such as Minor League Contracts and One-Year Deals) that generally don’t follow the above frameworks in terms of judging value to a given team. These situations are arguably less clear-cut than the prior types mentioned, making the potential benefits to each team type more subject to special situations that go beyond the point of this article for the reader. In wanting a basic understanding of the topic, considering such objectives above should help evaluate the majority of noteworthy signings.


Measures of Evaluation


The origin of sabermetrics can be owed to great minds trying to evaluate the worth of a player correctly. The current state of sabermetrics is using incredible amounts of intellect to attempt to predict the future worth of a player. And while both problems are still being worked on and improved every day, perfection is likely somewhat far (if even possible). For now, barring that the reader has not invented their own ultra-advanced value and predictor system, one will have to settle for the current best guesses of a player’s value and potential value.


To start with value, the primary method of assigning actual win value has been through the statistic WAR (Wins Above Replacement), which assigns value to a player based upon the number of wins they added in comparison to a given fringe Triple-A/Major League player. One win is said to equate to 10 runs, so a player produces 1 WAR for every 10 RAR (Runs Above Replacement) he produces. Major League teams are said to have their own internal system of player value assignment, although WAR serves as a suitable public replacement.


In relation to WAR, the ability to assign a dollar value of an additional Win is crucial in setting the standard for what teams should pay players. Fangraphs has established a basis for valuing a player’s dollar worth through the average free agent spending cost of WAR, as specified in this linked piece. It provides a good guideline to follow, but, as specified earlier, a player is worth a different amount to all teams. A measure could be established to account for distinct team qualities to more accurately specify the value to a given team, although no such measure has really gained widespread acceptance. Ergo, the usage of Dollars per WAR is a safe bet, as it is generally accepted in the sabermetrics community as a sound way of evaluation and can be used for most contract analyses. The basis of the evaluation lies in the idea of whether the team over or underpaid the market value of the projected production of WAR. A contract that pays more than the projected dollar value is considered player-friendly, while a contract that pays less than the projected dollar value is considered team-friendly.


Comparing present transactions to past transactions is another way to assign merit to deals. While something is only worth what one is willing to pay for it, this is often dictated by the matter of what someone else paid. Past deals are often cited in a wide arrangement of dealmaking that spans from eBay bidding to house buying, which makes an application of such logic to the baseball world unsurprising. In applying this, there would need to be similar deals within the past 2-3 years (the more recent, the better) that have similar lengths in contract, similar past production, and, ideally, the same position. If a prior deal fulfills all of these requirements, then it can rightfully be considered comparable and can be used as a precedent to analyze a deal. In using this, one evaluates whether a player was under or overpaid relative to a recent precedent. If Player A and Player B are similar in almost every way in terms of projected production, but Player B is set to earn $50 million less, then one could say that Player B’s deal is team-friendly relative to Player A. To that point, Player A’s deal would be considered player-friendly relative to Player B’s.


Both of these examples serve as a possible method to measure value. They should coincidentally serve as guidelines but not be limited by or necessarily be adhered towards. These methods are dependent on lots of other contract evaluation factors, which makes the consideration of other points of this process so crucial.


The Upside vs The Downside


Any type of contract for baseball players should be thought of as an educated investment. A team is spending on a player (asset) in hopes of the player producing runs for their team (return value). Like any investment, the investors are not entirely certain of the future outcome. A probability distribution represents the possible gains or losses that could be incurred. In a baseball sense, teams commit an “x” amount of dollars to a player in exchange for a set of probabilities that a player will produce a given amount. Most common fans often overlook this point, screaming the age-old insult that “he should at least be able to hit (insert stat of your choosing) if he is getting paid (this much money).” I encourage fans to distance themselves from such a thought - a player is getting paid for the chances that he may hit a certain amount, with the probability of the performance he displays likely factored into the contract. To give a clear visual, a contract should appear like this.


Common Logic


Player A = 4 fWAR


Reality


Player A =

Expected Production (fWAR)

Probability

< 2.5

0.1%

2.5 - 3

2.1%

3 - 3.5

13.6%

3.5 - 4.5

68.2%

4.5 - 5

13.6%

5 - 5.5

2.1%

> 5.5

0.1%

The chart assumes a completely normal probability distribution with a 4 fWAR mean and a Standard Deviation of 0.5 fWAR.


The above chart isn’t specific to a certain player. It only serves as an example of how contract signings should be approached in evaluation. The acknowledgment of the fact that contracts are only a range of probabilities leads to the conundrum of hindsight bias in association with good and bad deals. If all contracts are full of high upsides and downsides, should a fan really be mad for a player not producing at a given level? The short answer - no. Using the example above and assuming that all of the numbers are true probabilities of real outcomes, let’s say Player A produces 2.3 fWAR in the following season, which is said to have a chance of 0.1% of occurring. Given that this is incredibly rare and unlikely to reoccur, a team should not be faulted for signing the player for the amount that they did. The same type of thinking goes for the opposite end - in this example, Player A manages to produce 5.7 fWAR. While they admittedly got a great deal, the team should not be given credit for signing the player, as that event was highly unlikely. The only credit that could be given is if the team managed to have a more accurate projection of the real odds. The “real odds” are the natural probabilities of a player's performance, which are highly theoretical and are almost impossible to prove or disprove. Ergo, a team could only be given credit for a good signing if they consistently manage to predict player production better than everyone, as they likely have a measure of projection that is closer to the real odds.


Of course, the true probability of any future outcome is unknown, but common projection systems can provide a good guideline of what a given player will likely produce, possibly even including the different chances of different outcomes. Now, one has a range of probabilities - where to next? To properly price in the upside and downside, a clear measure of evaluation needs to be established, as well as the usage of basic arithmetic. Assuming that the reader has opted for a preferred measure of value, the projected amount of value needs to be multiplied by the probability of the event happening. The equation would look something like this, assuming the distribution above:


Player A’s Contract Value = (0.001 x PV<2.5) + (0.021 * PV2.5-3) + (0.136 * PV3-3.5) + (.682 * PV3.5-4.5) + (0.136 * PV4.5-5) + (0.021 * PV5-5.5) + (0.001 * PV>5.5)


PV = Projected Value based on Measure of Value (fWAR Market Value in Example)

Constants = Probability of Occurrence


Every individual team would likely have its own possible projected outcomes, as well as the inherent value of those outcomes. From the fan's perspective, the usage of this formula leads to a number for which one can determine overpays and underpays. If the dollar amount paid is above the Contract Value, it is an overpay. The same logic goes for an underpay - the dollar amount paid must be below the Contract Value. Of course, a team evaluation could entirely disagree with a fan’s approximation using the same type of logic. If a team projects a higher average WAR or assigns a larger dollar amount to each WAR, then a fan’s version of an overpay could be considered an underpay by the team. The same sort of thinking applies between teams - different values and varying projections lead teams to offer different contracts based on their assessment of fair value.


Considering the upsides and downsides in such deals are crucial to thinking logically about baseball, as, after all, a player’s every plate appearance is just a string of probabilities projecting chances of success and failure. With these measures in mind, a fan could establish a firm basis using their preferred estimates of value to establish a sound way to judge contracts. But even this does not consider all of the bases alone. A bit more needs to be touched on.


Opportunity Cost


If the reader is familiar with basic economics then opportunity cost should be very familiar. If not, the St. Louis Federal Reserve defines opportunity cost as “The value of the next-best alternative when a decision is made; it's what is given up.” When a team chooses to use its assets on one player, they are foregoing the use of those funds on any other player at the moment, whether for free-agent acquisitions or internal extensions. Within that same article on opportunity cost, the Fed recommends using three questions when considering buying something now. They are as follows:


  1. “How much do I value this?”

  2. “What am I giving up now to have this?”

  3. “What am I giving up in the future to have this now?”


I believe these three questions are perfectly applicable to baseball when understanding the opportunity cost of a given contract. The first question, “How much do I value this?”, was already addressed in the prior points. There are different measures of evaluation and value as well as varying circumstances utilized to get to a fair number. The second question, "What am I giving up now to have this?", primarily relates to the loss of the rest of the free agent market, with the signing of one expensive player often not leaving room for the acquisition of another (Steve Cohen is not to be included in this category). The third question, “What am I giving up in the future to have this now?”, deals with the lack of funds for future free agent classes and the possibility of an up-and-coming player needing an extension. All of these need to be observed in properly figuring out opportunity cost.


The “giving up now” aspect is fairly easy to articulate. After all, the approximate opportunity cost is “the value of the next-best alternative.” If Player A and B happen to be asking for the same amount, but Player A is expected to produce 4 fWAR and Player B 3.5 fWAR on average, then the opportunity cost of this decision is 3.5 fWAR. Of course, choosing Player A is a rational choice. The team is still losing out on some production, albeit less than what they just acquired. Plus, the evaluation of the contract is to be considered. If Player B’s asking price serves to be considered a bargain deal in the current market, then the cost further grows. The actual current opportunity cost is a function of both this lost production and potential market savings, which should be considered in this framework:


Current Opportunity Cost = (PWBA, MV - C)


PWBA = Projected Wins of Best Alternative, C = Cost, MV = Current Market Value


For “What am I giving up in the future?”, the answer is far from straightforward. Nobody can be exactly certain of everyone who will be in a future free agent class or their projected value. Of course, one could attempt to project this, but it would be filled with the same issues of uncertainty previously mentioned about projection systems. The best possible estimate of what is being given up in the future would be that of a projected free agent class, using the expected production of the top players at a cost that adjusts for rising wages within baseball. This would serve, at best, as a guideline for teams to consider when considering the future loss implications of signing a contract now. While exact figures would vary based on the projection systems being used, a useful framework similar to the style above would be used to analyze such a problem:


Future Opportunity Cost = (PWBAy, (MV - C)y)


PWNA = Projected Wins of Best Alternative, y = Year as Potential Market Participant, C = Cost, MV = Current Market Value


As stated, not as clear-cut. This formula factors in two dimensions, similar to the prior. However, both serve to the given year that the team would have been buyers but are not due to the past signing. This would be shown as the greatest amount of wins that could’ve been bought at a similar price (PWBA), as well as the greatest amount of financial savings between the cost of a potential player and actual market value (MV - C) that could’ve been had in a year (Y) where the team would have been a market participant if not for the deal. Both of these estimates of opportunity cost need to be kept in mind at the time of the signing.


Keeping the next best alternative in mind is crucial - knowing what is being missed out upon provides perspective as to what is ultimately the right move. Plus, it provides another standard to evaluate these deals, especially in hindsight. If the contract exceeds the value of the opportunity cost, then it can be regarded as successful. On the other hand, if the opportunity cost exceeds that of the contract, then it can be regarded as a failure.


Successful Contract = V > OC

Non-Successful Contract = V < OC


V = Value, OC = Opportunity Cost


Of course, grading a deal ten years later is much easier than now. There is so much additional knowledge that the task is much more feasible, especially when considering opportunity cost. To evaluate a deal and consider this factor now, mainly focus on the current opportunity cost - these are the only costs that management is guaranteed to miss out on. Projections could be applied to consider future opportunity costs in evaluation, although such estimates would be riddled with uncertainty. And to that degree, it would be unfair to judge a decision by management now based on a low-accuracy projection of the future. Focusing on the known facts of current opportunity costs is the logical option in analyzing this factor in a deal.


Like the others, by itself, this type of measurement does not serve as a good tell-all of whether a contract is to be considered good or bad. But as one tool of many, it is a great addition to the various ways contract evaluation can be approached.


The Conclusion