Using Football To Teach Finance

Using Football To Teach Finance

by James Mahar Jr. and Rodney Paul

peer reviewedJames Mahar Jr.  is an Assistant Professor of Finance at St. Bonaventure University. Rodney Paul  is an Assistant Professor of Economics at St. Bonaventure University.

ABSTRACT: Creating student interest is an important, sometimes difficult, task facing all instructors. One way to stimulate students' interest is through the use of examples that are interesting and relevant to the students. As the most popular sport in the United States, football provides numerous opportunities for presenting potentially dry, intimidating, academic financial concepts in terms that undergraduate students may find more relevant, understandable, and interesting. In this paper, the author provides football examples to demonstrate various financial topics. These include: using time value of money techniques to examine player contracts; the similarities between specialists and sportsbooks (bookies); bondholder-shareholder conflicts and Hail Mary passes; how IPOs and ticket scalping are similar; gambling and the various forms of market efficiency; real options; and long-term contracts.


One of the more difficult tasks facing any instructor is sparking student interest. One way to accomplish this is through the use of examples that are interesting and relevant to the students. Ardalan (1998) noted that when instructors use metaphors and other non-business examples in the classroom, students are able to relate “a familiar concept to a new one, [which] allows the subject to make better inferences about the target domain" (Ardalan 1998: 109)”. This enhancement of learning is consistent with the findings of Holyoak and Koh (1987).While the explanation behind how and why this enhanced learning occurs is still uncertain, using non-business examples to teach finance is widely accepted as an effective means of teaching.

Professional football is one of the most popular sports in the United States and offers numerous examples and metaphors that can be used in a finance class. Discussed in this paper are several examples from football that can be used to demonstrate various aspects of finance. It should be stressed that the football examples are not meant to replace traditional examples, but rather to provide students another view at finance topics through a context with which some students may be more familiar. As supplemental learning tools, football examples can be used for a wide range of financial topics. Table 1 (below) lays out a few specific topics and courses where football examples might be used to supplement more traditional cases from the business world. The examples in this table deal with many of the topics typically covered in an undergraduate finance class: the time value of money, market efficiency, the role of specialists, bondholder-shareholder conflicts, IPOs, and real options. A brief discussion of various finance courses where these examples are useful follows the table.

Table One


Introductory Finance

Advanced Corporate Finance

Financial Institutions


Time Value of Money and Contracts





Market Efficiency and the Betting Market





Risk Shifting and Hail Mary





Specialist and the Sportsbook





Ticket Scalping and Float





Football and Real Options







For many students, understanding the time value of money is one of the most difficult hurdles that they will encounter in an introductory finance class. Failure to grasp this crucial topic causes many students to do poorly in class and, often, to drop finance for a different major. Part of the problem could be that few introductory finance students can relate to textbook examples on this subject matter. Typical present value examples center on bonds and mortgages, two financial instruments with which the vast majority of traditional undergraduate students have little interest or experience. An alternative to these examples can be found in the National Football League.

NFL player contracts make excellent time value of money examples because, much like bonds, player contracts generally have contractually defined cash flows. Typically, NFL players sign contracts that consist of a signing bonus and an annual salary. Both the signing bonus and annual salary are negotiable and, in the case of the salary, often change year to year over the life of the contract (National Football League Players' Association, 2002).

Before contracts can be used as an example, a few institutional details should be discussed. First, the majority of NFL contracts are not guaranteed. That is, a player can be cut at any point, and the team does not need to pay him the remaining payments. The signing bonus, however, is usually guaranteed, and the player keeps it even in the event that he is cut from the team. The players, therefore, would like to see all of the money guaranteed and paid in the early years of the contract. These details, which can be glossed over in introductory classes, also allow more advanced students to grasp the concept of expected value calculations.

Present value calculations are based on the premise that money today can be invested to earn more in the future. The discount rate in this discussion would be set by market-wide factors. As Equation 1 (below) shows, for any positive required return, a dollar today is worth more than a dollar tomorrow.

PV = Σ (CFt/(1+r)t )                                    (1)


PV = present value

            t = time period in which the cash flow is received

            r = risk adjusted discount rate.

Adding to student interest is the fact that many sports reporters seemingly do not understand the concept of time value of money. They often report the value of a player’s contract as the sum of all of the cash flows of the contract. Table 2A shows the cash flows associated with select player contracts. When the time value of money is considered, the reported sums dramatically exceed the value actually received by the player. This bias may be important given the widely held belief that professional athletes are overpaid. This relationship is shown in Table 2B.

However, even this lower present value calculation is biased because many players will not remain with their team for the life of their contracts and, therefore, will never receive all of the payments originally provided for by the terms of the contract. Moreover, this risk (that the player will not stay with the team for the life of the contract) can be used to demonstrate the concepts of both expected cash flows and the differences between systematic and unsystematic risk. Risky cash flows, whose risk is tied to unique risk factors, should not be handled by changing the required return (which is based on market-wide factors).  To adjust for unique risks in cash flows, an expected cash flow should be calculated. The expectation is based on the probability of remaining with the team and under the same contract. It can be written as: 

Expected Cft = P(CFt)                                   (2)


 P = Probability of the player remaining under the same contract

CFt = the contractual cash flow for that year.

Table 2 C  shows the expected present values for the players. As would be expected, these values are significantly lower. This is useful for it shows not only that unique risk is accounted for by adjusting cash flows, but also because, unlike some text book examples, there is clearly little correlation between the player remaining under contract and the market-wide factors that influence the discount rate. This later distinction should make it easier for students to grasp the difference between market risk and unique risk. Additionally, this example can be used to show why players should prefer to receive a guaranteed signing bonus, rather than a risky contract, how present values fluctuate with changes in interest rates, the importance of using the correct probabilities in calculating expected values, and even to show how longer term contracts are more sensitive to changes in interest rates.


A. Player Contracts (all numbers in 000s of dollars)


Signing Bonus

Salary Year 1

Salary Year 2

Salary Year 3

Salary Year 4

Salary Year 5

Salary Year 6

Salary Year 7

Ronde Barber









Martin Gramatica









Mike Alsott


















B. Present Value (all numbers in 000s of dollars)


Reported Value

Present Value

r =5%

Present Value

r =8%

Present Value

r =10%

Present Value

r =15%

Present Value

r =20%



Ronde Barber









Martin Gramatica









Mike Alsott










C. Expected Present Values (all numbers in 000s of dollars).  p = probability of remaining under contract for the entire year.  This probability is assumed to remain constant over time.


Reported Value

Expected Value p=.8


Expected Value p=.8


Expected Value p=.8


Expected Value p=.8


Expected Value p=.8




Ronde Barber









Martin Gramatica









Mike Alsott









a Ronde Barber’s contract value was reported at $18 million by the St. Petersburg Times and at $18.75 million by  For consistency with the other two players we report the deal as the total of the undiscounted cash flows before any incentive bonuses.



The concept of efficient markets is very important to the study of the stock market in finance. Understanding terms and their meanings can be perplexing to introductory finance students who have little experience with financial markets.  Fortunately, the point-spread market in football provides an example to which many students can relate.

An efficient market adjusts rapidly to the arrival of new information. This means that current prices will reflect all available information. Fama (1970) divided the Efficient Markets Hypothesis (EMH) into three parts: the weak form, the semi-strong form, and the strong form. The weak form states that prices reflect all past market-based information, the semi-strong form asserts that current prices reflect all new information, and the strong form states that prices include all information, including insider information. These definitions of market efficiency can also be applied to the "betting markets" for professional football which in turn can be used to illustrate these conceptual definitions.

The wagering market for football games offers specific advantages to studying the EMH that other financial markets do not. First, gambling markets have the advantages of definitive start and end points for study and quick processing of returns or losses. While closed-end funds may offer the same, it is often difficult to select the natural start and end points for study (Ippolito, 1989). On the other hand, football lines are released a week in advance and are closed at the beginning of the games on Sunday or Monday. All information is assumed to be processed by the close of the line; therefore, the weak form of market efficiency can be studied very easily.  In addition, patrons receive their winnings or take their losses following the conclusion of the game,  thus leaving little concern over effects on the market due to the timing of payments.

Gandar, et al (1988), and Sauer, et al (1988), were the first to systematically study market efficiency using samples of NFL betting lines. They tested whether the betting line incorporated past publicly available information, such as scoring-per-game, yards-allowed-per-game, and records on grass and artificial turf. Their work showed that the line was an optimal and unbiased predictor of the outcome of games. Therefore, reading through public information sources, such as magazines or televised football shows, will not help one win in the gambling market. This is similar to the idea in financial markets that looking at past financial reports and other publications will not allow an investor to beat the market since this past information is already incorporated into the price. For this reason, we would say that both financial markets and the betting market for professional football are both largely weak and semi-strong form efficient.

While both financial and betting markets appear to be efficient, efficiency is not the same as perfection and there is evidence in both markets of anomalies or areas where there are apparent inefficiencies. For example, in gambling on football, large favorites (those favored by a touchdown or more) tend to be “over-bet” (Paul and Weinbach, 2003). Another recognized anomaly in football betting markets involves betting on the total number of points scored in a game. In this situation it has been shown that bettors “over-bet” the “over” for those games where the over/under is 47.5 or greater (Paul and Weinbach, 2002). These anomalies are similar to the January Effect (stocks tend to go up in January), the Small Firm Effect (small firms outperform large firms on a risk adjusted basis), and Market to Book Anomaly (low market-to-book stocks outperform high market-to-book stocks).

Under the EMH, anomalies should not persist because, once they are known, arbitrageurs should eliminate any trading pattern. Interestingly, the reasons that these anomalies do continue to exist in both markets are remarkably similar. For example, explanations for persistent stock market anomalies center on errors in specifying the model (such as ignoring liquidity or mis-measuring risk) or because of structural impediments to the arbitrageurs eliminating the anomaly (e.g. limits on short sales). Likewise, it has been suggested that profitability may exist due to binding betting limits placed on informed traders in this market. These restrictions prevent the informed bettor from making the large bets that would lead to a correctly adjusted betting line (Paul and Weinbach, 2002).


Coase (1937), and later Jensen and Meckling (1984), describe firms as a nexus of contracts between various stakeholders. At times, the various stakeholders have conflicting incentives and desires. One of the most important of these conflicts arises around the risk preferences of shareholders and bondholders.

Galai and Masulis (1976) and Myers (1984) discuss the widely acknowledged risk-shifting that can occur as a firm increases its leverage beyond some optimal point. The problem is particularly severe for a firm whose debt exceeds the market value of the its assets. In such instances, shareholders may have the incentive to accept high-risk projects, even if a particular project has a negative expected value. The reason for this behavior is that shareholders will assuredly lose if conditions do not change. Since bondholders are paid before shareholders in the event of liquidation, the shareholders have little to lose in taking great risks. Therefore, to act in shareholders’ best interest, firms in financial distress forego safe, low-risk, positive projects and accept risky, negative NPV projects.

The theory behind this behavior can be illustrated using the actions of a team that is behind in a football game. The extreme example of this is the "Hail Mary" pass that frequently accompanies the end of a football game. The “Hail Mary” is executed by the quarterback throwing a long, arching pass towards the end zone in the hope that the ball will fall into the hands of one of his teammates grouped in the area. The success rate on this pass is very low, yet teams do it on a regular basis. The rationale is that this high-risk play is the best chance of scoring quickly when compared to running the ball or throwing short-passes. Just as teams that are losing may choose to forego low-risk running opportunities in lieu of high-risk passing plays, firms that have large amounts of debt may increase their acceptable levels of risk since accepting high-risk projects may be the firm’s best chance of avoiding a forced bankruptcy.


Most students are familiar with the point spread on a football game. These point spreads, which are called "lines", can be seen each week in newspapers across the country, are frequently mentioned on sports sites on the internet, and are even stated by commentators on radio and television football programs. What most students may not realize is that the formation of these lines, as well as how the lines change, can provide insight into a simple financial market. In addition, the role of the sportsbook or bookie in this market can illustrate the similar role of the NYSE specialist. 

Many people think that a football game wager is itself a game between the bettor and some entity, such as the sportsbook of a casino or a local (illegal) bookie. When the betting market is run efficiently, this could not be further from the truth. The main goal of the sportsbook or bookie is to set a point spread that will balance the betting action on the favorite and the underdog. To illustrate this, consider the following football line from on September 14, 2002 :

 Buffalo Bills      +5          (-110)

            Minn.Vikings     -5          (-110)

In this example, the Vikings are favored by five points over the Bills. If the Vikings win by more than five points, those who bet on the favorite (the Vikings) will win. If the Bills win or the Vikings win by four or fewer points, then the underdog bettors will win. If the game ends in a Vikings win by five points exactly, the bet is considered a "push" and all wagers are returned.

The indication of (-110) after each team and point spread notes the commission on the game. To place a bet on either the underdog or favorite, the bettor must bet $110 to win 100. This indicates the "vigorish", or commission, which is charged by the sportsbook or bookie. This commission is similar in nature to those charged by brokers, dealers, and specialists on trades in financial markets.

The action of a sportsbook or bookie can be used to help explain market microstructure (how markets function and the institutional details of various market participants), which is a topic in most investment books (Reilly and Norton, 2003). More specifically in this area, studying the actions of a sportsbook can help to explain the role of the NYSE specialist.

When the sportsbook has set the line correctly and there is the same amount of money bet on both the underdog and the favorite, the sportsbook is not an active participant in the wager. It does not matter which side wins the game, the sportsbook captures its commission as money is transferred from the losing party to the winning party minus the vigorish on the losing bets. Thus, if the line is set correctly, and the market is in balance, the sportsbook will not be an active participant in the wager.

Similarly, when the NYSE specialist has set the price correctly, trades occur without the specialist being involved. Madhaven and Sofianos (1998) and Hasbrouck and Sofianos (1993) show that the specialist’s revenues come largely from the small fees collected on each trade and not from taking positions and trading on their own accounts. The specialist benefits from the volume of trades just like the sportsbook benefits from the volume of betting. The more trades that are placed or the more bets that are taken, the more the broker and sportsbook makes. Like the sportsbook, the NYSE specialist is generally not involved in the trading, but will become involved when there is an imbalance. When an imbalance occurs, the specialist trades on his/her own account and/or adjusts prices until balance is restored.

The similarities between a sportsbook and a specialist do not end there. Both will also temporarily stop trading when major information is about to be released. For example, a sportsbook will not publish a line when an injury to an important player leaves doubt as to whether or not that player will play. In the same way, a specialist will request a temporary trading halt when a major takeover is about to be announced or a CEO steps down.


IPO initial underpricing is a persistent phenomenon across time and  across the world. Ross, Westerfield, and Jordan (2001) cite Ritter estimates of an average underpricing of 15.6%. This under pricing is quite volatile, ranging from –1.5% in 1975 to a high of nearly 70% in 1999. Internationally, there is the same pattern in under pricing. Bradley and Jordan (2002) show that the under pricing of IPOs is partially due to share overhang. Share overhang occurs when only a portion of a corporation's outstanding shares are sold to the public. For firms that offer only a small percentage of their shares to the general public (that is, a small float or large overhang), demand for these shares can be greater than the supply, which is relatively fixed during the lock-up period. When this demand exceeds supply, the stock price jumps. The reported market value of the firm, which is based on the number of shares outstanding multiplied by the share price, is thus higher than the initial valuation (which is based on total shares outstanding, not merely float). In such a situation, the current stock price is also higher than the price the firm would fetch if all the shares were sold.

This under pricing can lead to some unusual occurrences. For instance, on March 2, 2000 3-Com sold 5% of its Palm Technologies subsidiary to the general public through an IPO. After the first day of trading, Palm had a market capitalization (based on total shares outstanding) of $45 billion even though its projected revenues were only about $1 billion. 3-Com, on the other hand, had a market capitalization of only $29 billion (approximately 64% of Palm) even though its revenues were expected to be over $3 billion (300% of Palm's). What made the situation even more strange was that 3-Com still owned 95% of Palm Technology stock.

This seeming anomaly is, in part, due to the difference between "float" and "shares outstanding". Float is the measure of the number of shares held by the public, while outstanding shares includes float but also includes all shares held by insiders at the firm, or in this case those shares held by the parent corporation. This difference can be compared to ticket scalping at football games. The ticket scalper standing outside the stadium with only a few tickets left may be able to sell a ticket for several times its face value due to the low supply. However, it is unlikely that all of the seats in the stadium could be sold for the same high price.

An additional similarity is that in each market, market imperfections can lead to overpricing.  Jones and Lamont (2003) report that short sellers reduce share price volatility by eliminating some of the over valuations witnessed during the internet boom of the late 1990s. In the stock market the lack of float can prevent short-sellers from lowering the valuation. Similar impediments exist in the ticket market as ticket scalping is illegal in many areas, which limits the number of scalpers and hence tickets available for resale.


Real option analysis is the application of financial option theory to real, rather than financial, assets. The use of real options to analyze business dealings stresses management’s ability to change behavior during the life of the contract, rather than merely being an inactive observer. The coverage of real options in finance classes is growing. This growth can be shown by the large number of Real Option seminars at financial conferences that show how to teach this topic as well as coverage in most corporate finance textbooks. Traditional textbook real option examples include the option to abandon a project before its useful life is over and the option to expand if things are going better than expected. Both of these uses of real option analysis can also be demonstrated with football examples.

The phenomena of players being cut prior to the end of their contracts has recently become the norm in the NFL. There are many reasons why a player may be cut before the contract ends. The two most common are poor performance and salary cap problems.  This unilateral termination of a contract is an excellent example of the early abandonment option. Here, the player is seen as a “project,” in the traditional finance sense, and cutting the player is nearly identical to ending a project early (i.e. the early abandonment option). Thus, a player may sign a long-term contract, but as soon as the player fails to be a positive investment, the team may cut him. Conversely, some player contracts have clauses that allow the team to extend the contract. This is much like the right to expand a capital budgeting project in the business world.

Brealey and Myers (2003) use real option analysis to show why it may be beneficial for firms to adopt higher cost alternatives if those alternatives have greater flexibility. The rationale for this is that when there is an uncertain future, the ability to adjust production is a valuable option.  The traditional example of this is a flexible production facility. This flexibility is particularly valuable in a rapidly changing environment. This too can be easily illustrated with a football example. A player is more valuable if he can play multiple positions. This ability to play multiple positions is especially important in the NFL, where injuries and changing game plans make the future uncertain. As a result, multi-positional players are more valuable than single-position players. While specialization does dominate for most star players, for more marginal players the ability to play more than one position is often critical. For instance, a multiple-position player (who may also play special teams) may "make the team" while a player who can only play a single position would be "cut" during pre-season.


Provided in this paper are several examples from football that can be used in a finance class to spark student interest and learning. Many students are familiar with concepts  in football, and if a mental link can be created from what is known to what is unknown (that is: from football to finance), then the student will be better able to assimilate the financial concepts. Additionally, football examples have the benefit of being interesting to many students. This may help fight the belief held by many undergraduate students that finance is a dry subject. It should be stressed, however, that these football examples are meand to suplement and not to replace the more traditional finance examples.


Ardalan, Kavous. "On the Use of Entertaining Metaphors in the Introductory Finance Course." Financial Practice and Education 8.1 (1998): 108-114.

Bradley, Daniel J. and Bradford Jordan. "Partial Adjustment to Public Information and IPO Underpricing." Journal of Financial and Quantitative Analysis (Forthcoming 2002).

Brealey, Richard A. and Stewart C. Myers. Principles of Corporate Finance. 7th Ed. New York, NY: McGraw-Hill Co., 2003.

Coase, Ronald H. "Nature of the Firm." Economica 4 (1937): 386-405.

Fama, Eugene. "Efficient Capital Markets: A Review of Theory and Empirical Work." Journal of Finance 25.2 (1970): 383-417.

Fama, Eugene. "Efficient Capital Markets: II." Journal of Finance 46.5 (1991): 1575-1617.

Galai, Dan and Ronald W. Masulis. "The Option Pricing Model and the Risk Factor of Stock." Journal of Financial Economics 3.1-2 (1976): 53-82.

Gandar, John, Richard A. Zuber, Thomas J. O'Brien, and Ben Russo. "Testing Rationality in the Point Spread Betting Market." Journal of Finance 43.4 (1988): 995-1007.

Hasbrouck, Joel, George Sofianos, and Deborah Sosebee. "New York Stock Exchange Systems and Trading Procedures." (April 1993). NYSE working paper #93-01.

Holyoak, Keith J. and Kyunghee Koh. "Surface and Structural Similarity in Analogical Transfer." Memory and Cognition 15.4 (1987): 332-340.

Ippolito, Richard A. "Efficiency with Costly Information: A Study of Mutual Fund Performance, 1965-1984." The Quarterly Journal of Economics 104.1 (1989): 1-24.

Jensen, Michael C. and William H. Meckling. "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure." The Modern Theory of Corporate Finance. Edited by Michael C. Jensen and Clifford W. Smith, Jr. New York, NY: McGraw-Hill Book Co., 1984.

Jones, Charles M. and Owen Lamont. "Short Sale Constraints and Stock Returns." Journal of Financial Economics 66.2-3 (2002): 207-239.

Ross, Stephan A., Randolph W. Westerfield, and Bradford D. Jordan. Essentials of Corporate Finance. 3rd Ed. Boston, MA: McGraw-Hill Irwin, 2001.

Madhaven, Ananth and George Sofianos. "An Empirical Analysis of NYSE Specialist Trading." Journal of Financial Economics 48.2 (1998): 189-210.

Myers, Stewart C. "Determinants of Corporate Borrowing." The Modern Theory of Corporate Finance. Edited by Michael C. Jensen and Clifford W. Smith, Jr. New York, NY: McGraw-Hill Book Co., 1984.

National Football League Players' Association. "2002 Off-Season Signing Averages and 2002 Club and Position Salaries." (October 2002).

Reilly, Frank K. and Edgar A. Norton. Investments. 6th Ed. Mason, OH: Thomson South-Western, 2003.

Paul, Rodney J. and Andrew P. Weinbach. "Market Efficiency and a Profitable Betting Rule: Evidence from Totals on Professional Football." Journal of Sports Economics 3.3 (2002): 256-263.

---. "The Reverse of the Favorite-Longshot Bias: Big Underdogs in the NFL." Applied Economics (Forthcoming 2003).

Sauer, Raymond D. "The Economics of Wagering Markets." Journal of Economic Literature 36.4 (1998): 2021-2064.

Sauer, Raymond D., Vic Brajer, Stephen P. Ferris, and M. Wayne Marr. "Hold Your Bets: Another Look at the Efficiency of the Betting Market for NFL Games." Journal of Political Economy 96.1 (1988): 206-213.


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