Early Season Inefficiencies in the NFL Sports Betting Market. A Thesis. Presented to. The Honors Tutorial College. Ohio University

Transcription

1 Early Season Inefficiencies in the NFL Sports Betting Market A Thesis Presented to The Honors Tutorial College Ohio University In Partial Fulfillment of the Requirements for Graduation from the Honors Tutorial College with the degree of Bachelor of Business Administration by Michael D. DiFilippo June 2012

2 Early Season Inefficiencies in the NFL Sports Betting Market 2 This thesis has been approved by The Honors Tutorial College and the Department of Finance Dr. Andrew Fodor Assistant Professor, Finance Thesis Advisor Dr. Raymond Frost Director of Studies, Business Honors Tutorial College Dr. Jeremy Webster Dean, Honors Tutorial College

3 Early Season Inefficiencies in the NFL Sports Betting Market 3 Reflection For the two articles discussed in this reflection, there were four authors including myself. The authors of the paper were: Dr. Andy Fodor, Ohio University; Dr. Kevin Krieger, University of West Florida; Dr. Justin Davis, Ohio University and myself. All of the aforementioned contributed to both papers and as such have been listed as authors. The two papers began as a single paper. After completing the project as a single paper we determined that the paper would have better publication prospects if it were divided into two papers. Below is a detailed description of how these two papers came to be, including a reflection on what I learned through the process of writing the papers. Generation of Topic The topic for the paper was formulated by Dr. Andy Fodor and Dr. Kevin Krieger. Both Dr. Fodor and Dr. Krieger have written extensively on the topic of sports betting market efficiency and therefore are knowledgeable about the sports betting market literature. The topic of the paper was formed when Dr. Fodor and Dr. Krieger surmised that betting markets would be inefficient during the first week of the NFL season due to a lack of current season information. Thus, bettors would increasingly rely on outdated previous season information when making bets. The professors figured that given the high amount of yearly turnover in NFL team rosters, the performance of teams season-over-season could vary substantially. Therefore, if betting lines were influenced by last season s performance, they are likely to be inaccurate relative to games later in the season as current season

4 Early Season Inefficiencies in the NFL Sports Betting Market 4 information is available. They contended that the inaccuracy in betting lines would allow for the forming of a profitable betting strategy that exploits this first week inefficiency in the NFL sports betting market. It was shortly after Drs. Fodor and Krieger decided to pursue this topic as a potential paper, that I began my tutorial with Dr. Fodor. During the first week of my tutorial, Dr. Fodor and I talked about this new idea and he suggested that we focus my tutorial around working on this paper. He explained that working on the paper would be a great learning experience for me because it would give me the opportunity to complete an empirical analysis with a large data set and also help me further understand the process of writing a scholarly article. We concluded that I would do all of the work on the paper including the empirical analysis, literature review and writing of the paper. Every week during the quarter I was given a task to complete and have ready for discussion and review during the following week s tutorial. Our plan was to work on the empirical analysis first, complete the written sections of the paper (data and methodology, results and conclusion) and then revise and edit during the winter break. Empirical Analysis of Data Before I could get started with the empirical analysis, Dr. Krieger had to gather the data for the paper. In order to ensure that we had a sufficient sample size to perform our empirical analysis, Dr. Fodor and Dr. Krieger decided to test the hypothesis over 1,917 games played during the NFL regular seasons. Dr. Krieger collected all of the sports betting lines and game results from

5 Early Season Inefficiencies in the NFL Sports Betting Market 5 sportsinsight.com, which tracks spreads and results for numerous sports. After collecting and organizing the data, Dr. Krieger passed the data along to Dr. Fodor and I and I began to work on the empirical analysis. Going into the empirical analysis I was very worried that I was going to struggle because I had not taken a statistics class since the winter quarter of my freshman year. However, Dr. Fodor did a great job of explaining the different methods to be used and why these methods were appropriate. The key to my success with the empirical analysis was the strong foundation Dr. Fodor set before we even began doing the analysis. He had a clear plan for the tests that needed to be performed to test our hypothesis. The first step in performing the empirical analysis was to determine whether the inefficiency that Drs. Fodor and Krieger hypothesized existed at a statistically significant level. Before, I was able to go about documenting the inefficiency, I first had to go through and categorize the games by the number of prior-season playoff teams that were playing in the game. We distinguished teams as prior-season playoff teams if that team had played in the playoffs in the previous season. Therefore, each game was given an identifier of 0, 1 or 2. We surmised that if a team made the playoffs during the previous season (signifying strong performance in that season) betting lines would be biased in their favor (making them too big a favorite or too small an underdog) in the first week of the next season when playing a team that did not make the playoffs in the prior season.

6 Early Season Inefficiencies in the NFL Sports Betting Market 6 After breaking down the games by the number of prior-season playoff teams playing in the game, I began to look for the inefficiency that Drs. Fodor and Krieger had hypothesized. This process involved calculating line errors from each game when a prior playoff team played a prior non-playoff team during week one of the eight seasons. I then calculated mean and median line errors and tested for statistical differences from zero. The average line error is calculated as the score of the playoff team (adjusted by the point spread) less the score of the non-playoff team. If the error is positive, the playoff team won by more than expected. If the line error is negative it means the playoff team did not beat the spread and therefore, the betting line was too high. If the line error is zero betting line was exactly correct. If the markets were truly efficient, one would expect that the mean (median) error would not differ significantly from 0, signifying that the markets have accurately predicted the outcome of the games. However, if the average line error is statistically different from 0, this is evidence of a bias in spreads signifying that an inefficiency exists. Whenever I conducted the above test, I found that the average line error for week 1 games when a prior playoff team played a prior non-playoff team was -4.28, which is significantly different from 0 at the 5% level. Comparatively, I calculated the line error for weeks 2-17 and found an average line error of 0.58, which is not statistically different than 0. The error of in the first week of the playoffs showed that the betting lines during week 1 of the NFL season were too high for prior playoff

7 Early Season Inefficiencies in the NFL Sports Betting Market 7 teams when playing prior non-playoff teams. This was evidence that the inefficiency Drs. Fodor and Krieger hypothesized did truly exist in the NFL sports betting market. The average line error that was found in Week 1 of NFL seasons is very significant to the literature because few prior papers identify inefficiencies that are significant across multiple seasons. After finding the hypothesized inefficiency, I began the process of further substantiating the finding, and exploring the implications of the finding, by conducting various other empirical analyses.. Some of the other analyses I conducted included exploring historical playoff appearance trends, prior playoff team betting lines and win percentages, performance of prior playoff teams against the spread, as well as some testing on over/under betting. Throughout the other analyses I conducted, I found many interesting results pertaining to our paper. One of the interesting findings is that on average only half of the teams that play in the playoffs in any particular season will return to the playoffs in the next season. This was particularly interesting because under our hypothesis, bettors in the first week see past performance as a predictor for future performance. However, according to that statistic, prior performance is not a good indicator of future performance, since only half of playoff teams return to the playoffs in the next season. Another interesting finding I made through my empirical analysis was that because of the bias bettors have for these prior playoff teams in the first week of the season, only 34% of the prior playoff teams beat the spread in the first week when playing a prior non-playoff team. We found that 34% is statistically different from 47.62% at the 10% level % is used because it is necessary to win 52.38% of

8 Early Season Inefficiencies in the NFL Sports Betting Market 8 games to make a profit when taking into account commissions charged by bookmakers. The test performed is equivalent to assuming the bettor bets again prior playoff teams (winning 66% of bets) and testing for a statistical difference from 52.38%.This low percentage of winning against the spread supports the presence of a bias towards prior playoff teams documented by the line error results. One of the most intriguing findings of the empirical analysis was evidence of a learning effect. Our results showed that the bias we had identified in the first week of the NFL season dissipates quickly as the season progresses. We attribute this finding to bettors relying less on past season information as information on the current season s teams becomes available. The most important finding that came out of the empirical analysis was from tests for profitability of a betting strategy based on exploiting the inefficiency we document. One of the weaknesses in many of the previous articles written on the efficiency of the NFL sports betting market was that bettors couldn t profitably exploit the inefficiencies that were identified. Before starting the write up phase of the testing, we decided it was important to check to see if we could have made a profit exploiting the inefficiency that we discovered. Given that prior playoff teams had a significantly smaller chance of beating the spread in a game, we decided the best strategy to exploit this inefficiency would be to bet against all of the prior playoff teams in the first week of the NFL seasons when these teams were matched against prior non-playoff teams. When we checked the profitability of the betting strategy across the seasons, we were amazed at what we found. The profitability of our simply strategy

9 Early Season Inefficiencies in the NFL Sports Betting Market 9 was 25.6% per game! A profit margin this high is unheard of in the sports betting literature. Writing of the Rough Draft After the completion of our empirical analysis, Dr. Fodor and I worked together to double check the statistical findings and then began the process of starting the rough draft of the paper. The first aspect of writing the rough draft was for me to write the descriptions of all of the tables we had created while doing the empirical analysis. This was an important step in the process of writing the paper because it allowed me to take the time to figure out what exactly the results in each table meant and how they were going to fit into the story we were trying to tell in the paper. By taking the time to write the descriptions of the tables first, I was able to get a great picture of the results of our tests before I wrote the full article about our findings. Once the table descriptions were written, the next step was for me to write a review of the existing academic literature pertaining to inefficiencies in NFL sports betting markets. I went about the process of writing the literature review by first reading all of the relevant academic journal articles that I could find and then briefly summarizing each. After reading all of the articles I was able to get a sense of which articles were relevant to our paper and which were not. Once I had selected the papers to include in my literature review, I began putting together the summaries of these papers in order to tell the story of the literature s stance on efficiency of the NFL sports betting market.

10 Early Season Inefficiencies in the NFL Sports Betting Market 10 Overall I found the process of writing the literature review to be fairly easy as I had completed literature reviews in the past for my previous tutorials. The most difficult part of writing the literature review was understanding terminology that is unique to the sports betting markets and statistical tests that the various papers used. I found that the easiest way to approach writing a literature review is to find the most recent substantial paper published in the respective field and then use that paper as a springboard to find relevant articles written previously. Upon completion of the rough draft of the literature review, I began writing the other parts of the paper including the data and methodology, results and conclusion sections. The hardest part of writing these various different parts was finding the best way to convey the message in a straightforward and uncomplicated way. I found it difficult for me to take all of the knowledge that I had accrued through the empirical analysis and translate that knowledge into simple and succinct writing. The section that I had the most trouble with was the data and methodology section because it was very much focused on heavy statistical techniques and theories that I did not have a very strong grasp on at the time. Similar to the data and methodology section, I also found the results section to be somewhat difficult to write because it was hard to determine the best order for presented the tables I had created through the empirical analysis. Once I determined the best order to present the results, I found it was fairly straightforward to tell the story of what the results of our tests showed. However, similar to the data and

11 Early Season Inefficiencies in the NFL Sports Betting Market 11 methodology section, I did struggle with describing some of our findings due to my inexperience pertaining to writing about statistical findings for an academic journal. After I had written the data and methodology and results sections, the only other section that I had left to write was the conclusion of the paper. I realized the conclusion section was one of the most important because it tied together everything that had previously been discussed in the paper and outlined why the article our significant to the literature. The hardest part of writing the conclusion for me was making it clear how our paper made a significant contribution to the literature. Being that I was not completely familiar with the literature, I found it difficult to properly place our article in the overall sports betting market efficiency literature. However, with guidance from Dr. Fodor, we were able to finish the conclusion section and the rough draft of the paper. Once we had the rough draft finished, the last task that I had to complete was to write the abstract for the paper. When Dr. Fodor first told me that I had to write an abstract, I figured it would be a simple task since it is typically only a paragraph long. However, I came to realize that the small size of the abstract makes it quite difficult to write because you are forced to describe a page paper in only one paragraph. After writing a couple of drafts and getting some advice from Dr. Fodor, I was able to come up with a strong abstract for the paper. Preparing the Paper for Publication After the rough draft had been finished, Dr. Fodor and I spent the remainder of the quarter editing and revising the paper. The majority of the edits that we did

12 Early Season Inefficiencies in the NFL Sports Betting Market 12 together on the paper pertained to flow of sentences and word choices. One of the biggest lessons I learned from writing this paper was the importance, and difficulty, of writing about complicated subjects in a simple and straightforward way. Also as we were editing the paper, I came to realize that my writing tended to be quite wordy and long-winded. Many of the edits that Dr. Fodor and I did focused on eliminating unnecessary words and simplifying sentences and paragraphs. There were countless times that Dr. Fodor and I were going over my paper and he would take two sentences and split them up or change their order to clear up the flow of the paragraph. One of the other keys lessons I learned while preparing the paper for submission to an academic journal was to focus on keeping my writing as short and concise as possible while still conveying the intended message. In addition to cleaning up some of the bad habits in my writing, Dr. Fodor also spent a lot of time placing particular words and phrases into the paper that are unique to academic journal articles. Given that this was the first time I had ever written a scholarly article, I was not familiar with, many of the terms that were part of the standard vernacular for journal articles. As I went through the editing process, I was able to pick up on them and utilize them more effectively when I was editing parts of the paper. After we had spent some time cleaning up the paper, Dr. Fodor took the paper and sent it off to our co-authors, Dr. Davis and Dr. Krieger for further edits and revisions. Over the course of winter break, Drs. Davis, Fodor and Krieger, worked on further editing and revising paper, eventually splitting it up into two different papers.

13 Early Season Inefficiencies in the NFL Sports Betting Market 13 The two papers that came out of the original rough draft that I had written during my tutorial are entitled Inefficient Pricing from Holdover Bias in NFL Point Spread Markets and Early Season NFL Over/Under Bias, both of which have been submitted to academic journals as part of this thesis. Over/Under Paper The second paper that was spun out of the original rough draft pertained to the over/under aspect of the NFL sports betting market. As part of the empirical analysis that I did with Dr. Fodor, we analyzed an additional inefficiency that existed in NFL sports betting markets in the first week of the season. Our findings showed that the totals in the over/under market gave predictions for scoring that were too high in the first week of the NFL regular season. The hypothesis was that since offenses are much more reliant on execution and timing in order to work effectively as a team, they are at a disadvantage early in the season compared to defenses which rely more heavily on player instincts. Given that offenses are at a disadvantage in the early season due to a lack of experience in playing with each other, we hypothesized that offenses will score fewer points on average in the first week of the season relative to later weeks in the season. Therefore, final score will be less likely to exceed the total line. The betting lines for the over/under bets are simply a prediction of how many total points will be scored in any particular game. If the two teams combined total score is higher than the betting line, and a bettor bets over then the bettor wins. Conversely, if the two teams score

14 Early Season Inefficiencies in the NFL Sports Betting Market 14 fewer combined points than the total line, a bettor who bet under would win. If the bettor chooses incorrectly the bet is lost. We hypothesized that over/under lines in the first week of the NFL season are too high, meaning games are more likely to have total score under the total line in the first week of the season than in later weeks. Therefore, we purposed a strategy of betting under on every game in the first week of the NFL season. After testing this betting strategy across the 8 seasons in our dataset, we found average profits of of 13.6% per game. The profits were again statistically significant, a rarity in sports betting literature. Submission for Publication After both of the papers had been revised and edited by my three faculty coauthors, Dr. Fodor submitted the paper entitled Inefficient Pricing from Holdover Bias in NFL Point Spread Markets to The Journal of Political Economy, a top-tier journal, and the paper entitled Early Season NFL Over/Under Bias to The Journal of Sports Economics, a second tier journal. Given our papers provide significant contributions to the literature due to high statistical significance and novelty and intuitiveness of our hypotheses, we are confident the papers will be published in strong, peer reviewed journals s in the near future. Final Reflections The process of writing my thesis taught me many invaluable lessons that will stick with me throughout the rest of my life. The most notable of these lessons are learning how to persevere when you feel overwhelmed, relying on others that are

15 Early Season Inefficiencies in the NFL Sports Betting Market 15 smarter than you when you don t know how to proceed and utilizing strict time management when you have a large project with a distant deadline. The first lesson I learned through the completion of my thesis is how to persevere through tough material. Before I started the process of writing the holdover bias paper I had no exposure to sports betting literature and didn t know the first thing about betting on sports. Needless to say, when Dr. Fodor suggested we write a paper on sports betting, I got concerned because it was a topic I knew nothing about. However, after hearing his idea and seeing how excited he was about the paper, I became determined to write the paper and stretch my intellectual capacity. Due to my lack of knowledge about sports betting, writing the paper took extra time as I often had to look up unfamiliar topics I would come across in the literature. Slowly, I was able to pick up on the important terminology and get a strong enough understanding of the sports betting markets to write the paper. Looking back on the process of writing the paper, I have a strong sense of accomplishment given that I was able to study and write a paper on an academic topic I was not familiar with. One of the key aspects of my success in writing the paper with little previous knowledge of the subject matter was relying on Dr. Fodor to guide and mentor me through the process. It is because of the critical role that Dr. Fodor played in the development and process of writing the paper that I was able to learn the second major lesson through this process, rely on others smarter than you whenever you don t know how to proceed. Writing this paper was the first time I had ever written a scholarly paper, let alone a scholarly paper based on heavy empirical analysis. Initially, I was

16 Early Season Inefficiencies in the NFL Sports Betting Market 16 very overwhelmed by the amount of work ahead of me and felt lost in the fact that I had never written a scholarly paper before. However, I voiced my concerns to Dr. Fodor and he was able to help me develop a plan and guide me every step of the way through the writing process. Had Dr. Fodor not spent the time to mentor me and guide me through the process, I would never have been able to successful complete the paper. Working with Dr. Fodor on this paper taught me the key lesson of whenever you are lost and don t know how to proceed, rely on those around you that are smarter and more experienced, and they will help you along the way. The third lesson pertains to time management when you have a big project with a distant deadline. I learned this lesson both through the writing of the original paper in the fall of 2011 and also in the spring of 2012 while writing this literature review and reflection. The lesson I learned is when you have a big project with multiple steps and a distant deadline, the best thing you can do is plan out the steps and schedule a date by which you will complete each step. By having a schedule and sticking to it, you will be able to ensure that you have ample time to complete each step and you will also have a barometer in which to measure your progress along the way. For both aspects of my thesis, I came up with a schedule and an order in which to complete each step. By sticking to the schedule, I was able to reduce my stress and also maximize my effectiveness. From now on as I move into the working world, I will keep this lesson in mind and will always strive to manage my time better by creating a schedule for my long-term projects and developing checkpoints to ensure I am staying on schedule.

17 Early Season Inefficiencies in the NFL Sports Betting Market 17 Writing this thesis has taught me a lot of valuable life lessons, only a few of which have been outlined in this reflection. The lessons that were described above, including the importance of persevering through tough work, relying on others for help and strict time management, all were crucial to my success in writing this thesis. These lessons will also be crucial in the next stage of my life as I go out into the business world. As I write this conclusion to my reflection on my thesis work, I can t help but also reflect on my entire collegiate career. Looking back on the fall quarter of my freshman year and the person that I was then, there is no doubt in my mind that the freshman version of me would not have been able to write the papers that are included in this thesis. A lack of maturity, dedication and focus would have limited my ability to write a paper of this magnitude. However, over the past three years, thanks to countless people along the way, I have matured and grown academically as well as professionally and personally. And I as sit here and put the finishing touches on my collegiate career through the writing of the last few words of this thesis, it is amazing to think back and see how far I have come. Throughout the past 3 years in college I have gone from an immature, undedicated freshman to a mature and focused business professional. This transformation could not have been possible without the many academic and life lessons I have learned along the way, a few of which I have outlined in this reflection. As I conclude these final reflections, I want to take the opportunity to say thanks to all that have helped me throughout my academic career. The countless lessons that I have

18 Early Season Inefficiencies in the NFL Sports Betting Market 18 learned at Ohio University will continue to resonate with me forever. Thank you to all for making me a better person and for helping to shape that immature, unfocused freshman into the mature and focused business professional that I am today.

19 Early Season Inefficiencies in the NFL Sports Betting Market 19 Inefficient Pricing from Holdover Bias in NFL Point Spread Markets Andy Fodor* Ohio University Finance Department Michael DiFilippo Ohio University Kevin Krieger University of West Florida Department of Accounting and Finance Justin Davis Ohio University Department of Management Keywords: Sports Wagering, Efficient Markets, Holdover Bias, Irrational Investment *Contact Author: 234 Copeland Hall Athens, OH (740)

20 Early Season Inefficiencies in the NFL Sports Betting Market 20 Abstract We identify inefficiency in the NFL gambling market indicative of sticky preferences by bettors. NFL teams that qualified for the playoffs in the prior season are favored by too large a margin in the opening week of the following season. Systematic betting based on this trend results in significant profitability over the seasons with an average return over 25% per game. We posit this can be explained by gamblers tendencies to cling to perceptions of teams formed from observation in the prior season. This confirms research in more traditional markets suggesting investors can be slow to update asset valuations.

21 Early Season Inefficiencies in the NFL Sports Betting Market 21 Introduction Basic efficient market theory suggests that gambling spreads serve as unbiased prices for wagers on athletic contests. The best available information regarding a game should be reflected in a spread so that each side of a handicapped contest is equally likely to prevail. 1 Bookmakers are thus able to approximately equalize the funds wagered on either side of a contest and thereby guarantee a riskless profit via commissions. This is the traditional model of bookmaking advanced in the literature (see, e.g., Zuber et al., 1985 and Sauer et al., 1988). The efficiency of the National Football League (NFL) betting market has been a topic of investigation in the finance literature for over forty years. Given that this market has grown into a multi-billion dollar arena for gambling, the primary stream of research has been aimed at identifying inefficiencies that are exploitable for financial gain. To this point, findings from these efforts have been mixed, at best. Numerous authors have identified trends in the betting markets that, if exploited over certain periods, would have led to significant profits. However, other authors have often found such results fail to persist out of sample. Some of the findings of systematic profitability generate from strategies lacking a strong underlying theory, thus exacerbating data mining concerns. 1 Bookmakers set point spreads, or lines, in the most common form of handicapping games. The point spread issued by the bookmaker (often a casino or internet company) establishes the favorite and the underdog of a game. This point spread serves as a correction based on the perceived likelihood of each team winning a game. The favorite is considered more likely to win a game, and thus, the spread is instituted in order to place the two sides of a wager on more equivalent footing. A wager is graded based on subtracting the spread from the favorite s final score and comparing this adjusted figure to the score of the underdog. Whichever side then has the higher score is the winning team of the against the spread wager. The team that wins an against-the-spread wager is said to have covered the game or the spread.

22 Early Season Inefficiencies in the NFL Sports Betting Market 22 Pankoff (1968) provided the initial study of efficiency in the NFL betting market, finding that the market was, overall, efficient. However, the first study considering abnormal profitability based on specific strategic wagering in the NFL was undertaken by Sturgeon (1974), who found that betting against the previous week s biggest winner was profitable. In subsequent years numerous studies have been conducted which consider various betting strategies in search of similar profitability. Many of these studies report success in this endeavor. Vergin and Scriabin (1978) consider a number of betting rules of thumb and report that betting on large underdogs (those of five or more points) generated approximately a 5% profit over a five-year period. Zuber et al. (1985) find NFL games (from the 1983 season) to be profitably predictable based on a number of team measures such as rushing yards, passing yards, fumbles, and interceptions, though they do not find statistical significance, in part due to the small sample size available. Gandar et al. (1988) reconsider the betting rules of Vergin and Scriabin (1978) and introduce new rules of thumb to study. Similar to Zuber et al. (1985) they document profitability based on trading rules, but no statistical significance. Golec and Tamarkin (1991) describe biases in NFL lines against underdogs potentially leading to a profitable betting opportunity, though the economic impact is not great. More recently, Paul and Weinbach (2011) find betting against big favorites to be profitable and statistically significant. This is confirmed independently by Wever and Aadland (2012) who note

23 Early Season Inefficiencies in the NFL Sports Betting Market 23 that wagering on large underdogs from the 1985 through 2010 NFL seasons would have proven to be a profitable approach. On the other hand, the documentation of profitability from such inefficiencies has been called into serious question. Sauer et al. (1986) describe how wagering based on the findings of Zuber et al. (1985) leads to substantial losses in out of sample testing. Dare and Holland (2004) find that previously documented inefficiencies of profitable betting on home underdogs are not consistent from season to season. Gray and Gray (1997) find in-sample profitability based on trading rules but acknowledge, in line with the findings of Sauer et al. (1986), that results are considerably mixed out of sample. Vergin (1998) finds that profitable trading rules developed by Lacey (1990), based on the NFL seasons, did not hold for the subsequent period. The difficulty in confirming the persistence, out of sample, of the profitability of betting approaches should not be unexpected. As Burkey (2005) notes, authors who search for profitable trading rules which, ex post, prove to have been successful in earlier periods, will surely succeed if they investigate enough strategies. In extreme cases, dozens of betting rules may be investigated in one study. For example, Woodland and Woodland (2000) reject 7 of 48 null hypotheses based on a 10% significance level. Badarinathi and Kochman (1996) consider 116 null hypotheses and reject 7 based on a 5% significance level. An inference of profitability of a specific strategy, based on such a widespread approach, would very likely be committing a

24 Early Season Inefficiencies in the NFL Sports Betting Market 24 type I error. Findings of profitability are particularly tenuous when little theoretical development is undertaken in developing a hypothesized strategy. We consider the question of whether bettors in gambling markets display irrationally sticky preferences for wagers in a manner similar to investors who are unwilling to update their asset preferences to reflect new information. Brown and Cliff (2005) document that investors are willing to pay unusually high premia for assets they hold in high sentiment. These high prices result in subsequent abnormally low returns, even in the presence of controls. Haruvy et al. (2007) document that individuals beliefs about prices adapt over time, but they are based in part on past experiences. As a more specific example, numerous authors document the willingness of investors to pay high prices for Internet stocks in the midst of the tech bubble due to sentiment (see, e.g., Cooper et al., 2002). This framework motivates our study of the holdover bias of NFL bettors from one season to the next. Specifically, we consider the case of the early weeks of American professional football seasons. Teams that qualified for the NFL playoffs in the prior season are systematically favored by too many points in Week 1 of the next season when they play opponents who did not qualify for last season s playoffs (or, in the rare cases where they are underdogs, they are underdogs by too few points). Simply wagering, against the spread, on every Week 1 opponent of last season s playoff teams would result in an average return of 25.6% per game over the NFL seasons. Unlike many other studies of profitability from betting strategies, our results are statistically significant as well.

25 Early Season Inefficiencies in the NFL Sports Betting Market 25 We posit that the more detailed explanation of these findings lies in the inability of the participants of this market, the bettors, to adjust their preferences. This theory is in line with the findings of Brown and Cliff (2005) and Haruvy et al. (2007) for more traditional markets. Many gamblers have a perception of a club based on the previous season. When a playoff participant faces a Week 1 opponent that did not qualify for last season s playoffs, a substantial number of bettors are apt to frame the contest as a match-up between a successful and an unsuccessful team and wish to wager accordingly. Bookmakers, cognizant of this irrational preference by gamblers, may adjust the lines they set on a game, forgoing the traditional riskless profit model in search of an expected higher profit. 2 If spreads of such games are, indeed, set in order to entice bettors to cater to their preferences at an effectively higher price, wagering against last season s playoff participants in early weeks of NFL seasons should prove profitable. In related work, Sapra (2008) documents that teams that perform well (poorly) in one season against the spread tend to revert in performance against the spread the following year. This is described as overreaction by bettors to previous impressions. Our findings are perhaps most similar in vein to those of Vergin (2001) who documents that NFL gamblers develop preferences for teams that perform well in the previous game, two to five games, or season. He also characterizes this effect as overreaction by bettors from the seasons. Our results provide out of sample verification of such bettor behavior for the period. However, our 2 Theoretical development and empirical validation of this modified, profit maximization framework was first undertaken by Levitt (2004) and confirmed by Paul and Weinbach (2007) and by Krieger et al. (2011) in out of sample findings. We elaborate further on this framework in the discussion section.

26 Early Season Inefficiencies in the NFL Sports Betting Market 26 results are also different in some important ways. Unlike Sapra (2008) or Vergin (2001), we focus on the specific case of holdover preferences from one season to the next and study how these preferences are specifically manifested in a season s opening week. 3 In doing so, we document strong profitability levels and, in addition, our results are statistically significant, a threshold few other studies of gambling profitability meet. We focus on only one hypothesis in our formulation of this paper, unlike studies that consider multiple betting rules of thumb, and we test our results out of sample for robustness. Our Week 1 results may emerge because longer periods of time work to more forcefully instill investor (or bettor) preferences. NFL gamblers typically adjust their impressions of teams on a weekly basis throughout a season. The final impression left at the end of one regular season, however, has over eight months to linger in the minds of bettors before gambling on Week 1 of the following season commences. The psychology literature notes that attitude strength, analogous here to an investor preference, is greater when an opinion has been held for a longer time (see, e.g., Holland et al., 2003; Glasman and Albarracin, 2006). Savvy bookmakers may exploit these preferences in search of higher expected profits, and thus, bettors willing to take against the herd positions may profit. Bettors update their evaluations of teams in the opening weeks of a season, and thus the opportunity to profit based on sticky beliefs regarding last season dissipates after Week 1. 3 Vergin (2001) analyzes a trading rule (one of 11 he considers) which bets against all playoff teams in the following season but does not consider the holdover bias question specifically for the early portion of next season. His result regarding last year s playoff teams is that they are no more or less likely to cover spreads in the following season.

27 Early Season Inefficiencies in the NFL Sports Betting Market 27 The 25.6% return demonstrated by our study is unprecedented in the NFL wagering literature, even compared to strategies developed in papers, which consider dozens of potential betting rules. Vergin and Scriabin (1978) report that betting on large underdogs (those of five or more points) generated approximately a 5% profit over their five-year study period. Zuber et al. (1985) win 59% of wagers in the latter half of NFL seasons based on models built from team performance and a number of variables measured in the first half of seasons. This translates to a 12.3% return. Gandar et al. (1988) analyze four mechanical-based and three behavior-based rules in an effort to profit in the NFL betting market. The most profitable of their strategies involves wagering on underdogs playing a favorite who easily covered the spread in the previous week and translates to an 11.1% return. Golec and Tamarkin (1991) find that betting home underdogs over the period returned 6.1%. Gray and Gray (1997) utilize a probit model to choose which teams to wager on in NFL games. Using the highest cutoff probability of winning as a threshold for wagering on a team, they demonstrate 7.7% returns in sample and (surprisingly) 16.1% returns out of sample. Vergin (2001) analyzes 70 potential NFL betting strategies and of these 70 strategies, the most profitable returns 18.7%. Using data from , Wever and Aadland (2012) find that betting on large home underdogs and even larger road underdogs yields an 11.2% return. While the magnitude of returns we report for the Week 1, prior playoff approach is newfound, the strategy s effectiveness is actually more impressive when considered in full context. We consider only one hypothesis in our study, and this

28 Early Season Inefficiencies in the NFL Sports Betting Market 28 hypothesis is soundly developed theoretically, in contrast to efforts which briefly introduce numerous potential betting rules. The returns of the approach are statistically significant, a threshold that almost no other paper considering the NFL gambling market meets. The returns of the approach are not statistically significant when investigated, out of sample, via seasons in the distant past; however, the returns of the strategy are still positive in these earlier seasons, even after factoring in bookmaker commission, a standard few other studies reach out of sample. Furthermore, we detail explanations for why the approach, though recently successful, may not have been as relevant in the long-ago seasons used for out of sample analysis. Overall, the effectiveness, development and robustness of the approach are a significant contribution to the literature. The rest of this study is presented as follows. First, we provide theoretical support for our suggested hypothesis. Next, we describe our data collection methods and the statistical methodology used. We then present results of the study. For robustness, we describe the performance of our strategy out of sample. In doing so we also discuss reasons why profitability of the strategy may continue going forward. We conclude in the final section. Hypothesis Development In the traditional model of bookmaking, bookmakers attempt to set a line for a game so that equal amounts of money will be wagered on each side, and the

29 Early Season Inefficiencies in the NFL Sports Betting Market 29 bookmaker may then claim a riskless profit due to the 10% commission that is charged on winning bets (e.g. Zuber et al., 1985; Sauer et al., 1988). 4 A refined model has been developed in recent years, claiming that bookmakers are willing to instead take some level of risk in order to increase their expected profitability. Bookmakers may do so by setting lines so that naïve bettors will flock to the side of a contest which is less than 50% likely to prevail in a wager. Avery and Chevalier (1999) note that a great deal of dumb money exists in the betting market and that bettors make errors in their wagering based on preferences for teams, visibility of teams, and momentum beliefs. A bookmaker might ignore this fact and set a line that achieves equal betting on each side of a game, or the bookmaker may shift the line in order to intentionally allow more of the betting to occur on the side of a contest less likely to win. Thus, by assuming some risk on individual contests, the bookmaker may increase profits over time. We offer the following example for clarification. A perfectly knowledgeable bookmaker handicaps the actual spread of a game between the New Orleans Saints and Cleveland Browns to be the Saints -9 points. The perfect bookmaker also knows most bettors would prefer to bet on the Saints (or. perhaps, against the Browns) and they are so eager to do so that betting would not be equalized between the two sides unless the line were Saints - 11 points. The bookmaker may set the line at Saints -10 points and therefore attract more than 50% of the money wagered on the Saints and be more than 50% likely to win these bets. This approach would result in an expected profitability greater than the 4 As another example, Lee and Smith (2002) note, Bookies do not want their profits to depend on the outcome of the game. Their objective is to set the point spread to equalize the number of dollars wagered on each team...

30 Early Season Inefficiencies in the NFL Sports Betting Market 30 5% guaranteed from the riskless, commission-only approach. Given a large enough bankroll, over time, a large number of games handicapped thusly will minimize any risk to the bookmaker. 5 The profit maximization approach is discussed by Strumpf (2003) who notes that hometown bookies may set spreads, which local teams are notably less than 50% likely to cover. Levitt (2004) conducted a seminal study confirming this approach by bookmakers in the NFL, based on special data from an NFL handicapping contest at the Las Vegas Hilton, and this finding was later supported by Paul and Weinbach (2007) and Krieger et al. (2011). One might ask if informed bettors (often professional gamblers known as sharps or wiseguys ) might not take advantage of such lines and nullify the bookmaker s profitability by wagering on the correct side of a contest. While sharps undoubtedly seek out such opportunities, their impact is limited by three factors. First, a sharp cannot be certain that his handicapping of any one game is superior to the bookmaker, and thus, risk aversion dictates prudence. Second, the bankroll of a sharp is typically considerably less than that of the bookmaker, and here again, risk aversion prevents sharps from too heavily exploiting even a spread they confidently identify as biased. Third, the impact a sharp can make in a betting market like the NFL is 5 While this structure supposes a perfect bookmaker, anecdotal documentation exists that real bookmakers are, indeed, willing to take such an approach to improve profits (see Millman, 2001).

31 Early Season Inefficiencies in the NFL Sports Betting Market 31 saturated by ordinary, naïve bettors. Betting limits placed on gamblers by internet companies or casinos further limit this impact. 6 Given the documentation of this framework, we posit that bookmakers intentionally set spreads in such a manner as to attract naïve bettors to wager on teams for which they re biased. We further describe below why this bias is likely to be based on sentiment for teams perceived as successful as demonstrated by their post-season presence in the previous NFL year. Bettors willing to take the contrarian approach may thus be able (like the sharps) to place wagers with positive expected value, even factoring in bookmaker commissions. Barberis et al. (1998) build a model describing how investor sentiment may impact asset returns. They cite the conservatism bias noted by Edwards (1968) in the psychology literature that holds that people are slow to update beliefs based on information. When beliefs are altered, the updates typically undershoot the true value that should be reflected. In our study we hypothesize a direct parallel for participants in the betting market for NFL games. In particular, we believe that bettors are cognizant that the end of one NFL season marks an important shift in the quality of a team. Substantial personnel turnover of both players and coaches occurs in between seasons, and many teams, particularly unsuccessful ones from the previous year, are likely to make dramatic strategic shifts in the eight-month offseason. Nevertheless, many investors may hold too tightly to their perceptions of success from the previous season and be willing to wager accordingly. Thus, the prices offered by bookmakers, 6 Typical maximum bets range between $10,000 and $25,000 for one side of an NFL contest. Any wagers larger than the maximum amount must be broken into separate wagers, allowing the bookmaker to change the spread in the interim.

32 Early Season Inefficiencies in the NFL Sports Betting Market 32 in the form of lines, may be set at specific levels in order to take advantage of these biases. Broad empirical evidence exists supporting Barberis et al. s (1998) theory that investor sentiment inflates asset prices and therefore yields lower future returns. Neal and Wheatley (1998) consider three different measures of investor sentiment: odd-lot sales frequencies, closed-end fund discounts, and net mutual fund redemptions. They note that the first two proxies help predict stock returns. Fisher and Statman (2000), rather than studying different proxies of sentiment, consider three different groups of stock market participants and conclude that the preferences of all three are negatively linked to future returns. Wall Street strategists and individual investor sentiment are each significantly negatively linked to the performance of stocks in the future while the sentiment of newsletter writers is insignificant but still negative in direction. Brown and Cliff (2005) note that it is difficult to demonstrate inefficiency due to sentiment in traditional markets. They conduct a survey of investors and note new evidence of inefficiency due to sentiment. Excessive optimism of investors is linked to future periods of market-wide overvaluation. The result is economically significant as well. In a laboratory setting, Haruvy et al. (2007) show that investors update prices over time, but prices are based on past trends that traders have experienced in markets. This is analogous to our theory that bettors hold on to perceptions from the prior NFL season. While prices converge to fundamentals in Haruvy et al. s experiment, bubbles do persist for a time.