Are Behavioral Biases Consistent Across the Atlantic? The Over/Under Market for European Soccer Rodney J. Paul – St. Bonaventure University Andrew P. Weinbach – Coastal Carolina University

Introduction In North American sports betting – Biases demonstrated in totals (over/Under) markets In North American sports betting – Biases demonstrated in totals (over/Under) markets This study examines European Football (Soccer) Leagues to test for similar bias This study examines European Football (Soccer) Leagues to test for similar bias

Betting on Totals What are Totals? What are Totals? Over/Under betsOver/Under bets Sportsbooks offer a “total” for total points scored in a game (both teams, combined)Sportsbooks offer a “total” for total points scored in a game (both teams, combined) Over – wager that score > total Over – wager that score > total Under – wager that score < total Under – wager that score < total Example – final score of 2-1 > 2.5 Example – final score of 2-1 > 2.5

A preference for the “over” Fans appear to prefer betting on the over (prefer scoring?) Fans appear to prefer betting on the over (prefer scoring?) Highest totals appear “too high” (under wins > over wins) Highest totals appear “too high” (under wins > over wins) National Football League – Paul and Weinbach (Journal of Sports Economics – 2002) National Football League – Paul and Weinbach (Journal of Sports Economics – 2002) College Football (NCAA) and Arena Football – Paul and Weinbach (Journal of Economics and Finance – 2005) College Football (NCAA) and Arena Football – Paul and Weinbach (Journal of Economics and Finance – 2005) National Basketball Association – Paul, Weinbach, Wilson (Quarterly Review of Economics and Finance – 2004) National Basketball Association – Paul, Weinbach, Wilson (Quarterly Review of Economics and Finance – 2004) Similar results found in Major League Baseball, National Hockey League, and Canadian Football League Similar results found in Major League Baseball, National Hockey League, and Canadian Football League For Monday Night Football – Better ratings for high scoring games – Paul and Weinbach (Journal of Economics and Business) For Monday Night Football – Better ratings for high scoring games – Paul and Weinbach (Journal of Economics and Business)

Source of the bias All North American Sports exhibit similar results All North American Sports exhibit similar results For games with highest totalsFor games with highest totals Under wins often enough to reject the null hypothesis of a fair bet (Win% = 50%) Under wins often enough to reject the null hypothesis of a fair bet (Win% = 50%) In some cases, under wins enough to reject the null hypothesis of no profits (win % = 52.4%) In some cases, under wins enough to reject the null hypothesis of no profits (win % = 52.4%) Why do totals appear to be inaccurate? Why do totals appear to be inaccurate? Traditional model of sportsbook behavior – over bettors drive totals “too high”Traditional model of sportsbook behavior – over bettors drive totals “too high” Levitt (2004) Model of sportsbook behavior – sportsbooks forecast game outcome and fan interestLevitt (2004) Model of sportsbook behavior – sportsbooks forecast game outcome and fan interest

Bias for Over in European Soccer? European Soccer Leagues European Soccer Leagues Low-scoringLow-scoring Huge fan baseHuge fan base Are European Soccer fans different? Are European Soccer fans different? No bias, or bias toward “under” may indicate differenceNo bias, or bias toward “under” may indicate difference If “over” bias observed, preferences consistent with North American bettorsIf “over” bias observed, preferences consistent with North American bettors Attraction of scoring may be universal trait Attraction of scoring may be universal trait

Testing efficiency Subjective probability = objective probability Subjective probability = objective probability Based on sportsbook oddsBased on sportsbook odds Do betting odds represent accurate forecasts of true outcomes? Do betting odds represent accurate forecasts of true outcomes?

Data full seasons for 22 leagues 2 full seasons for 22 leagues Only leagues with complete data Only leagues with complete data All bets based on proposition over/under 2.5 goals All bets based on proposition over/under 2.5 goals Odds adjustments used to adjust prices / rather than moving total Odds adjustments used to adjust prices / rather than moving total Odds reported as return or payback to the a 1 unit bet on the “over” Odds reported as return or payback to the a 1 unit bet on the “over” For example: a winning over bet with payback of 2.2 will return €2.2 for a €1 wager ( )For example: a winning over bet with payback of 2.2 will return €2.2 for a €1 wager ( ) Subjective probability calculated based on Gandar, et. al. (2002) methods Subjective probability calculated based on Gandar, et. al. (2002) methods

LeagueNumber of Obs. Average Return – Bet Over Average Return – Bet Under Subjective Prob – Over Win Objective Prob – Over Win Z-Test All *** B1 – Belgian League * D1 – German League Table I: Returns and Market Efficiency Tests for European Soccer Totals

LeagueNumber of Obs. Average Return – Bet Over Average Return – Bet Under Subjective Prob – Over Win Objective Prob – Over Win Z-Test D2 – German League * E0 – English Premier League E1 – English League 1 Champions E2 – English League * E3 – English League ** EC – English Nationwide Conference

LeagueNumber of Obs. Average Return – Bet Over Average Return – Bet Under Subjective Prob – Over Win Objective Prob – Over Win Z-Test F1 – France League F2 – France League G1 – Greece League * I1 – Italian League I2 – Italian League **

LeagueNumber of Obs. Average Return – Bet Over Average Return – Bet Under Subjective Prob – Over Win Objective Prob – Over Win Z-Test N1 – Netherland s League P1 – Portugal League ** SC0 – Scottish Premier League SC1 – Scottish League SC2 – Scottish League

LeagueNumber of Obs. Average Return – Bet Over Average Return – Bet Under Subjective Prob – Over Win Objective Prob – Over Win Z-Test SC3 – Scottish League SP1 – Spain League SP2 – Spain League T1 – Turkey League

Results Full sample - 15,570 observations Full sample - 15,570 observations “Under” returns % “Under” returns % “Over” returns % “Over” returns % Subj. prob (47.7%) Subj. prob (47.7%) Obj. prob (45.83%) Obj. prob (45.83%) Z: Z:

Bettor Biases Overs vs. Unders Overs vs. Unders Full Sample - “overs” appear overbetFull Sample - “overs” appear overbet Favorite-longshot bias Favorite-longshot bias “overs” with longest odds overbet“overs” with longest odds overbet “unders” with longest odds not overbet“unders” with longest odds not overbet Considering both biases better explains results Considering both biases better explains results

Conclusion Over bias similar to North American sports Over bias similar to North American sports Favorite longshot bias Favorite longshot bias Multiple biases present Multiple biases present