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Player absence and betting lines in the NBA
Finance Research Letters 13 (2015) 130–136
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Player absence and betting lines in the NBA William H. Dare a, Steven A. Dennis b,⇑, Rodney J. Paul c a
Oklahoma State University, United States Kent State University, United States c Syracuse University, United States b
a r t i c l e
i n f o
Article history: Received 28 October 2014 Accepted 26 February 2015 Available online 5 March 2015 JEL classification: G10 G14 G19 Z00
a b s t r a c t We examine the efficiency of betting lines in the NBA when players are absent. We show that the betting line tends to move away from the team with absences, particularly when a meaningful player is absent. We show that opening lines set by bookmakers have significant errors in games when a player is absent. No profitable betting strategy exists in wagering at the closing line, however, as biases are removed by either the sportsbook responding to new information or the sportsbook responding to the actions of bettors. Ó 2015 Elsevier Inc. All rights reserved.
Keywords: Player absence Bet Point spread Line Efficiency NBA
1. Introduction Gandar et al. (1998) show that point spread movements from the open to the close of betting on National Basketball Association (NBA) games significantly improve the forecast accuracy of game outcomes. Specifically, errors in the initial betting line (opening lines) set by bookmakers are reduced
⇑ Corresponding author at: College of Business, Kent State University, P.O. Box 5190, Kent, OH 44242, United States. Tel.: +1 330 672 1205; fax: +1 330 672 9806. E-mail addresses: [email protected] (W.H. Dare), [email protected] (S.A. Dennis), [email protected] (R.J. Paul). http://dx.doi.org/10.1016/j.frl.2015.02.004 1544-6123/Ó 2015 Elsevier Inc. All rights reserved.
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such that the final betting line (the closing line) is a fair bet, or a 50–50 proposition.1 The results in Gandar et al. (1998) suggest that informed traders eliminate any bias in bookmaker-priced opening lines. However, Baryla et al. (2007) examine NBA betting lines and find that lines are less accurate early in NBA seasons: there is an ‘‘early season bias’’ in some NBA betting lines.2 Baryla et al. (2007) show that early season betting lines generally move in the correct direction, but move by an insufficient magnitude to completely eliminate a profitable trading opportunity. The authors suggest that the level of information uncertainty early in a season could hinder bettors in completely eliminating opening line biases. This seems reasonable, as market participants would need to determine the impacts of off-season roster changes, and this may not be immediately apparent in the level of performance. If betting market participants learn through time about the performance of a team at the beginning of the season, bettors may also have to learn how player absences within a season may affect a team’s performance. Our hypothesis is that there will be significant betting line errors in games with player absences, and therefore significant betting opportunities. To investigate this hypothesis, we examine betting line movements for games in the 1996–1997 through 2004–2005 NBA seasons wherein players are absent. An important aspect of a player’s absence is the ‘‘value’’ of that player to the team. To give us a proxy for this importance, we use a formula known as the Approximate Value (AV) Index to scale a missing player’s value. We examine the opening and closing lines of NBA games to determine if this information is incorporated into betting lines. Our results suggest that lines typically move in the direction of the expected final game outcome based upon team absences, especially if the absent player(s) has a high AV Index value (a more valuable player is missing). Simple betting strategies using the available data yield statistically profitable results against opening lines, yet the majority of the biases are eliminated by the market close. However, there is evidence indicating the market slightly overreacts to player absence, but the returns to this strategy are not great enough to overcome the commission charged by the sportsbook. Our conclusion is that betting lines incorporate most, if not all, information concerning player absences. The remainder of this paper is organized as follows: Section 2 details our data and methodology, Section 3 outlines our results and Section 4 concludes. 2. Data and methodology Our database spans 10,555 NBA games from the 1996–1997 through 2004–2005 seasons. The betting lines are taken from the Stardust Race and Sports Book. Data concerning player absences are taken from databaseBasketball.com. For each game, we ascertain those players who did not play for any reason except ‘‘coach’s decision’’. Absences occur because of injury, sickness, suspension and other reasons, including personal reasons. One intriguing aspect of player absence information is that it may not be relayed to the public until just before game time. In field observations, the authors have observed enormous (2–6 point) betting line movements immediately following player absence announcements, especially if the player is a key player on the team. As the information frequently comes late, the only explanation for the line movements is that bookmakers must adjust the line based on the anticipated importance of the information. Market adjustments from betting market imbalances seem implausible due to the short time until the game is played and the somewhat rudimentary microstructure (at least by today’s financial market standards) of the market. 1 In the NBA, the betting line (known as the point spread) is determined by how many points the favored team will beat the underdog team. A betting line of 3 means the favored team must win by 4 points for a bet on the favored team to pay off. If the favored team wins by 2 points or less, or loses the game outright, then a bet on the underdog team wins. If the favored team wins by exactly 3 points, the bet is termed a ‘‘push’’ and all monies are returned to bettors. The opening line is the establishment of the betting line; it is first put out by top sports line makers, which is then combined with public opinion, and finally released as the opening sports betting line. In our database, the opening line comes from the Stardust Race and Sportsbook, which boasts that it is ‘‘where the line is made’’. The closing line is the last available price (point spread) before betting starts, which is at the tip-off of the game. 2 Specifically, Baryla et al. (2007) find that ‘‘following the betting line’’ is profitable early in the season, even when including transaction costs. Following the betting line when the line movement in the ‘‘totals’’ market is to the ‘‘under’’ is particularly profitable.
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In an attempt to value the importance of a player to the team, we use a statistic in the database Basketball.com data known as the Approximate Value (AV) Index (see the Appendix for more information on the AV Index). The AV Index is computed as follows: 3=4
AV ¼
Credits 21
ð1Þ
where
Credits ¼ PTS þ REB þ AST þ STL þ BLK-FG MISSED FT MISSED TO and PTS = total points, REB = total rebounds, AST = total assists, STL = steals, BLK = blocks, FG MISSED = field goals missed, FT MISSED = free throws missed, and TO = turnovers. As noted in the Appendix, a value of ten for the AV Index indicates a player of average ability (according to the source, a player with abilities equivalent to a very good sixth man), while a value of twenty indicates an exceptional MVP season. Because the AV Index is computed after a season is complete, the use of the current season AV Index is problematic because it requires knowledge of games yet to be played in the season. For this reason, we collect and use the AV Index for the season prior to the current season in our investigation of efficiency. For NBA ‘‘rookies’’ and for players who did not play in the NBA in the previous season, the AV Index is not computed and is given a value of zero. We acknowledge this is a weakness for the variable; however, we cannot discern a reasonable bias to our results, as the impacts should be both for and against efficiency. An additional consideration is that the AV Index for two players on different teams may be identical in our study, but because different teams have different weaknesses, the absence of a player on one team may be more important to a game’s outcome. One team may be particularly impacted by the absence of a star point guard because they like to ‘‘run the court’’, while the absence of a solid lowpost defender (who may or may not have a high AV score) may be particularly important to another team. Ideally, we would measure the value that each individual player brings to the team, and the value lost with his absence. But alas, such a value would be subjective to the viewer of the player/ team. 3. Results In our sample of nine NBA seasons consisting of 10,555 games, 5628 games had at least one player absent. In Table 1, we analyze the movements from the open to close of betting lines when a player is absent from a game. Panel A of Table 1 contains all line movements for the teams with the lowest AVs in the game (the lowest loss of value to their roster because of player absence). Panel B is the same measure but when the home team has a higher AV than the visiting team, and Panel C is for games where the visiting team has the higher AV. The left-most column of Table 1 shows the total AV Index for all players missing from a team. If both teams have a player missing, then the AV Index is the difference between the AV Indices of absent players for each team. That is, if Team A has two players missing, one with an AV Index of 8 and the other with an AV Index of 15, then Team A has an AV Index of 23. If Team B has one player missing with an AV Index of 12, then the AV Index for that game is 11 = 23 12 for Team A. In Table 1, we find that in games when a player is missing, the line moves away from that team 55% of the time. If the AV Index of the player(s) is greater than 5, then the line moves away from that team almost 68% of the time. The line movements are even greater when the visiting team has a player absent (Panel C). When the visiting team has an AV Index greater than 20, the line moves away from the visiting team more than 80% of the time. Unfortunately, the actual source of point spread movements is not known with certainty. Under the traditional models of sportsbook behavior, such as Pankoff (1968), Gandar et al. (1988) and Sauer et al. (1988), sportsbooks are setting prices (point spreads) to clear the market. Therefore, under these models, the point spread will move in the direction of the team that is receiving more money bet upon them. In the above example, this would be the team with the lower player absence value (AV Index).
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Table 1 Player absence and line movements in the NBA.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Moves to non-injured team
Moves to injured team
No line move
Percent move to non-injured team
2771 1925 912 297 114
2229 908 535 174 56
628 436 166 43 14
55.42 67.95 63.03 63.04 67.06
Move to home team
Move to visiting team
No line move
Percent move to home team
Panel B: Home team with more absences – ONLY All games 1426 1096 AV P 5 408 745 AV P 10 359 329 AV P 15 122 109 AV P 20 39 36
296 195 73 22 7
56.54 35.39 52.18 52.81 52.00
Panel C: Visiting team with more absences – ONLY All games 1675 803 AV P 5 1180 500 AV P 10 583 176 AV P 15 188 52 AV P 20 78 17
332 241 93 21 7
32.41 29.76 23.19 21.67 17.90
The movements in betting lines from the open of betting to the close are examined for games in which there is at least one player absent for at least one team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. In recent years, the traditional models have been challenged by Levitt (2004). Under the hypothesis of Levitt (2004), sportsbooks set prices (point spreads) to maximize profits by capitalizing on potential bettor biases. If true, point spreads would potentially represent inaccurate forecasts of the expected game outcomes. Therefore, the sportsbook may be moving the point spread in response to information (specifically, more detailed information on the nature and extent of absences related to the games of the day) in an attempt to maximize profits by exploiting known bettor biases. Therefore, the actions of bettors could have nothing to do with point spread movements. In addition, some combination of these two models (part bettors and part sportsbook) could also be the source of point spread movements in these markets. Without detailed information on the timing of information releases and actual sportsbook betting volume, these questions cannot be answered. Given that we are not privy to inside information on sportsbook behavior and do not have actual timings of press releases or interviews of players or coaches, we cannot address the source of these line movements. Therefore, we focus on market efficiency in the presence of player absences, attempting to identify simple strategies that could yield higher than expected returns. Table 2 depicts the winning percentage of a betting strategy where bets are placed on the team with the missing players. The investigation in Table 2 is similar to that in Table 4 of Gandar et al. (1998), except that Gandar et al. (1998) focus on all games, whereas we focus on only those games where there is at least one player absent. The common bet in football and basketball markets is to bet eleven dollars to win ten. An 11-for-10 bet translates into the winning percentage of 11/ (10 + 11) = 52.38% in order to make profits (it is then commonly rounded to 52.4% for convenience). The standard test of efficiency is to use a binomial test against 50% with a two-tailed test to test for rationality and then a one-tailed test against a win percentage of 52.4% to test for profits after transaction costs.3 In panel A, we investigate all games where a player is missing and wagers are made on the team with missing players. In panel B, we examine only those games where the home team has (more) missing players, and we bet on the home team. In panel C, we examine only those games where the visiting team has (more) missing players, and we bet on the home team. Our results in panel A of Table 2 are similar to those in Gandar et al. (1998) – the opening lines of bookmakers in games where a player is absent exhibit significant bias, particularly when the AV Index is greater than 10. However, the bias is not enough to allow for a profitable betting strategy when we include transaction costs. Panels B and C show that there is an overall bias in opening lines against home teams in games where there are absences. Our dataset does not allow us to determine the exact timing of the information release concerning a player absence. If the news release occurred after the market opened (typically the morning of game day and before the day’s roster has been set), then the ‘‘bias’’ we are interpreting in the opening line is incorrect. That is, the line moved from the opening line because the sportsbook and market learned of the player absence after the opening line was set. However, many player absences cover multiple games wherein market participants know the player will be out, so the market must have known about absences in those games. Our results are similar if we use only those games wherein a player has already been absent for at least one game, so we believe we are correct in our interpretation that the opening line has some bias when players are absent.
3
We used Stata in our analysis, which reports a Z-test from the standard binomial test.
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Table 2 The efficiency of opening lines in the NBA when players are absent.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Wins
Losses
Pushes
Winning percentage
t-Statistic H0: = 0.5
t-Statistic, H0: P 0.524
2769 1833 751 232 79
2767 1867 831 274 103
110 69 31 8 2
50.02 46.54 47.47 45.85 43.41
0.027 0.559 2.014** 1.874* 1.795*
NA NA 0.014 0.6365 1.3004
Home wins
Visitor wins
Pushes
Home winning percentage
t-Statistic H0: = 0.5
t-Statistic H0: P 0.524
Panel B: Home team with more absences – ONLY All games 1483 1286 49 AV P 5 963 852 33 AV P 10 392 354 15 AV P 15 136 112 5 AV P 20 43 38 1
53.56 53.06 52.55 54.84 53.09
3.753*** 2.610*** 1.393 1.531 0.557
1.221 0.562 NA NA NA
Panel C: Visiting team with more absences – ONLY All games 1481 1286 61 AV P 5 1015 870 36 AV P 10 477 359 16 AV P 15 162 96 3 AV P 20 65 36 1
53.52 53.85 57.06 62.79 64.36
3.716*** 3.35*** 4.122*** 4.25*** 3.012***
1.185 1.259 2.720*** 3.453*** 2.509***
Panel A is for all games wherein a player was absent for either team, and it examines a strategy of betting the team with the most absences. Panel B is for only those games where the home team has the most absences, and it examines a strategy of betting the home team. Panel C is for only those games where the visiting team has more absences, and it examines a strategy of betting the home team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. * Significance at the 10% level. ** Significance at the 5% level. *** Significance at the 1% level.
Panel B of Table 2 shows that the market overreacts to home team player absences. A bet at the opening line on all home teams with absences produces a winning percentage significantly greater than 50%. However, it is not significantly greater than 52.4%, so it is not high enough to cover transaction costs. Panel C of Table 2 shows that the visiting team is not punished enough when it has players missing. A bet at the opening line on all visiting teams with absences produces a winning percentage that is significantly below 50%, but again it is not significant enough to produce profits at the 52.4% winning percentage. Furthermore, if the visiting team has an AV Index greater than or equal to 10, a bet on the home team (against the visiting team) produces a winning percentage of 57.06%, which is significantly greater than 52.4%. As the AV Index of the visiting team’s missing player(s) increases, the winning percentage of betting on the home team (betting against the visiting team with absences) has an even greater winning percentage, as high as 64.36%. The evidence in Table 2 suggests that opening lines appear to be biased when a player is missing, and that there is a significant bias against the home team when the visiting team has missing players. As discussed earlier, we cannot rule out that the information on the absence was released after the market opened, causing the line to move. Table 3 shows that most biases are eliminated by the time of market close, but some slight biases remain. A simple strategy of betting on a team with player absences produces a win rate of 51.30%, which is significantly greater than 50% at the ten percent level. A simple strategy of betting on all teams with an AV Index greater than 5 produces a win rate of 51.73%, which is significantly greater than 50% at the five percent level. However, bettor biases against teams with significant absences are not enough to produce a win percentage necessary to overcome the transaction costs of betting through a sportsbook under the $11-for-$10 betting rule. Although simple strategies of betting on the team with more absences win often enough to reject a fair bet (50%), the null hypothesis of no profitability (52.4%) cannot be rejected. A comparison of Tables 2 and 3 shows that any potential biases (which led to profitable betting rules) that existed in opening lines are eliminated by the time of market close. In this regard, our results are similar to Gandar et al. (1998). These biases may have been removed by the actions of informed traders, who fully incorporate the extent of player absences into their wagers, or they could have been removed by the sportsbook itself as it changes prices (point spreads) on the game in response to information it receives in the hours leading up to tip-off.
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W.H. Dare et al. / Finance Research Letters 13 (2015) 130–136 Table 3 The efficiency of closing lines in the NBA when players are absent.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Wins
Losses
Pushes
Winning percentage
2830 1913 809 264 96
2687 1785 773 244 87
117 75 33 7 2
51.30 51.73 51.14 51.97 52.46
Home wins
Visitor wins
Pushes
Home winning percentage
t-Statistic H0: = 0.5 1.926* 2.106** 0.905 0.888 0.666 t-Statistic H0: = 0.5
t-Statistic H0: P 0.524 NA NA NA NA NA t-Statistic H0: P 0.524
Panel B: Home team with more absences – ONLY All games 1413 1354 52 AV P 5 925 891 33 AV P 10 388 362 11 AV P 15 140 111 2 AV P 20 44 37 1
51.07 50.94 51.73 55.78 54.32
1.122 0.798 0.950 1.843* 0.781
NA NA NA 1.077 NA
Panel C: Visiting team with more absences – ONLY All games 1333 1417 65 AV P 5 894 988 42 AV P 10 411 421 22 AV P 15 133 124 5 AV P 20 50 52 1
48.47 47.50 49.40 51.75 49.02
1.603 2.170** 0.347 0.562 0.198
NA 0.085 NA NA NA
Panel A is for all games wherein a player was absent for either team, and it examines a strategy of betting the team with the most absences. Panel B is for only those games where the home team has the most absences, and it examines a strategy of betting the home team. Panel C is for only those games where the visiting team has more absences, and it examines a strategy of betting the home team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. * Significance at the 10% level. ** Significance at the 5% level.
4. Conclusions We have examined NBA basketball games for the efficiency of betting lines in games where at least one player is absent from at least one team. We have shown that the betting line moves significantly against the team with absences in a majority of games, particularly when the index of player value, the AV Index (player quality lost), for the team is high and particularly for visiting teams. We have shown that opening lines set by bookmakers have significant errors in games where players are absent. We also show that there is a significant bias in opening lines against the home team when players are absent. The home team is penalized too much (in terms of the point spread) when the home team has missing players, and the visiting team is not penalized enough when it has missing players. At opening lines, a strategy of wagering on the home team when the visiting team has a high AV Index produces a win percentage that rejects the null hypothesis of zero profitability. However, we cannot rule out that information on the absence was released after the market opened, resulting in the line movement. By the time the market closes, biases in opening lines are removed and bettors cannot earn profits sufficient to cover transaction costs using the absence information. Overall, we find that NBA betting market participants can accurately interpret the ‘‘value’’ of the missing player(s) and can adjust the betting line accordingly.
Acknowledgments We thank Stephanie Aker, Kris Ahmann, Laura Davison, and Tyler Eiken for valuable research assistance.
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Appendix A. Approximate Value (AV) Index The Approximate Value (AV) Index was developed by Dean Oliver. You can read more about the AV formula at this website: http://www.powerbasketball.com/theywin2.html. We take the following excerpt concerning the AV Index from that website. The plan for the method was to end up with a scale of integers between 0 and about 20 rating players, with 10 representing an ‘average’ player. It was to be based upon several standards a player was to meet in order to gain points of approximate value. The whole thing was modeled on Bill James’ Value Approximation method for baseball. As James did, Dean Oliver assigned verbal descriptions to ranges of scores in order to see if the method produced results that matched general descriptions of players. Those descriptions are as follows: A score of about twenty indicates an exceptional MVP season. A score of seventeen or eighteen indicates a strong MVP candidate or an ordinary MVP season. A score of sixteen indicates an MVP candidate. A score of fifteen indicates a definite All-Star who is a marginal MVP candidate. A score of fourteen indicates a probable All-Star. A score of thirteen indicates a marginal All-Star. A score of twelve indicates a very fine season; an All-Star candidate. A score of eleven indicates an above average regular; an excellent player playing about 1800 min. A score of ten indicates an average regular or a very good sixth man. A score of nine indicates an average regular or a good sixth man. A score of eight indicates a fair regular or an average sixth man. A score of six or seven indicates an average bench player or a good player playing under 1500 min. A score of four or five indicates a player who plays about 1000 min and who does not deserve many more. Scores of three or less usually indicate players who are unimpressive in limited playing time.
References Baryla, Borghesi, Dare, Dennis, 2007. Learning, price formation and the early season bias in the NBA. Financ. Res. Lett. 4 (3), 155– 164. Gandar, John, Zuber, Richard, O’Brien, Thomas, Russo, Ben, 1988. Testing rationality in the point spread betting market. J. Financ. 43 (4), 995–1008. Gandar, John M., Dare, William H., Brown, Craig R., Zuber, Richard A., 1998. Informed traders and price variations in the betting market for professional basketball games. J. Financ. 53 (1), 385–401. Levitt, Steven D., 2004. Why are gambling markets organized so differently from financial markets? Econ. J. 114 (495), 223–246. Pankoff, Lyn D., 1968. Market efficiency and football betting. J. Bus. 41 (2), 203–214. Sauer, Raymond D., Brajer, Vic, Ferris, Stephen P., Marr, M. Wayne, 1988. Hold your bets: another look at the efficiency of the gambling market for National Football League Teams. J. Polit. Econ. 96 (1), 206–213.
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Player absence and betting lines in the NBA William H. Dare a, Steven A. Dennis b,⇑, Rodney J. Paul c a
Oklahoma State University, United States Kent State University, United States c Syracuse University, United States b
a r t i c l e
i n f o
Article history: Received 28 October 2014 Accepted 26 February 2015 Available online 5 March 2015 JEL classification: G10 G14 G19 Z00
a b s t r a c t We examine the efficiency of betting lines in the NBA when players are absent. We show that the betting line tends to move away from the team with absences, particularly when a meaningful player is absent. We show that opening lines set by bookmakers have significant errors in games when a player is absent. No profitable betting strategy exists in wagering at the closing line, however, as biases are removed by either the sportsbook responding to new information or the sportsbook responding to the actions of bettors. Ó 2015 Elsevier Inc. All rights reserved.
Keywords: Player absence Bet Point spread Line Efficiency NBA
1. Introduction Gandar et al. (1998) show that point spread movements from the open to the close of betting on National Basketball Association (NBA) games significantly improve the forecast accuracy of game outcomes. Specifically, errors in the initial betting line (opening lines) set by bookmakers are reduced
⇑ Corresponding author at: College of Business, Kent State University, P.O. Box 5190, Kent, OH 44242, United States. Tel.: +1 330 672 1205; fax: +1 330 672 9806. E-mail addresses: [email protected] (W.H. Dare), [email protected] (S.A. Dennis), [email protected] (R.J. Paul). http://dx.doi.org/10.1016/j.frl.2015.02.004 1544-6123/Ó 2015 Elsevier Inc. All rights reserved.
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such that the final betting line (the closing line) is a fair bet, or a 50–50 proposition.1 The results in Gandar et al. (1998) suggest that informed traders eliminate any bias in bookmaker-priced opening lines. However, Baryla et al. (2007) examine NBA betting lines and find that lines are less accurate early in NBA seasons: there is an ‘‘early season bias’’ in some NBA betting lines.2 Baryla et al. (2007) show that early season betting lines generally move in the correct direction, but move by an insufficient magnitude to completely eliminate a profitable trading opportunity. The authors suggest that the level of information uncertainty early in a season could hinder bettors in completely eliminating opening line biases. This seems reasonable, as market participants would need to determine the impacts of off-season roster changes, and this may not be immediately apparent in the level of performance. If betting market participants learn through time about the performance of a team at the beginning of the season, bettors may also have to learn how player absences within a season may affect a team’s performance. Our hypothesis is that there will be significant betting line errors in games with player absences, and therefore significant betting opportunities. To investigate this hypothesis, we examine betting line movements for games in the 1996–1997 through 2004–2005 NBA seasons wherein players are absent. An important aspect of a player’s absence is the ‘‘value’’ of that player to the team. To give us a proxy for this importance, we use a formula known as the Approximate Value (AV) Index to scale a missing player’s value. We examine the opening and closing lines of NBA games to determine if this information is incorporated into betting lines. Our results suggest that lines typically move in the direction of the expected final game outcome based upon team absences, especially if the absent player(s) has a high AV Index value (a more valuable player is missing). Simple betting strategies using the available data yield statistically profitable results against opening lines, yet the majority of the biases are eliminated by the market close. However, there is evidence indicating the market slightly overreacts to player absence, but the returns to this strategy are not great enough to overcome the commission charged by the sportsbook. Our conclusion is that betting lines incorporate most, if not all, information concerning player absences. The remainder of this paper is organized as follows: Section 2 details our data and methodology, Section 3 outlines our results and Section 4 concludes. 2. Data and methodology Our database spans 10,555 NBA games from the 1996–1997 through 2004–2005 seasons. The betting lines are taken from the Stardust Race and Sports Book. Data concerning player absences are taken from databaseBasketball.com. For each game, we ascertain those players who did not play for any reason except ‘‘coach’s decision’’. Absences occur because of injury, sickness, suspension and other reasons, including personal reasons. One intriguing aspect of player absence information is that it may not be relayed to the public until just before game time. In field observations, the authors have observed enormous (2–6 point) betting line movements immediately following player absence announcements, especially if the player is a key player on the team. As the information frequently comes late, the only explanation for the line movements is that bookmakers must adjust the line based on the anticipated importance of the information. Market adjustments from betting market imbalances seem implausible due to the short time until the game is played and the somewhat rudimentary microstructure (at least by today’s financial market standards) of the market. 1 In the NBA, the betting line (known as the point spread) is determined by how many points the favored team will beat the underdog team. A betting line of 3 means the favored team must win by 4 points for a bet on the favored team to pay off. If the favored team wins by 2 points or less, or loses the game outright, then a bet on the underdog team wins. If the favored team wins by exactly 3 points, the bet is termed a ‘‘push’’ and all monies are returned to bettors. The opening line is the establishment of the betting line; it is first put out by top sports line makers, which is then combined with public opinion, and finally released as the opening sports betting line. In our database, the opening line comes from the Stardust Race and Sportsbook, which boasts that it is ‘‘where the line is made’’. The closing line is the last available price (point spread) before betting starts, which is at the tip-off of the game. 2 Specifically, Baryla et al. (2007) find that ‘‘following the betting line’’ is profitable early in the season, even when including transaction costs. Following the betting line when the line movement in the ‘‘totals’’ market is to the ‘‘under’’ is particularly profitable.
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In an attempt to value the importance of a player to the team, we use a statistic in the database Basketball.com data known as the Approximate Value (AV) Index (see the Appendix for more information on the AV Index). The AV Index is computed as follows: 3=4
AV ¼
Credits 21
ð1Þ
where
Credits ¼ PTS þ REB þ AST þ STL þ BLK-FG MISSED FT MISSED TO and PTS = total points, REB = total rebounds, AST = total assists, STL = steals, BLK = blocks, FG MISSED = field goals missed, FT MISSED = free throws missed, and TO = turnovers. As noted in the Appendix, a value of ten for the AV Index indicates a player of average ability (according to the source, a player with abilities equivalent to a very good sixth man), while a value of twenty indicates an exceptional MVP season. Because the AV Index is computed after a season is complete, the use of the current season AV Index is problematic because it requires knowledge of games yet to be played in the season. For this reason, we collect and use the AV Index for the season prior to the current season in our investigation of efficiency. For NBA ‘‘rookies’’ and for players who did not play in the NBA in the previous season, the AV Index is not computed and is given a value of zero. We acknowledge this is a weakness for the variable; however, we cannot discern a reasonable bias to our results, as the impacts should be both for and against efficiency. An additional consideration is that the AV Index for two players on different teams may be identical in our study, but because different teams have different weaknesses, the absence of a player on one team may be more important to a game’s outcome. One team may be particularly impacted by the absence of a star point guard because they like to ‘‘run the court’’, while the absence of a solid lowpost defender (who may or may not have a high AV score) may be particularly important to another team. Ideally, we would measure the value that each individual player brings to the team, and the value lost with his absence. But alas, such a value would be subjective to the viewer of the player/ team. 3. Results In our sample of nine NBA seasons consisting of 10,555 games, 5628 games had at least one player absent. In Table 1, we analyze the movements from the open to close of betting lines when a player is absent from a game. Panel A of Table 1 contains all line movements for the teams with the lowest AVs in the game (the lowest loss of value to their roster because of player absence). Panel B is the same measure but when the home team has a higher AV than the visiting team, and Panel C is for games where the visiting team has the higher AV. The left-most column of Table 1 shows the total AV Index for all players missing from a team. If both teams have a player missing, then the AV Index is the difference between the AV Indices of absent players for each team. That is, if Team A has two players missing, one with an AV Index of 8 and the other with an AV Index of 15, then Team A has an AV Index of 23. If Team B has one player missing with an AV Index of 12, then the AV Index for that game is 11 = 23 12 for Team A. In Table 1, we find that in games when a player is missing, the line moves away from that team 55% of the time. If the AV Index of the player(s) is greater than 5, then the line moves away from that team almost 68% of the time. The line movements are even greater when the visiting team has a player absent (Panel C). When the visiting team has an AV Index greater than 20, the line moves away from the visiting team more than 80% of the time. Unfortunately, the actual source of point spread movements is not known with certainty. Under the traditional models of sportsbook behavior, such as Pankoff (1968), Gandar et al. (1988) and Sauer et al. (1988), sportsbooks are setting prices (point spreads) to clear the market. Therefore, under these models, the point spread will move in the direction of the team that is receiving more money bet upon them. In the above example, this would be the team with the lower player absence value (AV Index).
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Table 1 Player absence and line movements in the NBA.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Moves to non-injured team
Moves to injured team
No line move
Percent move to non-injured team
2771 1925 912 297 114
2229 908 535 174 56
628 436 166 43 14
55.42 67.95 63.03 63.04 67.06
Move to home team
Move to visiting team
No line move
Percent move to home team
Panel B: Home team with more absences – ONLY All games 1426 1096 AV P 5 408 745 AV P 10 359 329 AV P 15 122 109 AV P 20 39 36
296 195 73 22 7
56.54 35.39 52.18 52.81 52.00
Panel C: Visiting team with more absences – ONLY All games 1675 803 AV P 5 1180 500 AV P 10 583 176 AV P 15 188 52 AV P 20 78 17
332 241 93 21 7
32.41 29.76 23.19 21.67 17.90
The movements in betting lines from the open of betting to the close are examined for games in which there is at least one player absent for at least one team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. In recent years, the traditional models have been challenged by Levitt (2004). Under the hypothesis of Levitt (2004), sportsbooks set prices (point spreads) to maximize profits by capitalizing on potential bettor biases. If true, point spreads would potentially represent inaccurate forecasts of the expected game outcomes. Therefore, the sportsbook may be moving the point spread in response to information (specifically, more detailed information on the nature and extent of absences related to the games of the day) in an attempt to maximize profits by exploiting known bettor biases. Therefore, the actions of bettors could have nothing to do with point spread movements. In addition, some combination of these two models (part bettors and part sportsbook) could also be the source of point spread movements in these markets. Without detailed information on the timing of information releases and actual sportsbook betting volume, these questions cannot be answered. Given that we are not privy to inside information on sportsbook behavior and do not have actual timings of press releases or interviews of players or coaches, we cannot address the source of these line movements. Therefore, we focus on market efficiency in the presence of player absences, attempting to identify simple strategies that could yield higher than expected returns. Table 2 depicts the winning percentage of a betting strategy where bets are placed on the team with the missing players. The investigation in Table 2 is similar to that in Table 4 of Gandar et al. (1998), except that Gandar et al. (1998) focus on all games, whereas we focus on only those games where there is at least one player absent. The common bet in football and basketball markets is to bet eleven dollars to win ten. An 11-for-10 bet translates into the winning percentage of 11/ (10 + 11) = 52.38% in order to make profits (it is then commonly rounded to 52.4% for convenience). The standard test of efficiency is to use a binomial test against 50% with a two-tailed test to test for rationality and then a one-tailed test against a win percentage of 52.4% to test for profits after transaction costs.3 In panel A, we investigate all games where a player is missing and wagers are made on the team with missing players. In panel B, we examine only those games where the home team has (more) missing players, and we bet on the home team. In panel C, we examine only those games where the visiting team has (more) missing players, and we bet on the home team. Our results in panel A of Table 2 are similar to those in Gandar et al. (1998) – the opening lines of bookmakers in games where a player is absent exhibit significant bias, particularly when the AV Index is greater than 10. However, the bias is not enough to allow for a profitable betting strategy when we include transaction costs. Panels B and C show that there is an overall bias in opening lines against home teams in games where there are absences. Our dataset does not allow us to determine the exact timing of the information release concerning a player absence. If the news release occurred after the market opened (typically the morning of game day and before the day’s roster has been set), then the ‘‘bias’’ we are interpreting in the opening line is incorrect. That is, the line moved from the opening line because the sportsbook and market learned of the player absence after the opening line was set. However, many player absences cover multiple games wherein market participants know the player will be out, so the market must have known about absences in those games. Our results are similar if we use only those games wherein a player has already been absent for at least one game, so we believe we are correct in our interpretation that the opening line has some bias when players are absent.
3
We used Stata in our analysis, which reports a Z-test from the standard binomial test.
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Table 2 The efficiency of opening lines in the NBA when players are absent.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Wins
Losses
Pushes
Winning percentage
t-Statistic H0: = 0.5
t-Statistic, H0: P 0.524
2769 1833 751 232 79
2767 1867 831 274 103
110 69 31 8 2
50.02 46.54 47.47 45.85 43.41
0.027 0.559 2.014** 1.874* 1.795*
NA NA 0.014 0.6365 1.3004
Home wins
Visitor wins
Pushes
Home winning percentage
t-Statistic H0: = 0.5
t-Statistic H0: P 0.524
Panel B: Home team with more absences – ONLY All games 1483 1286 49 AV P 5 963 852 33 AV P 10 392 354 15 AV P 15 136 112 5 AV P 20 43 38 1
53.56 53.06 52.55 54.84 53.09
3.753*** 2.610*** 1.393 1.531 0.557
1.221 0.562 NA NA NA
Panel C: Visiting team with more absences – ONLY All games 1481 1286 61 AV P 5 1015 870 36 AV P 10 477 359 16 AV P 15 162 96 3 AV P 20 65 36 1
53.52 53.85 57.06 62.79 64.36
3.716*** 3.35*** 4.122*** 4.25*** 3.012***
1.185 1.259 2.720*** 3.453*** 2.509***
Panel A is for all games wherein a player was absent for either team, and it examines a strategy of betting the team with the most absences. Panel B is for only those games where the home team has the most absences, and it examines a strategy of betting the home team. Panel C is for only those games where the visiting team has more absences, and it examines a strategy of betting the home team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. * Significance at the 10% level. ** Significance at the 5% level. *** Significance at the 1% level.
Panel B of Table 2 shows that the market overreacts to home team player absences. A bet at the opening line on all home teams with absences produces a winning percentage significantly greater than 50%. However, it is not significantly greater than 52.4%, so it is not high enough to cover transaction costs. Panel C of Table 2 shows that the visiting team is not punished enough when it has players missing. A bet at the opening line on all visiting teams with absences produces a winning percentage that is significantly below 50%, but again it is not significant enough to produce profits at the 52.4% winning percentage. Furthermore, if the visiting team has an AV Index greater than or equal to 10, a bet on the home team (against the visiting team) produces a winning percentage of 57.06%, which is significantly greater than 52.4%. As the AV Index of the visiting team’s missing player(s) increases, the winning percentage of betting on the home team (betting against the visiting team with absences) has an even greater winning percentage, as high as 64.36%. The evidence in Table 2 suggests that opening lines appear to be biased when a player is missing, and that there is a significant bias against the home team when the visiting team has missing players. As discussed earlier, we cannot rule out that the information on the absence was released after the market opened, causing the line to move. Table 3 shows that most biases are eliminated by the time of market close, but some slight biases remain. A simple strategy of betting on a team with player absences produces a win rate of 51.30%, which is significantly greater than 50% at the ten percent level. A simple strategy of betting on all teams with an AV Index greater than 5 produces a win rate of 51.73%, which is significantly greater than 50% at the five percent level. However, bettor biases against teams with significant absences are not enough to produce a win percentage necessary to overcome the transaction costs of betting through a sportsbook under the $11-for-$10 betting rule. Although simple strategies of betting on the team with more absences win often enough to reject a fair bet (50%), the null hypothesis of no profitability (52.4%) cannot be rejected. A comparison of Tables 2 and 3 shows that any potential biases (which led to profitable betting rules) that existed in opening lines are eliminated by the time of market close. In this regard, our results are similar to Gandar et al. (1998). These biases may have been removed by the actions of informed traders, who fully incorporate the extent of player absences into their wagers, or they could have been removed by the sportsbook itself as it changes prices (point spreads) on the game in response to information it receives in the hours leading up to tip-off.
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W.H. Dare et al. / Finance Research Letters 13 (2015) 130–136 Table 3 The efficiency of closing lines in the NBA when players are absent.
Panel A All games AV P 5 AV P 10 AV P 15 AV P 20
Wins
Losses
Pushes
Winning percentage
2830 1913 809 264 96
2687 1785 773 244 87
117 75 33 7 2
51.30 51.73 51.14 51.97 52.46
Home wins
Visitor wins
Pushes
Home winning percentage
t-Statistic H0: = 0.5 1.926* 2.106** 0.905 0.888 0.666 t-Statistic H0: = 0.5
t-Statistic H0: P 0.524 NA NA NA NA NA t-Statistic H0: P 0.524
Panel B: Home team with more absences – ONLY All games 1413 1354 52 AV P 5 925 891 33 AV P 10 388 362 11 AV P 15 140 111 2 AV P 20 44 37 1
51.07 50.94 51.73 55.78 54.32
1.122 0.798 0.950 1.843* 0.781
NA NA NA 1.077 NA
Panel C: Visiting team with more absences – ONLY All games 1333 1417 65 AV P 5 894 988 42 AV P 10 411 421 22 AV P 15 133 124 5 AV P 20 50 52 1
48.47 47.50 49.40 51.75 49.02
1.603 2.170** 0.347 0.562 0.198
NA 0.085 NA NA NA
Panel A is for all games wherein a player was absent for either team, and it examines a strategy of betting the team with the most absences. Panel B is for only those games where the home team has the most absences, and it examines a strategy of betting the home team. Panel C is for only those games where the visiting team has more absences, and it examines a strategy of betting the home team. The AV is the total Approximate Value of players who are absent for a team (see the Appendix for an explanation of AV). A higher AV indicates that more valuable players are missing. If both teams have player absences, the AV is the difference between the values of players missing for each team. * Significance at the 10% level. ** Significance at the 5% level.
4. Conclusions We have examined NBA basketball games for the efficiency of betting lines in games where at least one player is absent from at least one team. We have shown that the betting line moves significantly against the team with absences in a majority of games, particularly when the index of player value, the AV Index (player quality lost), for the team is high and particularly for visiting teams. We have shown that opening lines set by bookmakers have significant errors in games where players are absent. We also show that there is a significant bias in opening lines against the home team when players are absent. The home team is penalized too much (in terms of the point spread) when the home team has missing players, and the visiting team is not penalized enough when it has missing players. At opening lines, a strategy of wagering on the home team when the visiting team has a high AV Index produces a win percentage that rejects the null hypothesis of zero profitability. However, we cannot rule out that information on the absence was released after the market opened, resulting in the line movement. By the time the market closes, biases in opening lines are removed and bettors cannot earn profits sufficient to cover transaction costs using the absence information. Overall, we find that NBA betting market participants can accurately interpret the ‘‘value’’ of the missing player(s) and can adjust the betting line accordingly.
Acknowledgments We thank Stephanie Aker, Kris Ahmann, Laura Davison, and Tyler Eiken for valuable research assistance.
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Appendix A. Approximate Value (AV) Index The Approximate Value (AV) Index was developed by Dean Oliver. You can read more about the AV formula at this website: http://www.powerbasketball.com/theywin2.html. We take the following excerpt concerning the AV Index from that website. The plan for the method was to end up with a scale of integers between 0 and about 20 rating players, with 10 representing an ‘average’ player. It was to be based upon several standards a player was to meet in order to gain points of approximate value. The whole thing was modeled on Bill James’ Value Approximation method for baseball. As James did, Dean Oliver assigned verbal descriptions to ranges of scores in order to see if the method produced results that matched general descriptions of players. Those descriptions are as follows: A score of about twenty indicates an exceptional MVP season. A score of seventeen or eighteen indicates a strong MVP candidate or an ordinary MVP season. A score of sixteen indicates an MVP candidate. A score of fifteen indicates a definite All-Star who is a marginal MVP candidate. A score of fourteen indicates a probable All-Star. A score of thirteen indicates a marginal All-Star. A score of twelve indicates a very fine season; an All-Star candidate. A score of eleven indicates an above average regular; an excellent player playing about 1800 min. A score of ten indicates an average regular or a very good sixth man. A score of nine indicates an average regular or a good sixth man. A score of eight indicates a fair regular or an average sixth man. A score of six or seven indicates an average bench player or a good player playing under 1500 min. A score of four or five indicates a player who plays about 1000 min and who does not deserve many more. Scores of three or less usually indicate players who are unimpressive in limited playing time.
References Baryla, Borghesi, Dare, Dennis, 2007. Learning, price formation and the early season bias in the NBA. Financ. Res. Lett. 4 (3), 155– 164. Gandar, John, Zuber, Richard, O’Brien, Thomas, Russo, Ben, 1988. Testing rationality in the point spread betting market. J. Financ. 43 (4), 995–1008. Gandar, John M., Dare, William H., Brown, Craig R., Zuber, Richard A., 1998. Informed traders and price variations in the betting market for professional basketball games. J. Financ. 53 (1), 385–401. Levitt, Steven D., 2004. Why are gambling markets organized so differently from financial markets? Econ. J. 114 (495), 223–246. Pankoff, Lyn D., 1968. Market efficiency and football betting. J. Bus. 41 (2), 203–214. Sauer, Raymond D., Brajer, Vic, Ferris, Stephen P., Marr, M. Wayne, 1988. Hold your bets: another look at the efficiency of the gambling market for National Football League Teams. J. Polit. Econ. 96 (1), 206–213.