Fit to Be Tied: The Incentive Effects of Overtime Rules in Professional Hockey

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1 Fit to Be Tied: The Incentive Effects of Overtime Rules in Professional Hockey Jason Abrevaya Department of Economics, Purdue University 43 West State St., West Lafayette, IN This version: May 23 ABSTRACT This paper examines the incentive effects of different payoff structures in the National Hockey League. A rule change prior to the season, which changed the way that teams were awarded points in overtime games, provides a natural experiment to test the reaction of teams to a change in the payoff structure. The rule change had the desired effect of increasing excitement during overtime play. However, this paper shows that the rule also had the effect of increasing the frequency of overtime games, an effect predictable from the change in incentives but one not intended by the league. JEL classification: J24, J33 Key words: incentive effects Phone: (765) ; Jason Chaimovitch of the American Hockey League kindly provided historical data.

2 1 Introduction During the last decade, several economists have turned to data from sports competitions in an effort to test theories about how economic agents react to different incentive schemes. The appeal of using data from the sports industry is that the incentives (e.g., contracts, potential winnings) and the rules governing competition are usually fully observable to the economist. Though exceptions exist, the same is generally not true for other industries, making empirical analysis of incentive schemes and economic agents behavior more difficult. See Prendergast (1999) for a thorough survey of this literature. Several previous studies have looked at the incentive effects in sports with individual competitors (starting with the work of Ehrenberg and Bognanno (199)). The paper most similar to the current study is Taylor and Trogdon (22), who consider the perverse incentives created by the payoff structure in a team sport. Taylor and Trogdon (22) find evidence for an incentive to lose created by the National Basketball Association s draft lottery system. This paper considers how the incentives facing teams were affected by rule changes enacted by the National Hockey League (NHL). The NHL is the major professional hockey league in North America and currently has 3 teams. The rule changes adopted by the NHL (prior to the season) were meant to address a specific problem facing the league an abundance of contests that ended in ties. Of the four major sports leagues in North America (National Football League, Major League Baseball, National Basketball Association, NHL), the NHL is the only one for which tied games pose a significant dilemma. In baseball and basketball, regular-season games are played until there is a winner. In football, while there exists the possibility of a tie (after an overtime period), there have been only two tied games in regular-season play since In the NHL, roughly one out of every seven regular-season games ended in a tie between the and seasons. 1 Generally speaking, American sports fans don t like ties. After a game is played for two or three hours, they like to see a winner. As a case in point, consider Major League Baseball s 22 All-Star Game which was ruled a tie after the managers ran out of players. Even though this game was meaningless (in the sense that it had no impact on league standings), fans were outraged by the decision not to continue the game until there was a winner. The crowd at the game chanted Refund! and Let them play! long after the decision was made. 2 A sports league s main objective is to increase and maintain demand for its product by providing excitement and enjoyment to its fans. For the NHL, there is an incentive to reduce the likelihood of tied games if there is distaste among its consumers for such outcomes. For a given team in the NHL, the main objective during the season is to maximize the number of points that it accumulates. 1 The problem arises from the simple fact that it is difficult to score in hockey. Teams only average a total of around 6 goals per game, making it more likely to have a tied game and also more difficult to break ties. Sports fans from around the world are familiar with this issue in soccer, where goals are even more difficult to score. 2 Source: All-Star tie generates more anger at baseball, July 9, 22, espn.com website. 1

3 The point rankings at the end of the season determine which teams make the playoffs as well as the playoff seeding. 3 To the extent that the team s objective of point maximization leads to more excitement for the fans, this objective will align with the league objective of increasing and maintaining consumer demand. If, however, teams strive to maximize points by adopting a style of play that is conservative or defensive, their efforts can be counterproductive to the league-wide objective if fans are less interested in such a style of play. Sports are, of course, not unique for exhibiting misalignment of objectives. As Prendergast (1999) points out,... compensation schemes often have unintended consequences caused by agents changing their activities in other ways that are beneficial to them but not to their employer. This paper will focus on the consequences of a simple change in compensation scheme made by the NHL. Section 2 describes the data and rule changes and compares outcomes from before and after the rule changes. Results from similar rule changes in a minor hockey league are also presented to shed light on the NHL results. The league successfully met one objective with its rule changes: reducing the number of overtime games that end in a tie. An unintended consequence of the rule changes, however, was to also increase the likelihood of overtime games. 4 Section 3 analyzes the team incentives associated with the compensation schemes before and after the NHL rule change. The relevant payoff distributions suggest a greater incentive for teams to reach overtime after the rule change. For a risk-averse team, an additional incentive to reach overtime is present in games with teams within its division. To determine whether these incentives are consistent with outcomes in the NHL, we focus on data from games in which the score is tied late into the contest. Finally, Section 4 concludes. 2 The Scoring Rules In a regular-season NHL game, there are 6 minutes of regulation play divided into three 2- minute periods. If the game is tied after 6 minutes of play, there is a 5-minute overtime period. If either team scores during overtime, the game is over and the scoring team is the winner. If neither team scores during overtime, the game ends in a tie. The data used in this paper were compiled from individual game boxscores obtained from the online archive of the USA Today ( The archive contains information on games played from the season through the 21-2 season. Since the data for each game was contained in a separate file, a C++ program was written in order to process the files and save the 3 One could argue that profit maximization is the ultimate objective, but conditional on the chosen payroll and current roster, maximization of points seems a reasonable objective. From a career-concern perspective, a team s coach probably cares mostly about maximizing his team s points during the regular season as well. Players may have more selfish concerns since future contracts depend on personal performance. 4 Though unintended, this outcome may actually have increased profits if additional concession sales, television ads, etc. are generated by the longer games. 2

4 necessary data in a usable format. The resulting dataset consists of 7821 regular-season games over seven years, which represents 98.8% of the 7913 regular-season games that were played. A small fraction of the games were not included because the boxscore was not available or could not be processed. For each game, we have information on the teams involved, the number of goals scored by each team, the exact time at which each goal was scored, and the number of shots-on-goal in each period (and overtime, if applicable). Prior to the season, the NHL awarded each team points for a loss, 1 point for a tie, and 2 points for a win. The total number of points accumulated by a team during the season determines whether or not the team makes the playoffs and, if so, the team s playoff seeding. Starting with the season, the NHL enacted two rule changes concerning overtime games: Rule Change 1: A team that loses in overtime receives 1 point. Rule Change 2: Overtime is played with 4 skaters (plus the goalkeeper) per team, rather than the 5 skaters used in regulation play. The top part of Table 1 summarizes the point system in the NHL before and after the rule change. An overtime loss is the only result with a different point value in the two systems. Wins, ties, and non-overtime losses were treated the same before and after the rule change. The goal of both rule changes was to make the overtime period more exciting for the fans. Prior to the rule change, league officials thought that too many overtime games were ending in a tie. Under the old rules, teams were willing to settle for a tie (1 point) rather than risk losing the game ( points); as a result, teams would play defensively in the overtime period. The first rule change, by treating ties and overtime losses equivalently, was intended to remove the risk associated with playing aggressively. The second rule change, which reduced the number of skaters on each team, was also intended to boost offense in the overtime period. The tempo of the game is much quicker with 4-on-4 play, making it more difficult for teams to play a defensive style of hockey in the overtime. The new scoring system resulted in the outcome that league officials had intended. Table 1 summarizes some statistics concerning overtime play before and after the rule change. Before the rule change (from the season through the season), 71.1% of overtime games ended in a tie; after the rule change (from the season through the 21-2 season), only 55.5% of overtime games ended in a tie. (This difference is statistically significant, with a two-sided p-value of..) Even in games that eventually ended in a tie, there was considerably more offense after the rule change: an average of 5.46 shots-on-goal in overtime after the rule change as compared to an average of 3.97 shots-on-goal in overtime before the rule change (a 37.5% increase). To show that the changes are not merely the result of some time trend in the data, Figures 1 and 2 give the 3

5 Table 1: Before and After Rule Changes Old OT Rules New OT Rules (95-96 to 98-99) (99- to 1-2) Points awarded for: Win 2 2 Tie 1 1 Loss (OT) 1 Loss (non-ot) # games 4,251 3,57 Pct. going 19.8% 22.2% into overtime Pct. of OT games 71.1% 55.5% ending in a tie Avg. OT shots-on-goal in OT games Avg. OT shots-on-goal in games ending in tie season-by-season plots of overtime percentage and percentage of overtime games ending in a tie. The rule change in both figures is indicated by the vertical dashed line. The change in the compensation scheme also had an unintended effect, however. As seen in Table 1, the percentage of overtime games rose from 19.8% to 22.2% (a relative increase of 12.1% in the likelihood of overtime). The difference is statistically significant at the 1% level (two-sided p-value of.84). Before the rule change, a total of two points were awarded to the teams in a given game (regardless of whether or not the game went into overtime). After the rule change, a total of two points were awarded in non-overtime games and games ending in a tie, but a total of three points (two to the winner, one to the loser) were awarded in overtime games not ending in a tie. The potential for a larger pie being available makes overtime an appealing outcome for the teams, all else being equal. This incentive effect, which is the main focus of this paper, is consistent with the rise in the percentage of overtime games after the rule change. As noted previously, the two overtime rule changes by the NHL were associated with a rise in the percentage of overtime games and a decline in the percentage of overtime games that ended in a tie. Both rule changes presumably contributed to the latter effect (fewer ties) since they both encouraged a more aggressive style of play during overtime. There is no reason, however, to necessarily expect that Rule Change 2 (fewer skaters in overtime) would have an impact on the percentage of games that went into overtime. Unfortunately, the data from the NHL do not allow 4

6 % OT Games Season Figure 1: Season-by-Season Overtime Percentages.75 % Tie (for OT games) Season Figure 2: Season-by-Season Tie-Game Percentages 5

7 Table 2: American Hockey League Results Time Period Overtime Rules # of games % of games % of OT games going into OT ending in a tie on-5 play, -point loss 2, % 68.2% on-5 play, 1-point loss 2,16 2.4% 59.2% on-4 play, 1-point loss 2,64 2.4% 55.% us to disentangle the effects of the two rule changes since they were made simultaneously. In an attempt to address this issue, we consider similar rule changes that were made in the American Hockey League (AHL), a minor (professional) league in North America. Among the minor hockey leagues, the AHL is closest to the NHL in terms of quality and style of play. Many AHL players have prior NHL experience and many others will eventually play in the NHL. Like the NHL, the AHL moved to an overtime system characterized by 4-on-4 play and one point awarded for an overtime loss. Unlike the NHL, however, these two changes were not made simultaneously. In the AHL, Rule Change 1 was instituted at the start of the season whereas Rule Change 2 was instituted at the start of the season. Table 2 summarizes the overtime results from three different time periods in the AHL. 5 The first time period ( ) corresponds to the NHL s old overtime rules, and the third time period ( ) corresponds to the NHL s new overtime rules. The second time period is the transition period, in which 4-on-4 play was not yet being used. Comparing the first and third rows of Table 2 to the corresponding quantities for the NHL in Table 1, note that both leagues experienced very similar changes in the percentage of overtime games and the percentage of overtime games ending in a tie. The AHL had an absolute increase of 1.9% in overtime games (as compared to 2.4% for the NHL) and an absolute decrease of 13.2% in overtime games ending in a tie (as compared to 15.6% for the NHL). The numbers for the AHL s transition period ( , second row of Table 2) suggest that awarding a point for an overtime loss was the rule change responsible for the increase in the percentage of overtime games. The percentage went from 18.5% to 2.4% with this rule change and remained unchanged at 2.4% with the introduction of 4-on-4 play. The results also suggest that both rule changes had an impact on the percentage of overtime games that ended in a tie. This percentage dropped from 68.2% to 59.2% with Rule Change 1 and dropped again to 55.% with Rule Change Results from the are omitted since part of the season was played with 5-on-5 play and part with 4-on-4 play. The league office did not have the detailed game results from this season required to determine which results were from 5-on-5 play and which were from 4-on-4 play. 6 It s not possible to say which change had more of an impact since there is no period in which 4-on-4 play and -point overtime losses existed. 6

8 Table 3: Descriptive Statistics for Gross and Net Points Gross Points Net Points (relative to opponent) No OT OT (old) OT (new) No OT OT (old) OT (new) Expected Value Standard Deviation The Incentives of Overtime If two teams are tied near the end of regulation play, the desire to go into overtime depends on the alternative payoffs available in an overtime game and a non-overtime game. The new NHL overtime rule changed the payoff structure in overtime games by guaranteeing at least one point to each team. To determine the incentives for teams tied near the end of regulation play, we approximate the distributions of the payoffs. First, we assume that either team has an equal chance of winning the game before the end of regulation (conditional on the teams being tied late in the game). Second, we assume that either team has an equal chance of winning the game in overtime (conditional on the game reaching overtime). 7 Third, we use the observed frequencies of ties in overtime games (71.1% under the old rules, 55.5% under the new rules) as the probabilities for the overtime payoff distributions. The resulting payoff distributions are given in Figure 3; the three scenarios are (1) no overtime, (2) overtime under the old rules, and (3) overtime under the new rules. Note that the no overtime payoffs do not depend on which rule was in place since non-overtime points were not affected. The payoff distributions of Figure 3 indicate that a risk-averse team would prefer to have the game decided in overtime rather than regulation under either overtime rule. The first panel of Table 3 gives the expected value and standard deviation under the three scenarios. Although the expected overtime payoff under the old rules is the same as the expected non-overtime payoff (one point), the variation is much lower with one point being the likely outcome. The new overtime payoff distribution stochastically dominates the old payoff distribution. The expected incremental payoff to reaching overtime under the new rules is.222 points. Regardless of a team s risk tolerance, the incentive to reach overtime (in terms of gross points received) is stronger under the new overtime rules. The NHL league standings (and, in turn, playoff seedings) are determined by a team s rank relative to other teams. As a result, if a team is playing against an opponent for which relative ranking is important, the team would also care about the net points (relative to its opponent) it would receive in the game. This concern is most prevalent for games played between teams in the 7 The first and second assumptions are roughly supported by the data. It is true that the better team wins slightly more often (e.g., the home team wins 51.9% of overtime games), but there is no evidence that the probability of a team winning is different before and after the scoring change. 7

9 Percent 5 Percent 5 Percent No OT 1 OT (old) 2 1 OT (new) 2 Figure 3: Gross Point Distributions 8

10 Table 4: Percentage of Games Going into Overtime Old OT Rules New OT Rules Change p-value (95-96 to 98-99) (99- to 1-2) Divisional 2.5% 24.7% +4.2%.162 Non-divisional 19.5% 21.4% +1.9%.726 p-value same division since the top team in each division receives a high seeding in the playoffs. (In the 21-2 season, there were six divisions with five teams in each division.) Using the same simple assumptions as above for the gross-point distributions, we construct distributions for a team s net points (relative to its opponent) under the three scenarios. These distributions are shown in Figure 4, with their expected values and standard deviations given in the second panel of Table 3. The expected payoff in all three scenarios is zero due to symmetry. The incentive for a risk-averse team to reach overtime is apparent for both rule regimes, with the incentive somewhat stronger under the new rules. In particular, the bad state of a net point value of -2 in overtime is eliminated under the new rules. For a within-division game, there is likely to be at least one team that takes a risk-averse posture concerning the net-point payoffs. The higher-ranked team might try to avoid the -2 outcome from a non-overtime loss by playing defensively if the game is tied late in regulation. Even if the opponent tries to play aggressively, we would still expect more overtimes for these games under the new rules. Though there is no way of quantifying the following statement, casual empiricism strongly suggests that: The likelihood of a goal being scored in hockey is reduced if either team adopts a defensive strategy. Table 4, which compares overtime percentages for divisional and non-divisional games, is consistent with this story. The percentage of overtime games is higher for within-division games under both rule regimes. The increase in overtime games under the new rules is higher for within-division games, an absolute increase of 4.2% (relative to an absolute increase of 1.9% for non-divisional games). The p-values reported in the table indicate the (two-sided) significance level for the differences in probabilities. Figure 5 plots the probability of reaching overtime and the probability of no additional goals being scored conditional on the game being tied at a given point in the third period. The probabilities were calculated and graphed separately for games played under the old overtime rule and games played under the new overtime rule. The probabilities are all close to 1 with one minute left in the game since overtime is extremely likely and a goal being scored in the final minute of a tied game is extremely unlikely. As expected, all of the probabilities drop as we move backward in time (i.e., more time remaining in the game). The probabilities for the two different overtime rules seem to diverge a bit at around 8 minutes left in the game. With more than 8 minutes remaining, 9

11 Percent 5 Percent 5 Percent No OT -- NET OT (old) -- NET OT (new) -- NET 2 Figure 4: Net Point Distributions 1

12 1. OT, New Rule OT, Old Rule No Goals, New Rule No Goals, Old Rule Minutes Left in Game Figure 5: Probability of Overtime or No Goals for Tied Games the probability of overtime or no additional goals is higher under the new overtime rule. To see if the differences in Figure 5 stem from a general change in overtime or goal probabilities (rather than incentives present in tied games), we plot the same probabilities for one-goal games (games for which the score differential is one goal) in Figure 6. In this graph, the probability of no additional goals is slightly higher under the old rule at all values of minutes left. The probability of overtime is slightly higher under the new rule with 8 or fewer minutes left in the game. Both of these findings are consistent with the new incentive structure since (1) the team behind by a goal late in the game has more incentive under the new rules to tie the game and reach overtime, and (2) the team ahead by a goal late in the game has more incentive under the old rules to keep their lead and avoid overtime. To see more detail concerning the higher frequency of overtime games for within-division games, we plot the probabilities of no additional goals (conditional on a tied score) for within-division games only. Figure 7 compares these probabilities under both rules. As in the plot for all tied games (Figure 5), the probability of no additional goal is higher under the new rule. Unlike Figure 5, this difference continues very late into the game; even with 5 or fewer minutes left in a tied game, the likelihood of a goal under the new rules is quite a bit lower than under the old rules. Since the analysis to this point has not controlled for other variables that might affect overtime and goal probabilities, we now consider estimation of some linear regression and probit models. 11

13 .6 OT, New Rule OT, Old Rule No Goal, New Rule No Goal, Old Rule Minutes Left in Game Figure 6: Probability of Overtime or No Goals for One-Goal Games.9 No Goal, New Rule No Goal, Old Rule Minutes Left in Game Figure 7: Probability of No Goals for Tied Within-Division Games 12

14 Variable oldrule indivision dayof season hgf vgf hga vga teamdiff Table 5: Description of Variables Description 1 if prior to season, otherwise 1 if between teams from same division, otherwise number of days since season began average number of goals scored by home team during the season average number of goals scored by visiting team during the season average number of goals allowed by home team during the season average number of goals allowed by visiting team during the season difference in team quality, measured by (hgf hga) (vgf vga) Table 5 lists the variables that are used as covariates in the estimation. The variables oldrule and indivision indicate if the game was played under the old rules and whether the game was within division, respectively. The dayof season variable is meant to allow for the incentives to be affected by whether the game is early in the season or late in the season. There are four team-related variables (hgf, vgf, hga, vga) used to control for the two team s overall offensive and defensive abilities. These four variables also help to control for any sort of time trend in scoring that might have occurred in the NHL during the time period being considered. All else being equal, we would expect fewer overtime games for teams that score a lot of goals and allow a lot of goals. The variable teamdif f proxies for the difference in team quality. Games between evenly matched opponents (i.e., values of teamdiff close to zero) are more likely to reach overtime. Table 6 reports the results from estimation of several linear-regression and probit models. Three different sets of games are considered: (1) all games (7821 observations), (2) games tied with 2 minutes left (1717 observations), and (3) games tied with 1 minutes left (1559 observations). To gauge the level of offense late in the game, a regression with third period shots-on-goal as the dependent variable is performed for each set. In games played under the old rules, there are an average of.311 additional shots-on-goal in the third period holding all else fixed (statistically significant at the 5% level). The effect of indivision is insignificant and close to zero. In the set of games tied with 1 minutes remaining, the estimate on oldrule is still significant and larger than the estimate for the full set of games. The estimate on indivision is negative (as predicted by the incentive story) but not significantly estimated. We also estimate probit models with an overtime indicator and a no-additional-goal indicator as dependent variables. For the third set of games, the no-additional-goal indicator reflects whether or not a goal was scored in the final 1 minutes of play. In addition to the probit estimates and standard errors, marginal effects (at the mean of the data) are also reported for easier interpretation. For these models, the incentive story would lead us to expect negative estimates for the oldrule variable and positive estimates for the indivision variable. Of the twelve oldrule and indivision probit estimates in Table 6, only one has unexpected sign (though it is insignificant). For the set of 13

15 Table 6: Regression Results All Games Games tied with 2 mins. left Games tied with 1 mins. left Third-Period Overtime No Goals in Third-Period Overtime No Goals in Third-Period Overtime No Goals in Shots-on-Goal Last 2 Mins. Shots-on-Goal Last 2 Mins. Shots-on-Goal Last 1 Mins. (OLS) (Probit) (Probit) (OLS) (Probit) (Probit) (OLS) (Probit) (Probit) oldrule (.144) (.335) (.361) (.2183) (.639) (.713) (.2331) (.67) (.665) indivision (.1118) (.352) (.379) (.2328) (.673) (.749) (.2475) (.72) (.697) dayofseason (.9) (.3) (.3) (.19) (.6) (.6) (.21) (.6) (.6) hgf (.154) (.484) (.524) (.336) (.93) (.156) (.3496) (.971) (.972) vgf (.1532) (.483) (.522) (.3244) (.933) (.175) (.369) (.981) (.984) hga (.132) (.42) (.46) (.2874) (.818) (.945) (.2992) (.849) (.852) vga (.1335) (.419) (.459) (.2855) (.818) (.947) (.326) (.851) (.852) teamdiff (.123) (.342) (.365) (.2151) (.672) (.773) (.234) (.74) (.77) const (.6717) (.217) (.2313) (1.5184) (.4131) (.4827) (1.665) (.4277) (.43) # obs Standard errors are reported in parentheses (robust standard errors for OLS estimates). For the probit columns, the marginal effect of each variable evaluated at the mean of the data is reported under the standard error. A single asterisk denotes statistical significance at the 1% level; double asterisks denote statistical significance at the 5% level. 14

16 all games, the overtime probit estimates indicate that old-rule games are about 2.16% less likely to go into overtime and within-division games are about 2.7% more likely to go into overtime (holding all else fixed). For games tied with 2 minutes left, these effects are even larger in magnitude; oldrule games are 3.72% less likely to go into overtime, and within-division games are 7.13% more likely to go into overtime. The chance of no additional goals being scored, conditional on a tie with 2 minutes left, is about 4.52% higher for within-division games. The probit estimates for the set of games tied with 1 minutes left have the expected signs on the oldrule and indivision variables, but these estimates are insignificant due to the lack of variation in the dependent variables (since there are relatively few goals scored late in tied games). 4 Conclusion This paper has analyzed the effects of a change in incentive schemes implemented by the NHL. The change had the desirable effects of making overtime play more exciting for fans and having fewer overtime games end in ties. The percentage of overtime games ending in a tie dropped from 71.1% to 55.5%. Unfortunately for the league, due to the perverse incentive of rewarding teams for reaching overtime, the percentage of overtime games also rose (from 19.8% to 22.2%). The net effect was that the overall percentage of games ending in a tie dropped from 14.1% to 12.3%. Had the likelihood of reaching overtime remained constant, a more desirable drop in the percentage of ties would have been achieved (from 14.1% to 11.%). Several alternatives to the rule changes adopted by the NHL would have removed the additional incentive for reaching overtime. One such alternative was an option discussed at length prior to the change awarding 3 points for a non-overtime win, 2 points for an overtime win, 1 point for a tie or overtime loss, and points for a non-overtime loss. Another alternative would have been to simply leave the point system unchanged and use the 4-on-4 play for a more extended overtime period (e.g., 1 minutes instead of 5 minutes). References Ehrenberg, R. G. and M. L. Bognanno, 199, Do tournaments have incentive effects? Journal of Political Economy 98, Prendergast, C., 1999, The provision of incentives in firms. Journal of Economic Literature 37, Taylor, B. A. and J. G. Trogdon, 22, Losing to win: tournament incentives in the National Basketball Association, Journal of Labor Economics 2,

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