# DOES THE NUMBER OF DAYS BETWEEN PROFESSIONAL SPORTS GAMES REALLY MATTER?

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2 study. We then provide the results of our analysis in the third section and offer some concluding points in the paper s final section. Method North American football is a popular team sport. In Canada, the first football teams emerged in the 1860s. The Canadian Rugby Football Union was established in 1884, leading to the formation of the CFL in Currently, the CFL includes eight teams split geographically between Eastern and Western Divisions. Table 1 lists the current franchises. Table 1 Current Canadian Football League (CFL) Teams Western Division British Columbia Calgary Edmonton Saskatchewan Eastern Division Winnipeg Hamilton Toronto Montreal The CFL operates an 18-game regular season played annually between late June and early November. Playoffs subsequently occur over a three-week period, culminating in the awarding of the Grey Cup, North America s oldest professional football trophy. Typically, regular season games in the CFL are scheduled on Thursday, Friday, Saturday or Sunday of any particular week. Note that this departs from the approach of the United States National Football League (NFL) in which games are almost exclusively scheduled on Sundays. Due to the CFL s practice of spreading out games over as many as four days in a week, it would not be uncommon for, say, Team A to play Team B on Thursday in week j and then be assigned to play Team C on Saturday in week j+1. Team C, meanwhile, may have played its game during week j on a Friday. Consequently, Team A plays Thursday and Saturday in the two weeks, while Team C plays on a Friday and the following Saturday. With one extra day off in preparation for its week j+1 game against Team C, Team A may obtain a competitive advantage. Therefore, we note that Team A has a marginal days rest (MDR) value of +1 heading into its game versus Team C. As a concrete example of this phenomenon, consider the following snapshot of the actual 2007 CFL schedule as provided in Figure 1. Note that Montreal was scheduled to play at Winnipeg in Week 2 on Thursday, July 5 th. Montreal then played in Hamilton during Week 3 on Saturday, July 14 th. Hamilton, on the other hand, played on Saturday, July 7 th in Week 2. This provided Montreal with two extra days off prior to its Week 3 game versus Hamilton. In this particular case, Montreal had a value of MDR = +2.

3 Figure 1 Partial 2007 CFL schedule We analyzed results from the CFL regular seasons (inclusive) to determine the winning percentages for teams exhibiting different MDR values. We defined winning percentage as the percentage of games in which a team with a given MDR earned a victory. Admittedly, we recognize that the outcome of a particular game is not simply affected by the specific MDR. Team strength, obviously, is a factor in game outcome since some franchises are generally more dominant than others within a specific season. Moreover, some teams (e.g. British Columbia) are generally required to travel further distances for road games than, say, an Eastern Canadian team that has numerous opponents within close proximity. British Columbia may, therefore, require an extra day off between games simply due to the logistics and hassles of airline travel. We selected seven years worth of CFL data in order to mitigate the effects of team strength and travel distance, thus obtaining a stronger indication of the impact of MDR on team performance. It was our initial conjecture that higher MDR values would yield higher winning percentages given the fact that a team with more days off between games than its opponent would be more rested and physically prepared for the subsequent contest. We also felt that positive MDR values would result in winning percentages greater than since a team with more days off than its opponent ought to win more times than it loses, ceteris paribus. We analyzed those cases in which a team had a strictly positive MDR heading into a specific CFL game. If both teams had an equal MDR, then the number of days off would be a non-issue for this particular matchup. Moreover, we restricted our attention to MDR values of +1, +2 and +3. Recall that CFL contests are typically scheduled from Thursday through Sunday on any given week. Therefore, the largest MDR value we could observe for teams that play in consecutive weeks would be +3 this would be the case if Team A and Team B faced each other in week j+1, with Team A having played a game on Thursday in week j while Team B played on a Sunday during that week. Therefore, Team A would have three extra days off (Friday, Saturday and Sunday) as compared to Team B for their week j+1 matchup. Results Table 2 provides the winning percentage results for MDR values of +1, +2 and +3. These winning percentages are also graphically illustrated in Figure 2.

4 Table 2 Winning percentages for different MDR values Marginal days rest Winning percentage P value Figure 2 Winning percentage comparisons Not surprisingly, the winning percentages for the three MDR values are all above Therefore, possessing extra days off prior to a game appears advantageous. However, it may be surprising to note that the relationship between winning percentage and MDR is not linear. We had expected a steadily increasing winning percentage as the MDR values rose, but this does not appear to be the case. Although the highest winning percentages are encountered with an MDR of +3, the percentages for +2 are the lowest of the three MDR values analyzed. In addition, we tested the statistical hypothesis that these winning percentages were statistically different from 0.500, the winning percentage under a null hypothesis of no effect for MDR on team performance. Remarkably, only in the case of MDR = +1 did we obtain statistical significance (at a p- value of 0.014). We also explored whether there was a significant difference among the winning percentages themselves for the various MDR values. As reported in Table 3, this clearly shows that the winning percentages themselves are not statistically different.

5 Table 3 Comparing different MDR values Marginal days rest P value +3 versus versus versus On the whole, this analysis apparently casts doubt on the conjecture that MDR is advantageous to team performance. Although the winning percentages for the three MDR values are all above 0.500, they do not exhibit a linearly increasing pattern. In addition, two of the three winning percentages are not statistically different from (the null hypothesis winning percentage). Notwithstanding the complaints that fans, media and team managers may make over perceived inequities, it appears that matchups involving teams with a different number of days off do not generate competitive advantages. Recall that the CFL regular season lasts from mid-june through early November. As an extension to our data analysis, we explored the impact of MDR on winning percentage as function of the particular month in which a game was played. We pursued this analysis to observe if winning percentages remained relatively consistent throughout a regular season. Figure 3 illustrates the results. We did not report on MDR values of +3 since there were too few games upon which to draw meaningful conclusions once we partitioned these games into their respective months. For the very same reason, we did not provide results for MDR of +1 and the month of June, nor did we offer any results for November (we note that a CFL regular season concludes by the first week of November, so there are very few regular season games played during this month).

6 Figure 3 Monthly analysis of winning percentage and MDR For either value of MDR, the winning percentages display a (generally) downward pattern as the season progresses. For MDR = +1, the winning percentage is highest in June before falling in July. Although it climbs in August, it tumbles for the remainder of the year. A similar relationship is observed for MDR = +2. The winning percentage falls from July through September, before marginally rising in October. This is indeed an intriguing pattern. Although we demonstrated earlier that positive MDR when considering the snapshot of an entire season does not offer a statistical advantage, it would appear that the impact of an extra day or two of rest is by no means consistent during the season. Teams that enjoy positive MDR earlier in the season apparently have a greater winning percentage than if this equivalent MDR was obtained later in the year. A possible explanation would be that later in the season, teams may be facing each other for the second or third time during a year. (Since the eight CFL teams play an 18- game regular season, a given team will face the same opponent on multiple occasions). Having already competed against this opponent, a team may be more aware of the other squad s particular strengths, strategies and weaknesses. In the parlance of sports, they would have become familiar foes. Marginal days of rest would therefore not be as important later in the year. Earlier in the year, the teams would be facing each other for the first time so an extra day or two of rest could yield substantial advantage. Conclusions We have analyzed CFL regular season game results from in an effort to demonstrate whether the difference in the number of days off between games impacts team performance. Teams that have an MDR = +1 have a winning percentage significantly different from 0.500, the winning percentage that would be obtained under the null hypothesis of no impact of MDR on game outcome. However, this was the only significant winning percentage we were able to obtain. Contrary to popular perception, there is no increasing advantage for teams that enjoy larger MDR values.

7 We did observe that MDR is more important earlier in the regular season rather than later in the year. Therefore, when sports managers and league officials are developing schedules, it would be wise to avoid situations in which teams frequently have more days off than their opponents early in the regular season. This would result in a more equitable schedule, one that would not provide consistent advantages for particular teams. Later in the season, the days off issue appears less important. We analyzed the case of a professional sports league that plays a relatively small number of games (18) during its regular season. A possible extension to our work would be to investigate a league such as the National Basketball Association (NBA) or National Hockey League (NHL) in which teams play a larger number of games (a total of 82 in each league). This could provide an additional perspective on whether the number of days off between games truly matters in the outcome of professional sports. References Bartsch, T., Drexl, A., & Kröger, S. (2006). Scheduling the professional soccer leagues of Austria and Germany. Computers & Operations Research, 33(7), Bean, J., & Birge, J. (1980). Reducing traveling costs and player fatigue in the National Basketball Association. Data Mining Knowledge Discovery, 10, Costa, D. (1995). An evolutionary tabu search algorithm and the NHL scheduling problem. INFOR, 33, Della Croce, F., & Oliveri, D. (2006). Scheduling the Italian football league: An ILP-based approach. Computers & Operations Research, 33(7), Duran, G., Guajardo, M., Miranda, J., Sauré, D., Souyris, S., Weintraub, A. & Wolf, R. (2007). Scheduling the Chilean Soccer League by Integer Programming. Interfaces, 37(6), McCormick, M. (2009). Roughriders challenged by regular airline travel for CFL games. Regina Leader-Post, August 24 th, B2. Nemhauser, G., & Trick, M. (1998). Scheduling a major college basketball conference. Operations Research, 46(1), 1 8. Schreuder, J Combinatorial aspects of construction of competition Dutch professional football leagues. Discrete Applied Mathematics, 35,

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