An Analysis of Fights in the National Hockey League

The authors use data from fight logs during the 2016-2017 regular National Hockey League (NHL) season to test for a difference in the proportion of games with and without fights for each of the thirty NHL teams. Only one team (Toronto Maple Leafs) was more likely to be involved in a fight at a home game than at an away game. Teams that fought proportionally more often in the second half of the season made the playoffs; teams that fought significantly less often did not. And, long distance air travel (flights involving more than 1000 miles or trips that required crossing at least one time zone) resulted in disproportionately more games with fights for eight different NHL teams.


Introduction
In 1945, George Orwell [1] wrote: "Serious sport has nothing to do with fair play. It is bound up with hatred and jealousy, boastfulness, disregard of all the rules and sadistic pleasure in unnecessary violence. In other words, it is war minus the shooting." Fighting has long been a part of the game in ice hockey, more so than in any of the three other major North American sports leagues (basketball, baseball, and football). Ice hockey players are even allowed to engage in fights. In 1922, the National Hockey League (NHL) introduced Rule 56 which made "fisticuffs" an official part of the game, thereby formalizing and regulating fighting. Following the season-long lockout of 2004-2005, the NHL enacted a new rule that states that "a player who instigates a fight in the final five minutes of a game will receive a game misconduct and an automatic one-game suspension." Some hockey fans admire the violence. According to Goldstein [2], violent sports provide "functional pleasure." That is, fans take pleasure in the violence they witness. Bernstein [3] suggests that fighting is actually a deterrent to even more dangerous behavior on the ice that might lead to catastrophic injuries.
That is, severe penalties or game misconducts hold players accountable by reminding them there are consequences for their actions. The impact of hockey violence on attendance is, however, inconclusive. Using game-by-game data on the 1983-1984 season, Jones, Ferguson, and Stewart [4] find that violence is positively related to attendance for all teams in the NHL. Moreover, the authors find that the lust for "blood sports" is greater among American than Canadian fans.
Paul [5] measures the impact of violence in hockey on attendance. In an analysis of game-to-game attendance in the 1999-2000 NHL season, Paul finds that fights per game (as opposed to penalty minutes) were highly significant with a positive impact on attendance, more so for teams in the United States than for Canadian teams. But, Anderson [6] questions the wisdom of violence that leads to the removal or loss of star players which could reduce fan interest. Rockerbie [7] argues that fighting does not make economic sense. Using data over the 1997-1998 through 2009-2010 seasons, he finds a small negative effect on attendance.
What constitutes a "fight" in the NHL? A "fight" is a one-on-one altercation or a bench brawl resulting in a five-minute penalty to two or more players or a ten-minute misconduct or game misconduct penalty to the instigator (who starts the fight). Such penalties can have a decisive effect on the outcome of a game.
There are many reasons for fights: "bad blood" between players, retaliation, retribution, intimidation, disabling star players, among others. "Cabin pressure" on long flights might also take its toll on NHL players. That is, long distance air travel might be a factor that explains why weary short-tempered players drop their gloves.
In this brief research note, we compare for each NHL team during the 2016-2017 regular season the proportion of games resulting in at least one fight in home games v. road games, the first half of the season v. the second half of the season, and back-to-back games (at home or away) v. all other games. Does air travel involving more than 1000 miles or crossing one or more time zones result in disproportionately more games with fights? Is the proportion of games with fights greater when an American team plays a Canadian team (than when two Canadian or two American teams play one another)? In short, are there any patterns to fighting in the NHL that might help ice hockey fans better understand the game?

The Data
The archive of hockey fights in the NHL [8]

Methodology
A series of one-and two-tailed t-tests was run on the difference between two population proportions using STATA.
The comparisons involving the proportion of games with fights in 1) home v. away games or 2) games through the first half of the 82-game regular season v. the second half of the season are both two-tailed t-tests. For the team-by-team comparisons involving home v. away games, the null hypothesis (H 0 ) is stated as follows: where π is (again) defined as the proportion of games with at least one fight.

Presentation of Results
The results of the various t-tests are reported in Tables 1-7. Table 1 summarizes for each of the thirty NHL teams during the 2016-17 regular season the proportion of home and away games with at least one fight. Surprisingly, there are no differences between the two proportions (using α = 0.05), with only one exception. The Toronto Maple Leafs were more combative at home than away (p = 0.008). Table 2 summarizes the results of the two-sample t-tests on the difference between proportions (fights through the first 41 games v. fights through the last 41 games of the 2016-2017 regular season). There were discernible differences for four teams (at the α = 0.05 level) and four more teams (at the α = 0.10 level). The former group included three teams that did not make the playoffs and all three teams (Arizona Coyotes, Colorado Avalanche, and Detroit Red Wings) were less combative in the second half of the season. The one team (New York Rangers) that did make the playoffs appeared to be more combative in the second half of the season. Three of the four teams in the latter group (Chicago Blackhawks, Nashville Predators, and Washington Capitals) were involved in proportionally more games with fights in the second half of the season and all three teams made the playoffs. The only team that deviated from this patternthat is, fight more in the second half of the season and make the playoffs, fight less and fail to make the playoffs-was the Columbus Blue Jackets. Table 3 summarizes the results of the first of five comparisons involving a one-tailed t-test. The team that plays back-to-back nights typically has tired legs and limited practice time between games. One would think that the team that plays on consecutive nights might be more inclined to fight. A look at Table 3 shows that all but six teams (using α = 0.10) overcame the short turnaround time       Table 7 are similar to Table 4 & Table 5 but examine differences for teams that crossed one or more time zones before their next game. Table 6 shows that five teams:          Teams that scuffled significantly less often in the second half of the season failed to make the playoffs. And, surprisingly, teams that scuffled significantly more often in the second half of the season did make the playoffs. Three NHL teamsall of which made the playoffs-were revealed to be more belligerent when they were scheduled to play road games on consecutive nights. Long distance air travel appears to make a difference. Eight different teams that traveled more than 1000 miles or traveled across one or more time zones before their next game were involved in fights more often than when distant travel was not an issue.

Concluding Remarks
Finally, fighting appears to be more frequent in games involving only Canadian teams. In the words of Don Cherry, Canadian ice hockey commentator for CBC Television: "Anybody who says they don't like fighting in the NHL has [sic] to be out of their minds."