Does the Current NHL Point System Influence Game Play?

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Zach Shearin, Presenting his Research at the 2017 IISE Regional Conference

Zach Shearin, an undergraduate Industrial and Management Engineering student at Rensselaer Polytechnic Institute and a die-hard Carolina Hurricanes fan, used analytics to analyze the National Hockey League’s point system through an operations research and statistical analysis lens.  This work started as Zach’s project for my Operations Research Methods (ISYE 4600) course.  He then continued research and analysis as an undergraduate researcher.  The NHL’s current point system awards more total points to games ending in overtime than games ending in regular time.  In this work, we evaluate if this a fair system, and if it influences style of game.  We find that the current point system results in statistically more passive play in the last five minutes of regulation for an even-score game than the first fifty-five because both teams want to ensure at least one point. The “3-2-1-0” point system minimizes discrepancies with win-loss record, and does not compromise the competitiveness and entertainment of the game and is recommended.  Zach presented this research at the 2017 Regional Institute of Industrial and Systems Engineering Conference, which earned him a second place finish.  We have submitted this work to the 2018 IISE Conference; our submitted conference paper can be downloaded here: [Shearin and Pazour, NHL Point System Fairness Optimization and Game Play Stat Analysis].

NHL

The NHL Point System is used to determine the teams who make the playoffs.  The current point system awards points based on whether the game was determined in regular time or overtime.

Regular Time Overtime
Points for Win 2 2
Points for Loss 0 1
Total Points Awarded 2 3

Specifically, more total points (3) are awarded if a game ends in a tie, rather than ending in regular time.  Thus, our first question we asked was:

  1. Does the Current NHL Point System Influence Style of Play?

Statistical analysis was used to determine if the point system impacts style of game play. To do so, per-minute shots, face-offs, penalties, hits and blocks are statistically compared in the first 55 minutes and last 5 minutes that has even-scored play.  Our hypothesis is that the point system impacts play of game because if the game is tied and it is close to the end of regulation (i.e., in the last 5 minutes of the game), many teams adopt a new strategy to the way that they play.  Specifically, both teams tend to be more defensive/passive to guarantee each team a point if regulation ends in a tie, with an additional point awarded to the winner of overtime.

Data from every game in the 2003-2004, 2005-2006, 2014-2015 and 2015-2016 seasons were collected and parsed using R and C++.  An R-package, called “nhlscrapr,” was used to gather all the data in Excel spreadsheets, and the data was then parsed using C++.  Unfortunately, no data is available for the time periods before 2002-2003.  Thus, the play of game analysis cannot be directly compared to the point systems. One exception is the point system change between the 2003-2004 and 2005-2006 seasons.  This change accounts for the addition of a shootout to the end of overtime, but this does not impact style of play in regulation significantly because it is only a minor change to the structure of the game.  With the available data, per-minute shots, face-offs, penalties, hits and blocks were all assessed. Each data entry records a game with time in the first 55 minutes and last 5 minutes that has even-scored play.  The duration of even play in these time periods is used to calculate the per minute value of each statistic.  Paired z-tests using an alpha value of 0.05 assessed whether the means (per minute) for the first 55 minutes and last 5 minutes of each hockey game were statistically different.

Results: Is Play of Game Statistically Different?

The total number of games played in a standard NHL season is 1230 ([30/2]*82 = 1230).  Each of the four seasons tested had between 337 and 364 of their games with time tied in both the first 55 minutes and last 5 minutes of play.  This is a little less than a third of the regular season games (27.3% to 29.6%).  The per minute means and variances used in the paired Z-tests were calculated for each of the different hockey events and are shown in  Table 3.

Table 3: Per Minute Means and Variances from Data Collection

Table3

For each of the different hockey events measured, the hypothesis was tested as follows:

hypothesis

The results are presented in Table 4, which presents the Z values and the corresponding p-values, for each of the statistics and seasons.

Table4

The test of the hypothesis for the different events strongly indicate more passive play in the last five minutes than in the first fifty-five.  They indicate that both per minute penalties and hits are much higher in the first 55 than in the last 5 minutes for all sampled seasons.  Face-offs are found to be statistically higher in the last five minutes. Face-offs occur due to goals, icing, off-sides, penalties, a hand pass, the puck going out of play and the goalie holding the puck.  Of these, goals, penalties and possibly off-sides would indicate aggressive play, increasing the number of face-offs.  The z-tests indicate that penalties are statistically less significant in the last five minutes, so they do not contribute to the significantly higher rate of face-offs in the first 55 than in the last 5.  Since face-offs are significantly higher per minute in the last five minutes than the first fifty-five, this measure indicates more passive play in the last five minutes (icing and goalie holding the puck).

Blocks are higher in the first 55 per minute than in the last 5 per minute, but this is not at a statistically significant level.  Blocks do indicate a more aggressive level of play, but they are reactionary to what the other team is doing.  At the 90% confidence level, shots per minute in the first 55 minutes with even play were higher (with statistical significance) than shots per minute in the last five minutes up until the most recent season (the 2015-2016).  Although shots per minute were higher in the first 55 than in the last 5, they were not higher at confidence level of 90%.  A major factor that likely influenced this change was the modification of the overtime format between the 2014-2015 and 2015-2016 seasons.  The format change from 4 on 4 hockey to 3 on 3 hockey, which likely contributed to significant change in strategy for games that were approaching the end of regulation with a tie score.

The change in strategy for the 4 on 4 to 3 on 3 could likely have changed teams’ strategies of play when the game theoretically will end in a tie based on their understanding of their teams’ skill set.  A team with a more uneven spread of players (i.e., some all-stars and some below-average players) would likely be less aggressive and more willing to end regulation in a tie because of confidence in winning the game in overtime, whereas a team with a more even spread of talent would likely be more aggressive in the end of regulation because they are less likely to win in overtime.  This topic will likely be explored with further research.

Many hockey experts and fans alike argue that the system needs to be changed (Reiff, 2016).  But most also agree that hockey play in overtime should be treated differently from regular time.  Both teams played a full game of hockey equally well and the rules of the game are altered significantly to determine the winner much more quickly.  If the game ending is not altered (as is the case in the playoffs), games could last a lot longer.  For example, on Thursday, May 5, 2016, the Nashville Predators and San Jose Sharks played a playoff hockey game with three 20-minute overtimes (nearly the length of two entire games) because the three 20-minute regular time periods ended tied and no one scored a goal until the middle of the third overtime.  The games during the regular season are altered to significantly reduce the potential time a game could last.  The game ending is altered (thus no longer playing real 5 vs. 5 hockey), and both teams deserve to acquire points from high quality hockey played in regular time. However, introduction of reward for losing has to be balanced with teams that have few games go to overtime and still a winning record.

This led us to our next research question:

  • Is the Current NHL Point System Fair?

To answer this question, we compare five point systems to the playoff picture captured by win-loss record.  Four are previous or current rules: “Pre-1983,” “1984-1999,” “2000-2004,” and “2005-Present”.  The “3-2-1-0” system is one many critics argue the NHL should implement (Reiff, 2016).  Each of these point systems is assessed by using data from the 2005-2006 to 2015-2016 seasons (excluding the abbreviated 2012-2013 season). These are the only seasons in the history of the game that used the current point system in place: 2 points for a win and 1 point for an overtime loss.

An integer linear program determines which teams make the playoffs for a given point system. A team can make the playoff by either being top of their decision, or through a wildcard spot.  These become the binary decision variables in the optimization model.

Decision Variables:

Notation Definition Description
D_i = {0,1} 1 if team i made playoffs by top division; 0 otherwise (o.w.)
W_i = {0,1} 1 if team i made playoffs by wildcard; 0 o.w.

To determine which teams make the playoff, the objective of our model is to maximize the total number of points of the teams that make playoffs, giving more weight to making it from being top of the division than wildcard spots.

Optimization Model

The current NHL structure and playoff requirements were used as the constraints and decision variables in the model formulation. Constraint sets enforce that exactly 16 total teams make playoffs, and 8 of these teams come from each of the conferences.  A team can only make the playoffs in one way, either as top of the division or as a wildcard.  Exactly 3 teams from each division can make the playoffs based on being top of their division.  The second constraint, coupled with the fourth constraint, ensures that exactly two teams from each conferences make it as a wildcard.

Inputs to the model include the total points each team receives in a given season for a given point system.  As illustrated in the Table below, the points awarded are different in each of the point systems based on the outcome of the game.

Point System Name: Current Win-Loss Record 3-2-1-0 2000-2004 1984-1999 Pre-1983
Situation: Point Values:
Regular-time Win 2 2 3 2 2 2
Regular-time Loss 0 0 0 0 0 0
Tie NA NA NA 1 1 1
Overtime Win 2 2 2 2 2 NA
Overtime Loss 1 0 1 1 0 NA
Points Awarded Change? Yes No No Yes No No

The “Points Awarded Change?” row refers to whether the total number of points awarded for a game change due to the result of the game.  An example of “Yes” is in the current system.  Three total points are awarded in an overtime game, whereas two total points are awarded in a regular time game.  In the current format, a team’s record is denoted in three separate columns: wins, regular-time losses, and over time losses. For example, if a team had 42 wins and 40 losses  with 8 of them occurring in overtime, their record would be recorded as 42-32-8 (42-40).

  • Results

For each of the ten seasons assessed, the playoff picture was determined for each of the point systems using the integer linear programming model.  The win-loss record playoff picture was used as a baseline to compare all other point systems.  Figure 1 demonstrates the total number of differences in the playoff picture between the assessed point system and the win-loss record playoff picture.

Figure1

There are three different categorizations of discrepancies in the playoff picture, denoted by color: red, orange and yellow.

  • A “red” difference denotes that a team made top division in win-loss but not at all in the assessed system or vice versa.
  • An “orange” difference denotes that a team made wildcard but not at all in the assessed system or vice versa.
  • A “yellow” difference highlights when being top division and wildcard is flipped for the assessed point system.

The “3-2-1-0” point system has the least number of differences with win-loss record alone, and the “Pre-1983” point system has the most.  Since the “2000-2004,” “1984-2000,” and “Pre-1983” point systems are all fairly similar, they each had a close number of discrepancies with win-loss record alone and their playoff pictures were very similar to one another.

A sample season, the 2015-2016 season is used to highlight differences in the result of the point system used.  The playoff structure for each system is outlined in Table 2 below.  In addition to the color scheme used in Figure 1, teams that varied from win-loss record in their top division spots are highlighted in green (e.g. Lightning made it in the A1 spot in the 1984-1999 point system instead of the A2 spot; however, because they made playoffs as top division in both, no discrepancy was counted for this scenario).

Table 2: 2015-2016 Playoff Picture for Each Point System

  Win-Loss Record Current (Actual) 3-2-1-0 2000-2004 1984-1999 Pre-1983
Eastern Conference:
M1 Capitals Capitals Capitals Capitals Capitals Capitals
M2 Penguins Penguins Penguins Penguins Penguins Penguins
M3 Rangers Rangers Rangers Rangers Rangers Rangers
A1 Panthers Panthers Panthers Panthers Lightning Lightning
A2 Lightning Lightning Lightning Lightning Panthers Panthers
A3 Bruins Red Wings Bruins Red Wings Red Wings Bruins
WC1 Islanders Islanders Islanders Islanders Islanders Islanders
WC2 Flyers Flyers Flyers Flyers Flyers Flyers
Western Conference:
C1 Stars Stars Stars Stars Stars Stars
C2 Blues Blues Blues Blues Blues Blues
C3 Blackhawks Blackhawks Blackhawks Blackhawks Blackhawks Blackhawks
P1 Kings Ducks Ducks Kings Kings Ducks
P2 Ducks Kings Kings Ducks Ducks Sharks
P3 Sharks Sharks Sharks Sharks Sharks Kings
WC1 Predators Predators Predators Predators Predators Predators
WC2 Avalanche Wild Wild Wild Wild Wild
Discrepancies with Win-Loss 0 2 1 2 2 1

In the Eastern Conference, the only major discrepancy in the playoff picture occurred with the Detroit Red Wings and the Boston Bruins. In the current system, the Bruins and Red Wings both had the same number of points at 93 apiece.  The Bruins’ record in the current format was 42-31-9 (42-40) and the Red Wings’ record was 41-30-11 (41-41).  Using the current point system, the Red Wings made the playoffs and the Bruins did not make the playoffs, even though they had the same number of points (Bruins also had more wins).  This would not have occurred if Win-Loss Record, the 3-2-1-0 point system or the point system used before 1983 were used.  The most entertaining of these three point systems would arguably be the 3-2-1-0 point system.  The point system used before 1983 allows the game to end in a tie and divvies points accordingly, and the win-loss record point system does not take into account the change in structure of overtime play.

In the Western Conference, the only major difference between win-loss record and all other point systems was whether the Colorado Avalanche or the Minnesota Wild took the second wildcard spot.  All other differences, highlighted in green, outlined changes in rankings for top of the division, which only influence seeding in the playoffs.  The Colorado Avalanche had a record of 39-39-4 (39-43) and the Minnesota Wild had a record of 38-33-11 (38-44).  The Colorado Avalanche would have made it if using win loss record alone, but they would not have made it using any of the other point systems.  The reason that the Wild made it in all but win-loss record alone is due to their much higher number of games ending in overtime.  They had 7 more games ending in overtime while only one win less than the Avalanche.  Essentially, the 7 overtime losses, which are close games that end regulation in a tie, are worth more than the 1 greater win in non-win percentage point systems.

  Conclusions and Recommendations

This work analyzed a professional sporting league, the NHL, through an operations research and statistical analysis lens. Doing so, identified some inconsistencies with the current point system. Specifically, the current point system rewards games ending in regulation and overtime in an attempt to address fairness that using win-loss record alone would not. The current system, however, simultaneously results in statistically more passive play in the last five minutes of regulation for an even-score game than the first fifty-five because both teams want to ensure at least one point. The “3-2-1-0” point system minimizes discrepancies with win-loss record, and does not compromise the competitiveness and entertainment of the game and should be used. In the 3-2-1-0 point system, teams would not be incentivized for passive play at the end of the regular period, because the allocation of points favors ending it in regular time.  The total number of points awarded does not change (3), but how many are assigned to each team changes (regular time: 3-0 and overtime: 2-1).

Also, go talented undergraduate Industrial and Systems Engineers, go Operations Research, go Statistics, and go Engineers!

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