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In search of goals: increasing ice hockey’s attractiveness by a sides swap

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Journal of the Operational Research Society

Abstract

The popularity and business impact of major sports have been growing globally over time. This paper focuses on ice hockey, specifically the National Hockey League in North America. It reports a striking irregularity in ice hockey’s scoring dynamics relative to comparable sports such as soccer and rugby, namely a scoring surge in the middle section of the game. We explore an explanation for this irregularity related to the convention on the spatial location of the teams’ benches (which are fixed throughout the game) and on-ice sides (which are switched every period). Because a large number of the players’ substitutions occur while the play is in progress, this convention determines the distance forwards and defenders need to travel to make a substitution, and thus indirectly substitution strategies and scoring. We consider two simple operational changes that could increase the number of goals in the NHL by approximately 5 and 10%, respectively, corresponding to roughly 350 and 700 additional goals each season. This would partly offset the current downward scoring trend and thus enhance the game’s attractiveness. The estimated impact of the proposed reforms, one of which is largely costless, is robust across several specifications—using per-minute and per-second scoring data and controlling for various factors, such as bookmakers’ odds.

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Figure 1

Note Black and white rectangles denote the location of the respective teams’ benches and sides (defensive zones). The shaded rinks indicate the periods featuring the long change and thus more attacking (higher scoring) play. (Color figure online)

Figure 2

Source www.quanthockey.com/TS/TS_GoalsPerGame.php. Note The thick line shows the series for the regular season, and the thin line shows the series for the playoffs. Both series include regulation time as well as overtime goals, but exclude the notional goal awarded for winning the shootout. The dotted lines covering the 2004–2005 period represent the “lockout” season. (Color figure online)

Figure 3
Figure 4

Note Final minutes were excluded for reasons discussed In Section 1, specifically 59′–60′ in hockey, 45′ and 90′ in soccer, and 39′–40′ and 79′–80′ in rugby. (Color figure online)

Figure 5

Note The light thick, dark thick and thin lines report periods 1, 2, and 3, respectively. The solid lines report games with goal differences of 0 (left panel) and 3 or more goals (right); the dashed lines show goal differences of 1 (left) and 2 (right). (Color figure online)

Figure 6

Note The predicted number of goals per period by season (left) and their increases under the alternative proposals (right). The dots show the means, and the lines are the 95% confidence intervals. (Color figure online)

Figure 7

Note The dotted line shows actual scoring, the solid line shows estimated levels in Model 2 under the status quo, and the dashed line shows predicted scoring in Model 2 under Starting Long. (Color figure online)

Figure 8

Note The dotted line shows actual scoring, the solid line shows estimated levels in Model 3 under the status quo, and the dashed line shows predicted scoring in Model 3 under Starting Long. (Color figure online)

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Notes

  1. For examples, see Jackman (1987), Asano and Matsushima (2014) and Wright (2014), respectively.

  2. For attendance statistics see, for example, www.hockeydb.com/nhl-attendance; for business data see, for instance, www.statista.com/topics/960/national-hockey-league.

  3. In terms of the convention, see, for example, rule 636d of the NHL Rule Book, available at www.usahockeyrulebook.com/page/show/1084715-rule-636-start-of-game-and-time-of-match-time-outs. In regards to the literature, even Thomas (2007), whose Figure 1 (p. 2) clearly shows the same scoring pattern as in our Figure 3, does not discuss it. The short blog posts by Plank (2010) and Pettigrew (2013) seem to be the first to discuss this phenomenon.

  4. The median shift-length was 43.8 seconds in the 2015–2016 regular season, see the data at www.sportingcharts.com/nhl/stats/average-ice-time-per-shift/2015/.

  5. For actual NHL examples of sides/bench related counter-attacks, see  www.youtube.com/watch?v=Ubp3xhl_UAA  or www.youtube.com/watch?v=LU-XWPzo8io. For an informative explanation of changing on the fly in the NHL, see www.youtube.com/watch?v=QdaiacSrya0.

  6. We discuss later how differences in the variance of the defenders’ shift-length across periods could provide direct evidence that the sides/bench convention affects on-ice behavior and scoring. In the final section we also consider the effect of power plays if penalty calls differ across the periods.

  7. For the former quote, see www.nhl.com/news/analysis-rules-changes-could-create-more-scoring/c-730220, for the latter, see www.nhl.com/ice/m_news.htm?id=787279.

  8. The former change may be disliked by some fans (for example, those seated behind their own goal), whereas the latter change carries the logistic cost of having to move all of the equipment twice over the course of the game, and teams being unable to access their own bench directly from their dressing room. More related discussion appears in the Conclusions section.

  9. Kaplan et al (2014) use per-second scoring to great effect in modelling ice hockey data.

  10. To name the key changes: (i) the two-line offside rule was repealed; (ii) introduction of a penalty for the defensive team shooting the puck over the glass deliberately; (iii) no line change allowed following icing; and (iv) reduction of the area where the goalie is allowed to play. There were also additional changes in the interpretation of existing rules, relating mainly to stricter penalty calls on fouls.

  11. Our rugby data come from ProZone for the 2002–2012 seasons of Super Rugby (958 regular-season matches), which (unlike most tournaments) awards a bonus-point to either team for scoring at least four tries. Lenten and Winchester (2015) show that this incentivizes more tries to be scored late-on in matches. In addition, there also exists a ‘narrow-loss’ bonus, which could conceivably have a similar effect. Our soccer data are drawn from the Trefik database and contain 26429 matches from six major European leagues, domestic cups, as well as European and World Championships. For more details about this dataset, see Lenten et al (2013).

  12. For more on outcomes in various sports using dynamic learning for stochastic processes, see Percy (2015).

  13. In addition to these indirect pieces of evidence, a possible way to consider the direct effect of existing sides/bench locations on the players’ behavior is through the differences in the forwards’ and defenders’ shift-lengths across the periods. Our explanation of the second-period scoring surge implies that in the second period, defenders may sometimes find it harder to substitute on the fly and may thus have a longer shift than in the other two periods. Knowing this, however, they may try to substitute at an earlier opportunity than usual, which may offset this effect. Therefore, while the joint effect on the average duration of the defenders’ second-period shift is ambiguous, the effect on the variance is not. In particular, the variance of the length-shift should be higher for defenders in the second period than in the first and third periods, and vice-versa for forwards. Unfortunately, per-period data on shift-length that would enable us to test our conjecture are not readily available.

  14. Intuitively, the teams of a tied game are more concerned about not losing the one point that a draw currently guarantees them than about not securing the additional point for winning the game in regulation time.

  15. The latter exclusion is to remove the high-scoring effect of the goaltender’s substitution and empty nets, the former is to remove the low scoring at the start of each period (largely due to the initial face-off occurring in the middle of the ice rink and initial caution during each line’s first shift). Both effects are exhibited clearly in Figures 3 and 5.

  16. Throughout the paper we consider goals scored at time 0:00–0:59 to be scored in the 1st minute, i.e., t = 1, etc.

  17. The multiplicative specification we have estimated is of the form: \( GM\left( {P,t} \right) = { \exp }(\mu_{P} + \beta t), \) where the interpretation of the coefficients differs somewhat (for Poisson-type modeling of NHL scoring, see Buttrey et al, 2011). As the results are very similar to the additive specification, we do not report them here, but they are available upon request.

  18. For comparable estimates using back-of-the-envelope calculations, see Willis (2014).

  19. Model 2 uses a slightly smaller sample compared to the other models; 4620 games had to be excluded as they did not have odds data available to calculate the UNBAL variable. The number of observations in this model is therefore 1192860; that is, each of the 60 minutes of 19878 games.

  20. Similarly, in our Super Rugby sample, aggregate scoring falls from an average of 48.43 points per match in regular-season games to 44.41 points per game in playoff matches.

  21. The values of (per-second) parameters within Model 3 can be compared to the (per-minute) estimates of Model 2 when multiplied by 60.

  22. There also exist numerous parallels of this study to Hurley (2009), which similarly uses operations research techniques to revise group allocation methods to optimize an objective—fairness of competition according to athlete birthdate. For a comprehensive survey of the operations research literature relating to sport, see Wright (2009).

  23. Specifically, in many European leagues, the three forwards about to come onto the ice sit (in all periods) closer to the opponent’s goal, whereas in the NHL they sit closer to their own goal. This may reflect a somewhat greater relative focus on defense in the NHL, and in principle, could determine the magnitude of the effects of our proposed reforms across the elite leagues. We have been unable to obtain the data on how substitution strategies depend upon the time remaining and the score, and what the proportion of substitutions on the fly is. In principle, the latter could differ across the periods, and/or change as a consequence of players executing more enforced stoppages under the long change. These considerations could thus have some quantitative effect on scoring dynamics under the proposed reforms.

  24. In many European arenas even a bench swap would be straightforward as both teams enter the benches through the same corridor in-between the two benches.

  25. Let us mention that both proposals are likely to slightly decrease the proportion of games going to overtime. We have estimated that the probability of the game finishing in a draw after regulation time would decline by about 0.6-0.7 percentage points under Starting Long and 1.3 percentage points under Always Long. These estimates were obtained by simulations of 100,000 games, assuming the second-period surge estimate from Model 1.

  26. For a comprehensive discussion of case studies from sports involving perverse unintended consequences, see Kendall and Lenten (2017).

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Acknowledgements

We would like to thank Vladimir and Stanislav Kraus of Trefik, a bookmakers’ data provider (see: www.trefik.cz), for sharing the data and helping with data processing. We also appreciate comments and suggestions from Graham Kendall, Michael Lopez, Stephen Pettigrew, and two anonymous referees for this journal. The usual disclaimer applies. The third author would like to acknowledge financial support from the European Social Fund (CZ.1.07/2.3.00/20.0296).

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Correspondence to Petr Stehlík.

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Friesl, M., Lenten, L.J.A., Libich, J. et al. In search of goals: increasing ice hockey’s attractiveness by a sides swap. J Oper Res Soc 68, 1006–1018 (2017). https://doi.org/10.1057/s41274-017-0243-2

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