Patrice MarekUniversity of West Bohemia, Plzeň, Czech Republic

MathSport International 2015 Loughborough University 29th June – 1st July 2015

Effects of Rule Changes in NHL

Presentation OutlineDescription of Problem

Data

Analysed Rule Changes

Hypotheses Formulation

Hypotheses Testing

Conclusion

References

Description of ProblemEvolution of ice hockey.

Technological advance, e.g. goaltender mask (Jacques Plante, 1959–60) – slow effect.

Rule changes – quick effect.

Main reasons for rule changes. Safety of spectators and players.

Attractiveness of matches.

Measures of attractiveness (used in paper). Number of scored goals in a game.

Number of ties.

Data34 seasons were used in the analysis.

Data from the 1979–80 season to the 2014–15 season (2004–05 season was cancelled).

“Consistency of data”. The last big expansion of NHL was made between the 1978–79 and 1979–1980 season (four teams joined the league).

Results only in the 60-minute regulation time were used.

Only regular season matches were used.

Analysed Rule Changes1983–1984 season: Five-minute overtime period was introduced (loosing team received no point).

1999–2000 season: Four skaters in the overtime (instead of five). Loosing team in the overtime received one point.

2003–2004 season: Maximum length of goaltenders’ pads was set at 38 inches.

2005–2006 season: Many rule changes – shootout after five-minute overtime, salary cap, reduction of neutral zones, goaltenders’ equipment reduction (11 percents).

2011–2012 season: Goaltenders’ pads shall not exceed eleven inches. Size of pads is set to be anatomically proportional.

2013–2014 season: More reduction to the size of pads due to a change in the calculation of anatomically proportional size.

Hypotheses FormulationH0: Average number of goals scored in the regulation time in a season X+1/X+2 is the same as in a season X/X+1.

No effect expected (dashed line), increase expected (full line).

2

3

4

5

6

7

8

9

1979−1

980

1980−1

981

1981−1

982

1982−1

983

1983−1

984

1984−1

985

1985−1

986

1986−1

987

1987−1

988

1988−1

989

1989−1

990

1990−1

991

1991−1

992

1992−1

993

1993−1

994

1994−1

995

1995−1

996

1996−1

997

1997−1

998

1998−1

999

1999−2

000

2000−2

001

2001−2

002

2002−2

003

2003−2

004

2005−2

006

2006−2

007

2007−2

008

2008−2

009

2009−2

010

2010−2

011

2011−2

012

2012−2

013

2013−2

014

2014−2

015

Aver

age

Num

ber o

f Goa

ls

HomeAwayTotal

Hypotheses FormulationH0: Relative number of ties in the regulation time in a season X+1/X+2 is the same as in a season X/X+1.

No effect expected (dashed line), increase expected (dotted line), decrease expected (full line).

0.1

0.15

0.2

0.25

1979−1

980

1980−1

981

1981−1

982

1982−1

983

1983−1

984

1984−1

985

1985−1

986

1986−1

987

1987−1

988

1988−1

989

1989−1

990

1990−1

991

1991−1

992

1992−1

993

1993−1

994

1994−1

995

1995−1

996

1996−1

997

1997−1

998

1998−1

999

1999−2

000

2000−2

001

2001−2

002

2002−2

003

2003−2

004

2005−2

006

2006−2

007

2007−2

008

2008−2

009

2009−2

010

2010−2

011

2011−2

012

2012−2

013

2013−2

014

2014−2

015

Rel

ativ

e nu

mbe

r of t

ies

Hypotheses TestingFirst, we performed a Pearson's chi-squared test of compound hypothesis H0: Number of goals scored in a game during a season is Poisson distributed.

Hypothesis was not rejected (using significance level 0.01).

P-value 0.017 means that we will focus on another distributions in our future work, e.g. negative binomial distribution.

In this paper, we work with Poisson distribution.

Hypothesis H0: Average number of goals scored in the regulation time in a season X+1/X+2 is the same as in a season X/X+1 was tested by the Conditional test (C-test).

C-test uses simple fact that conditional distribution of Y1 (number of goals scored in one season) conditionally given Y1 + Y2 = k (sum of number of goals scored in both seasons) is binomial.

Hypotheses TestingH0: Average number of goals scored in the regulation time in a season X+1/X+2 is the same as in a season X/X+1.

Rule changes are highlighted (blue for “no effect expected”, green for “increase expected”). (–,x) indicates one-sided alternative hypothesis (average is higher).

H0: Relative number of ties in the regulation time in a season X+1/X+2 is the same as in a season X/X+1. Test for the difference in two population proportions was used. This test uses the approximation of the binomial distribution by the normal distribution.

Rule changes are highlighted (green for “decrease expected”, red for “increase expected”). (–,x) or (x,–) indicates one-sided alternative hypothesis (relative number of ties is higher (or lower)). Hypothesis for the 1983–84 season rule change with expectation of no effect was not rejected. Decrease expected in 2003–04, 2010–11 and 2013–14: not confirmed.

Hypotheses Testing

Major rule changes in the NHL since 1979 were analysed.

Hypothesis that number of goals scored in a game during one season is Poisson distributed was not rejected. (small p-value future work)

The effect of rule changes was tested from two perspectives – their effect on the average number of goals and relative number of ties.

1983–84 season: Five-minute overtime period was introduced (loosing team received no point) – as expected, no effect from both perspectives.

1999–2000 season: Four skaters in the overtime (instead of five). Loosing team in the overtime received one point – expected effects, i.e. higher average of goals and higher number of ties, are shown only for level of significance 0.1.

Conclusion

2003–04, 2005–06, 2011–12 and 2013–14 season: usually some equipment reduction with expectation of an increase in the average number of goals and decrease in the relative number of ties.

Effect can be seen only for major rule change (two-line pass legalisation and reduction of neutral zone) in 2005–2006 season where average number of goals is higher than in previous season and using significance level 0.1 it is possible to show that relative number of ties decreased.

Conclusion

Figures in the presentation

[A] Voukoun Pad Save, author: clyde. Licence: Creative Commons BY-NC 2.0. Avaiable at https://www.flickr.com/photos/24733811@N04/6850487749.

[B] The original Mask of Jacques Plante in the Hockey Hall of Fame, author: Horge. Licence: Creative Commons BY 3.0. Available at https://commons.wikimedia.org/wiki/File:Plante_Mask.jpg

Reference list of the paper

[1] Hockey History. Hockey History - Birthplace, Ancestors, NHL, 2015. http://hockey-history.com/nhl/historical-results/.

[2] L. H. Kahane and S. Shmanske. The Oxford Handbook of Sports Economics, Volume 1: The Economics of Sports. Oxford University Press, New York, 2012.

[3] M. J. Maher. Modelling association football scores. Statistica Neerlandica, 36(3): 109–118, 1982.

[4] J. Przyborowski and Wilenski H. Homogeneity of Results in Testing Samples from Poisson Series. Biometrika, 31(3/4):313–323, 1940.

References

Reference list of the paper

[5] N. J. Salkind. Encyclopedia of Measurement and Statistics. Thousand Oaks, CA: SAGE Publications, Inc, 2007.

[6] The National Hockey League. Official Rules 2010–2011. Dan Diamond and Associates, Inc.,Canada, 2010.

[7] The National Hockey League. Official Guide & Record Book 2013. Dan Diamond and Associates,Inc., Canada, 2012.

[8] The National Hockey League. Official Rules 2013–2014. Dan Diamond and Associates, Inc.,Canada, 2013.

[9] J. M. Utts and Heckard R. F. Mind on Statistics. Cengage Learning, Stamford, 2015.

References

Thank you for your attention!