There are two main reasons for changing rules in the ice hockey. The first reason is a safety of players and spectators and the second reason is an attractiveness of matches. This paper studies effects of rule changes that were made because of the second reason, e.g., allowing a two-line pass, narrowing a neutral zone, overtime in the case of a tie match. Rule changes are analyzed from two perspectives – the first one is a distribution of goals scored in a match and the second one is a relative number of ties after a 60-minute regulation time. All seasons since the last big expansion of the NHL in 1979 are used in this analysis. The second part of this paper is dedicated to study of the three-point system that is often named as a cure for a high number of ties in the NHL. This system was earlier introduced in the world’s most important ice hockey leagues, i.e., in the Czech Republic, Finland, Germany, Russia, Switzerland and Sweden and its effect in these leagues is analyzed.

1. Effects of Rule Changes and Three-
point System in NHL
Patrice Marek
University of West Bohemia, Czech Republic
16th
Conference on Applied Mathematics APLIMAT 2017
January 31 – February 2, 2017, Bratislava, Slovakia

2. Presentation Outline
Description of Problem
Data
Analysed Rule Changes
Approach and Problems
Test: Distribution of Goals
Test: Relative Number ofTies
Test:Three-point System
Conclusion
Remark: Presentation of paper Effects of Rule Changes and Three-Point
System in NHL, full text available at https://www.researchgate.net/
publication/313470869_EFFECTS_OF_RULE_CHANGES_AND_THREE-
POINT_SYSTEM_IN_NHL
2

3. Description of Problem
3
Evolution 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.
Distribution of scored goals in a game.
Number of ties.

4. Data
4
34 seasons of NHL were used in the analysis.
Data from the 1979–80 season to the 2014–15 season (2004–05 season was
cancelled, i.e., no match was played).
“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.
Data for analysis of the three-point system:
Sweden, Germany: 1997–1998 and 1998–1999.
Russia: 1998–1999 and 1999–2000.
Czech Republic: 1999–2000 and 2000–2001.
Finland: 2003–2004 and 2004–2005.
Switzerland: 2005–2006 and 2006–2007.

5. Analysed Rule Changes
5
1983–1984 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).
2010–2011 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.

6. Approach and Problems
6
To avoid problems with consistency of data we test each rule
change on data of the season directly before and directly after the
change (almost the same players, almost the same teams, almost
the same equipment).
We test each change separately. To test all changes together we
can formulate compound hypothesis and Bonferroni correction (or
some similar) to maintain significance level.
Each change is tested from two perspectives:
Distribution of goals (usually considered to be Poisson or
negative binomial distribution). We are able to detect change in
mean value or variance.
Relative number of ties in regulation time of a match.

7. Distribution of Goals
7
H0: Distribution of total number of goals scored in the regulation
time in both seasons are identical.
H1: non-H0
This can be tested by chi-square test of homogeneity.
No effect expected (dashed line), increase expected (full line).
2
3
4
5
6
7
8
9
1979−1980
1980−1981
1981−1982
1982−1983
1983−1984
1984−1985
1985−1986
1986−1987
1987−1988
1988−1989
1989−1990
1990−1991
1991−1992
1992−1993
1993−1994
1994−1995
1995−1996
1996−1997
1997−1998
1998−1999
1999−2000
2000−2001
2001−2002
2002−2003
2003−2004
2005−2006
2006−2007
2007−2008
2008−2009
2009−2010
2010−2011
2011−2012
2012−2013
2013−2014
2014−2015
AverageNumberofGoals
Home
Away
Total

8. Distribution of Goals
8
Symbol • indicates rejection of null hypothesis ( ) (blue for
“no change expected”, green for “change expected”). Each
row means test against the previous season.
↵ = 5%

9. Relative Number of Ties
9
H0: Relative number of ties in the regulation time in both seasons
are identical.
H1: non-H0, or an appropriate one sided alternative.
Test for difference in two population proportions can be used.
No effect expected (dashed line), increase expected (dotted line),
full line (decrease expected).

10. Relative Number of Ties
10
Symbol •• indicates rejection of null hypothesis ( ) and
symbol • rejection for (blue is used for “no change
expected”, green for “increase expected”, red for “decrease
expected”).
↵ = 5%
↵ = 10%

11. Three-point System
11
The three-point system is usually named as cure for high amount
of ties.
We obtained data for 6 countries (year = year of change). Change
were from 2–1–0 system without overtime to 3–2–1–0 system with
overtime.
1998: Sweden, Germany
1999: Russia
2000: Czech Republic,
2004: Finland (used 2–2–1–0 system with overtime before the
change),
2006: Switzerland.

12. Three-point System
12
For example, for the Czech Republic we obtained:
Average number of goals (AvgG) and sample variance of goals
(s2) are related to the test of distribution. Here the hypothesis that
both distributions are identical is not rejected (p-value 0.163).
Relative number of ties (Rel. Ties) is related to the test of relative
number of ties in the regulation time. Here the hypothesis that
relative number of ties in the regulation time in both seasons are
identical is not rejected (p-value 0.784).
Matches AvgG s2 Ties Rel.Ties
1999–2000 364 5.74 6.10 74 0.203
2000–2001 364 5.45 5.46 77 0.212
p-value 0.163 0.784

13. Three-point System
13
There are shown characteristics before and after the change.
GOALS Matches AvgG s2 p-value
Sweden 276→300 5.61→5.76 5.93→6.61 0.978
Russia 462→380 4.89→4.94 5.26→5.86 0.923
Germany 342→364 6.31→6.66 6.13→6.23 0.654
Czech Rep. 364→364 5.74→5.45 6.10→5.46 0.163
Finland 364→364 5.23→5.23 5.17→5.45 0.516
Switzerland 264→264 5.92→6.16 5.58→4.96 0.651
TIES Matches Ties Rel.Ties p-value
Sweden 276→300 54→61 0.196→0.203 0.591
Russia 462→380 84→70 0.182→0.184 0.536
Germany 342→364 63→72 0.184→0.198 0.677
Czech Rep. 364→364 74→77 0.203→0.212 0.608
Finland 364→364 82→82 0.225→0.225 0.500
Switzerland 264→264 47→47 0.178→0.178 0.500

14. Conclusion
14
Major rule changes in the NHL since 1979 were analysed.
The effect of rule changes was tested from two perspectives – their
effect on distribution of goals and relative number of ties.
1983–1984 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 – we expected no
change of distribution of goals but this was rejected (average
5.21→5.39, sample variance 5.35→4.77) and we expected increase
of relative number of ties but null hypothesis was not rejected.

15. Conclusion
15
2003–04, 2005–06, 2011–12 and 2013–14 season: usually some
equipment reduction with expectation of change of distribution of
goals and decrease in the relative number of ties.
Effect can be seen only for the major rule change (two-line pass
legalisation and reduction of neutral zone) in 2005–06 season:
average 5.02→5.94, sample variance 5.00→5.54 and relative
number of ties 0.256→0.228 (rejection for 10% level of sign.).
Three-point system: does not work for change of distribution of
goals and for relative number of ties.
Proposed solution with more aggressive changes inspired by rugby.
4 points for a win in the regulation time,
2 points for a win in the overtime (OT),
1 point for loose in the overtime,
1 bonus point for scoring more than 3 goals in regulation time.
1 bonus point for losing by 1 goal in the regulation time.
No team can get more than 5 points.

16. Conclusion
16
Final ranking in 2000/2001 season (original system is 3-points-
system).
Team Number of points Final position
2 pts sys 3 pts sys 5 pts sys 2 pts sys 3 pts sys 5 pts sys
Vsetín 67 99 153 1 1 1
Znojmo 55 82 129 5 2 2
Pardubice 58 82 126 2 3 3
Litvínov 56 81 123 4 4 6
Sparta Praha 55 80 124 6 5 5
Vítkovice 57 80 118 3 6 9
Slavia Praha 54 79 125 8 7 4
Zlín 55 79 120 7 8 8
Třinec 51 75 122 9 9 7
Plzeň 51 74 114 10 10 10
České
Budějovice
51 72 113 11 11 11
Havířov 42 62 99 12 12 12
Kladno 42 62 90 13 13 13
KarlovyVary 34 49 81 14 14 14

17. References
Figures used in the presentation:
[1st slide] Vermette Celebrates Tyutin's Goal, author: clyde. Licence: Creative
Commons BY-NC 2.0. Available at Flickr.com
[3rd slide] 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
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18. Effects of Rule Changes and Three-
point System in NHL
Patrice Marek
University of West Bohemia, Czech Republic
Thank you for your
attention!
16th
Conference on Applied Mathematics APLIMAT 2017
January 31 – February 2, 2017, Bratislava, Slovakia