The document discusses analyzing the "bogey phenomenon" in sports, where certain teams or players consistently perform better than expected against a specific opponent. It proposes combining the Wald-Wolfowitz Runs Test with an upset result identification method using betting odds. An example application to men's tennis finds evidence that Ferrer was the bogey player of Lopez from 2005-2009 based on a statistically significant number of unexpected losses by Lopez according to betting odds. Further work is suggested to improve the methodology.

1. 1
The Bogey Phenomenon in Sport
Rory Bunker
Behavior Signal Processing Laboratory (Sports Behavior Group)
Graduate School of Informatics
Nagoya University, Japan
IX Mathsport International Conference
11 - 13 July 2022

2. 2
Introduction
• Loosely speaking, bogey teams (team sport) or bogey players (in
individual sports) tend to beat a particular opposition (the non-
bogey) despite seemingly being weaker ‘on paper’.
• Whether bogey teams/players exist has been the subject of
much debate — particularly among sports fans and media.
• The concept has been briefly mentioned in fields including
education [Bruce‘14] and sociology [Chiweshe’18] [Poulton‘04].
• However, the topic has received very little attention in the
sports science and sports statistics literature.
• In this study, a method is proposed that combines:
• The Wald-Wolfowitz Runs Test (WWRT), a non-parametric
test for randomness in a two-valued sequence
• An unexpected (upset) result identification result method
that uses betting odds and actual results as its key inputs

3. 3
Examples
• In football, Manchester United is considered the bogey team of
Newcastle United.
• Watford has not beaten Manchester City since 1989 (although
note that this does not imply that Manchester City is their bogey
team, since Watford may have been expected to lose on each
occasion).
• Some are considered to exist at specific competitions:
– Portugal being the bogey team of England in football world
cups
– England and Argentina are the respective bogey teams of
Australia and France at rugby world cups
• In this study, the focus is on bogey players in tennis, which has
had less media attention than football but is more
straightforward to analyse (only has 2 possible outcomes).

4. 4
Related areas of research
• Related areas of study include studies on the hot-hand
effect and streaks in sports.
• Streaks can include:
– Individual player actions: e.g., successful 3-pointers in
basketball
– Team-level outcomes: e.g., a team’s run of
consecutive wins at their home venue
• Concept of positive recency: tendency to predict future
outcomes to be the same as previous outcomes.
[Ayton & Fischer ‘04], see [Bar-Eli+’06] for a review

5. 5
Definition
Defining a bogey player
A player who performs consistently better than would be
expected against a specified opposition (the non-bogey
player) over a certain period, given factors including the
difference in rankings, recent form, court surface, etc.
• This definition implies that the bogey phenomenon exists
between pairs of players, similar to pairwise comparisons (e.g.,
the Bradley-Terry model).
• It also suggests that there is a temporal element to the
phenomenon — it may exist for some period of time but not for
other periods.
• Incorporating betting odds into the method (next slide) means the
factors that are underlined in the above definition do not have to
separately be included.

6. 6
Benefit of using betting odds
• Betting odds incorporate many different factors including
strength, venue, form, and — in the case of team sports — player
availability, etc.
• The average odds, taken across multiple bookmaking companies,
will have greater reliability (the dataset in this study includes
average odds from oddsportal.com).
Venue
Form
Strength
…
Betting
odds
• So, betting odds can be used as a single variable in the method
rather than needing to include these different variables separately.
…

7. 7
Materials & Methods
Dataset
• Publicly available data from professional men’s tennis from
tennis-data.co.uk is used — the same as used by [Angelini+22]
• The dataset contains 38,868 matches from 4 July 2005 - 22
November 2020 and contains data including:
– All ATP tour matches from Master’s, ATP finals and Grand
Slams (Men’s ATP)
– Average bookmaker odds (oddsportal.com)
• The final number of matches was 33,976 after passing the dataset
through the clean() function in the welo R package [Angelini+22].
38,868
matches
33,976
matches
clean()
Data Data_Clean

8. 8
Materials & Methods
Wald-Wolfowitz Runs Test (WWRT)
• The WWRT has been used by several researchers in sports statistics,
e.g., in basketball [Arkes & Martinez‘11], [Koehler & Conley’03],
[Vergin‘00].
• It is a non-parametric test for randomness in a two-valued sequence.
• The test considers runs, which are successions of symbols followed
or preceded by different symbols. Players with:
– many lengthy streaks => fewer runs
– many alternating wins & losses => many runs
• The WWRT considers:
– the distributions of streaks of different lengths based on the
number of runs
– compares it to the distribution that would be expected if
successive outcomes were independent.

9. 9
Materials & Methods
Wald-Wolfowitz Runs Test (WWRT) — Example
Suppose there is a two-valued sequence:
+ + + - - - + + -
Let:
n = # of positive values in the sequence,
m = # of negative values in the sequence, and
R = # of runs in the sequence
In this case, we have n = 5, m = 4, R = 4.
H0 is that each element in the sequence is independently drawn
from the same distribution.
Run1 Run2 Run3 Run4

10. 10
Materials & Methods
WWRT — Expected number of runs & Z-test
The Z-statistic is calculated as
(the p-values can be easily calculated using statistical software)
where the expected number of runs and variance of R is
respectively.

11. 11
Materials & Methods
Two players, A & B have played each other T times in the past.
1) Construct a historical result set, HR, which consists of upset
‘Us’ and non-upset results ‘Ns’.
for t ∈ T
2) Construct an upset result type set, UR, which consists of the
types of upset results — upset wins (UWs) & upset losses (ULs).
but
Note that
A was expected to win based on the
betting odds-implied probabilities
But B won
the match
Unexpected (upset) Result Identification
O = odds
S = sets won
for t ∈ T

12. 12
Materials & Methods
Approach Flow
• The WWRT is firstly applied to the historical result set (HR)
• Then, if the result is statistically significant (and # runs > 1),
we check the upset result set (UR)
Apply
WWRT
to UR

13. 13
Andy Murray vs Roger Federer
• A Sydney Morning Herald article from 2013 suggested that Roger
Federer was the bogey player of Andy Murray—but specifically at
Grand Slam tournaments.
• In each of these examples, the date that the article was
published is important and is used to subset the original dataset.
https://www.smh.com.au/sport/tennis/its-murray-v-djokovic-20130125-2dcuv.html

14. 14
Andy Murray vs Novak Djokovic
• A forum comment on menstennisforums.com from May
2011 suggested that Andy Murray was the bogey player
of Novak Djokovic
https://www.menstennisforums.com/threads/will-nadal-be-able-to-reach-the-rg-
final.182597/?u=36369

15. 15
Kei Nishikori vs. Jo-Wilfried Tsonga
https://www.heraldsun.com.au/sport/tennis/jowilfried-tsonga-hopes-to-avoid-australian-
open-bogey-kei-nishikori/news-story/2dfaab3f641494447405ae65fc7e7592
• A Herald Sun Article from 2017 suggested that Kei Nishikori
was the bogey player of Jo-Wilfried Tsonga.

16. 16
Results
• WWRT could not be run in this case (division by zero)
• However, it is clear that the bogey phenomenon does not exist
between Federer and Murray at Grand Slams.
Murray vs. Federer

17. 17
Results
• When WWRT was applied to the HR set, a one-
tailed p-value = 0.148 > 0.05 was obtained
• Therefore, no bogey effect existed between Murray
& Djokovic during the period considered
Murray vs. Djokovic

18. 18
Results
• Applying WWRT to the HR set resulted in a p-value = 0.032 <
0.05, so proceed to the next step
• The UR set has three upset wins to Nishikori and two upset
wins to Tsonga
• If we run WWRT, but this time on UR, we get p-value = 0.063
Nishikori vs. Tsonga
Apply
WWRT
to UR
set

19. 19
Next Steps
Avenues for further work
• Use k-category extension of WWRT (with k = 3).
– This will enable the set consisting of upset wins, upset
losses and non-upset results to be analysed at the same
time rather than in two steps.
• Investigate other approaches apart from WWRT:
– Autocorrelation tests
– Entropy [Zhang+13], which was used to analyze winning
streaks in NHL Ice Hockey [Steeger+21].
• Apply to other sports and compare whether the existence of
the bogey phenomenon differs across sports.
• Correction procedures, e.g., Bonferroni-Holm, if a larger
number of statistical tests are performed.

20. 20
Code
GitHub Repository
https://github.com/rorybunker/bogey-phenomenon-sport
• The version of the method discussed in this presentation is
implemented in python in bogey_identification_tennis.py.
• The dataset is also available in CSV format.
• A new version is being created,
bogey_identification_tennis_v2.py, which uses a k = 3
category runs test (which can be applied to 3-valued
sequences).

21. 21
Thank You
Acknowledgements:
KAKENHI 20H04075, JST Presto JPMJPR20CA

22. 22
Appendix

23. 23
Example Output
==== STEP 2 RESULTS ====
Upset results set (UR):
Date Result
2005-08-27 UL
2006-10-12 UL
2007-10-05 UL
2007-10-17 UL
2008-03-06 UL
2008-10-15 UL
2009-04-14 UL
Number of UWs: 0
Number of ULs: 7
0.0% of upset results were UWs
100.0% of upset results were ULs
0.0% of matches were UWs
43.75% of matches were ULs
Ferrer D. vs. Lopez F.
==== STEP 1 RESULTS ====
Historical results set (HR):
Date Result
2005-08-27 U
2006-10-12 U
2007-10-05 N
2007-10-17 U
2008-03-06 U
2008-10-15 U
2009-04-14 N
2011-04-13 N
2011-10-15 N
2012-04-27 N
2013-05-31 N
2014-02-27 N
2015-10-04 N
2016-05-28 N
2016-10-11 U
2017-06-01 U
Wald-Wolfowitz Runs Test
Number of runs: 5
Number of Ns: 9; Number of Us: 7
Z value: -2.039650254375284
One tailed P value: 0.020692586443467945; Two tailed P
value: 0.04138517288693589