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Analysis of the best of five games of 11 points scoring system in singles badminton matches

Authors:
  • Hong-Ik Univ, Korea
Hyunsuk Yang, Wone Keun Han, & Dongwook Park*
College of Engineering, Hongik University, Seoul, Korea
Abstract
A model based on the probability of the server winning the rally was employed to evaluate the
influence of the newly proposed scoring system, the best of five games of 11 points scoring system,
being experimented by the Badminton World Federation on singles badminton matches. The model, based
on the assumption of statistical independence on each point’s outcome, was used to generate predictions
ranging from the game- and match-winning probabilities to game- and match-length statistics for matches
under both the new and the current scoring system, the best of three games of 21 points. Validity of
these results was checked against tournament data, four sets each for the two scoring systems, as well as
previously published results, with satisfactory agreement in most cases. The results show that duration of
singles matches would be reduced noticeably under the new scoring system without affecting the match
outcome of the current scoring system.
Key words: Badminton, scoring system, singles, probability model
Badminton is a sport enjoyed by millions around the
world, and over the years, it has gone through several
changes in scoring system regarding how a game or a
match is to be won. In recent years, the changes were
implemented, first under the auspices of the International
Badminton Federation (IBF), and then later Badminton
World Federation (BWF), in order to adapt the game’s
characteristics to fit in with the changing times (Wikipedia,
2015). Most recent major overhaul of the rules was
implemented in 2005 by the BWF in the form of a best of
three games of 21 points scoring system (321 format). In
an attempt to make the playing time even shorter and more
predictable (BWF, 2014a), the BWF decided in 2014 to
Submitted : 10 October 2016, revised: 24 November 2016
accepted : 29 November 2016
Correspondence : dwpark@hongik.ac.kr
test a new rule, instating it in the BWF law of badminton
(BWF, 2015) as one of the alternative scoring systems.
Under this rule, a match would be decided by a best of
five games of 11 points scoring system (511 format),
with each game concluding at 11 points without a deuce or
setting feature (BWF, 2014b). There have even been
tournaments held under the experimental rule (BWF,
2014b) and some feedback from the players, trainers and
fans in general on the new rule (Badzine, 2014).
A number of research have been performed in the past
regarding the overall effects of rule changes in badminton
and also other sports. Arias, Argudo, and Alonso (2011)
presented a review of 139 studies dealing with rule modification
in various sports, with an emphasis on classification of the
studies. Wright (2014) gave a survey and an analysis of
numerous articles covering competition rules in 21 different
sports, focusing on the analytical methods employed and
International Journal of Applied Sports Science
s
ISSN 2233-7946 (Online)
2016, Vol. 28, No. 2, 226-234. ISSN 1598-2939 (Print)
Korea Institute of S
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Analysis of the best of five games of 11 points scoring system in singles badminton matches 227
on issues of fairness and consequences of rule changes.
There have also been published results on more specific
influences of badminton rules changes on the temporal and
notational aspects. Ming, Keong, and Ghosh (2008), for
example, performed a time motion and notational analysis
of 21-point and 15-point badminton match play for singles
and found that the total number of shots and rallies in a
match were significantly affected. Laffaye, Phomsoupha,
and Dor (2015) analyzed the characteristics of six Olympic
badminton men’s singles finals that were played under
three different scoring systems through a longitudinal study
and found a significant increase in the shot frequency but
a substantial decrease in the effective play time and work
density over the years. Some of the noteworthy work in
the past involving modelling of a match with a
probabilistic approach have focused on topics such as the
game-winning probability based on combinatorics under
the 21-point-game-with-setting rule (Hsi & Burych, 1971),
advantages/disadvantages of serving first in men’s doubles
under the ‘old’ rule (15-point game with side-out) (Marcotte,
1989), optimization of service type over the course of a
singles match under the 321 format (Bedford, Barnett, &
Ladds, 2010), and a simple analysis of the 321 format
without including the serve effect (BadmintonCentral.com,
2010). Perhaps the most comprehensive work to this date
is the article by Percy which addressed various issues
pertaining to the rule change from the ‘old’ (315 format
with side-out) to ‘current’ (321 format without side-out)
systems (Percy, 2008).
In this paper, we present a direct comparison between
the current 321 format and the experimental 511
format in regard to their influence on singles matches by
using a probability model taking into account the service
effect. Our analysis will focus on highlighting the game-
and match-winning probabilities and also game- and
match-lengths - as represented by the number of points
played - associated with singles matches under the two
respective scoring systems. It is hoped that the results of
our study would help shed some light on how the 511
scoring system fares against the 321 format in the
context of preservation of the match outcome characteristics
and also effects on match-lengths. The significance of such
an effort lies in that the BWF-sanctioned 511 format
may be able to offer a viable option for managing
badminton matches and tournaments, with the important
advantage of requiring less time.
We assume that the outcome of each point is a
statistically independent and identically distributed event,
which is determined solely by the point-winning
probability associated with the server, taken to be constant
throughout the course of a match. It is generally true that
the outcome of each point, game, and even matches can
depend on the previous outcomes as well as the current
score, thereby making these events correlated to varying
degrees in many cases. In spite of this, we have decided
to employ the statistical independence assumption because
incorporating such statistical dependences into the model is
a very complex task and we wanted to focus on the direct
consequences of the rule change instead. Thus, the model
for a singles match is completely characterized by two
parameters p1 and p2, each representing the probability that
Player A or Player B wins the corresponding rally point
when he or she has the serve. Let P(m,n,x) represent the
probability that the score of the on-going game is m:n
(Player A: Player B) with the ensuing serve belonging to
Player x (x = 1, 2 for Players A, B, respectively) in a
game first started with Player A’s serve. The recursive
relations appropriate for calculations of P(m, n, x) are as follows:
P(m,n,1) = P(m-1,n,1)*p1 + P(m-1,n,2)*(1-p2)(1)
P(m,n,2) = P(m,n-1,1)*(1-p1) + P(m,n-1,2)*p2(2)
where the initial conditions are such that P(0,0,1) = 1 and
P(0,0,2) = 0 for Player A having the first serve in the
game. This approach has also been used by several in the
past (Bedford, Barnett, & Ladds, 2010; Brown, Barnett, &
Pollard, 2008). Beginning with the first serve of the game,
various running-scores and the associated probabilities of
228 Hyunsuk Yang et al.
occurrence are generated in this manner as each additional
rally point is played.
For each game, there are four different possible cases to
consider depending on the first server and the game winner.
Let P1(2)game denote the probability that Player A(B) is the
winner, given that Player A starts the game, and Q1(2)game
the probability that Player A(B) is the winner, given that
Player B starts the game. Note that P2game = 1 - P1game and
Qgame = 1- Q1game. Under the 511 format, the first player
to reach 11 points wins the given game regardless of the
final margin. Thus,

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. Meanwhile, under
the 321 format, the first player to reach 21 points, with
the margin of at least two, wins the given game. In the
event that the score reaches a 20-all tie, the players play
by the deuce rule, in which the first to lead the opponent
by two points takes the game, unless the score becomes
29-all wherein the winner of the next point, i.e., the first
to reach the 30-point mark, wins the game (22:20, 23:21,
..., 30:28, 30:29). Therefore, the probability of Player A
winning the game can be calculated by summing over the
probabilities of all possible cases, namely P(21,n,1) (n =
0,1,,19), P(m,m-2,1) (m = 22,23,,30) and P(30,29,1).
Q1(2)game can be obtained in a similar fashion.
Meanwhile, once the probability distribution of the
game-ending scores is obtained as described above, it is
straightforward to calculate the probability distribution of
the total number of points (N = m + n) played in the
game. The mean and standard deviation of N, which are
related to the average and fluctuation of the game duration,
respectively, can then be calculated in a simple manner,
In both formats, the initial server of the first game is
randomly determined, but thereafter, the winner of the
previous game is awarded the first serve of following
game. Here, it shall be assumed that each game is
statistically independent, aside from the initial serve
consideration just mentioned.
Let us first take the 321 format, in which the
match-ending score must be either 2-0 (two-games-to-zero)
or 2-1 (two-games-to-one) in favor of the winning player.
The winning player must take the first two games in
straight fashion in the 2-0 scenario (WW) and win one of
the first two games and the last game, i.e., the third, in the
2-1 scenario (LWW or WLW). Thus, the probability of
Player A winning by the first scenario is either P1game ×
P1game (when A serves first) or Q1game× P1game (when B
serves first), depending on the first server. The probability
of Player A winning via the second scenario is P1game ×
P2game × Q1game + P2game × Q1game × P1game (when A serves first)
or Q1game × P2game × Q1game + Qgame × Q1game × P1game (when
B serves first). The possible match-winning scores under
the 511 format are 3-0, 3-1 and 3-2, with one (WWW),
three (WWLW, WLWW, LWWW) and six sub-scenari os
(WWLLW, WLWLW, WLLWW, LWWLW, LWLWW,
LLWWW) in each respective case. The match-winning
probability associated with each (sub-)scenario can be
computed in a manner similar to that of the 321 format,
with the exception of having to use this time the
game-winning probabilities P1game, P2game, Q1game, and Qgame
derived earlier for the 511 format. The overall
match-winning probability for a given player can then be
determined simply by adding the probabilities for all
possible sub-scenarios in each format.
In the process of evaluating the match-winning
probability as described above, it is possible to obtain the
mean and variance of N, the total number of points in a
match, associated with a particular match-winning scenario.
By taking a weighted average of these quantities over all
possible sub-scenarios, the overall expected values are
derived.
Analysis of the best of five games of 11 points scoring system in singles badminton matches 229
Three sample values of p1 (= 0.4, 0.5, 0.6) were chosen
to demonstrate and distinguish the characteristics of the
game under the 321 and 511 formats, while the value
of p2, the corresponding probability of the opponent, was
allowed to vary between 0 and 1 to account for
possibilities of encountering an opponent of all skill levels.
Before proceeding with presentation of the calculation
results, it should be pointed out that the results of the
previous works for the 321 format (Bedford, Barnett, &
Ladds, 2010; BadmintonCentral.com, 2010; Percy, 2008)
were reproduced exactly with our model when a direct
comparison was possible. Figure 1 displays the game-winning
probability of Player A, under the 511 and 321
formats, respectively, for the three different values of p1
(= 0.4, 0.5, 0.6). Clearly, the general trends between the
two sets of curves are quite similar. As the value of p2 is
increased from 0 toward p1, P1game decreases from 1, slowly
at first and then more rapidly to 0.5. P1game continues to
decrease toward 0 as p2 approaches 1, showing a
saturation-like behavior near the end region. This general
trend is more pronounced for the cases of the 321
format compared to those of the 511 format, which can
be attributed to the fact that longer games of the former
format enhance the skill-level discrepancy between the two
players.
Figure 2 shows the match-winning probability of Player
A under the 511 and 321 formats for p1 = 0.4, 0.5,
0.6. The match-winning probability curves are more
saturated, i.e., flatter, in the end regions and steeper near
the p1 = p2 location compared to the game-winning
probability counterparts. The most important development
is that the difference of match-winning probability under
two different game formats has been drastically reduced
across the entire range of p2, compared to the game-winning
probability curves of Figure 1. Apparently, over the course
Figure 1.
The first server’s game-winning probability unde
r
two different scoring systems (the solid lines are
for the 5
11 format and the broken lines are
for the 3
21 format). The dependence on the
opponent’s point-winning probability p
2
is shown
for three different values of the first server’
s
p
robabilit
y
p
1
.
Figure 2.
The first server’s match-winning probability unde
r
two different scoring systems (the solid lines are
for the 5
11 format and the broken lines are for the
3
21 format). The dependence on the o
ponent’
point-winning probability p
2
is shown for three
different values of the first server’s
p
robabilit
y
p
1
.
of a match spanning more than one game, the differences
due to the different scoring systems largely disappear,
causing the match-winning probabilities for the two scoring
230 Hyunsuk Yang et al.
systems to converge toward each other.
In the upper portion of Figures 3(a) and 3(b), the
average number of points in a game is displayed for three
different values of p1 under the two formats, again
assuming that Player A serves first. In all figures, the
average number of points in a game peaks in the vicinity
of p1 = p2 - due to the evenly-contested nature of play
(leading to longer games) - and falls off - albeit in an
asymmetric manner - as the disparity between the two
players grows. Also, note that both the peak and mean
(averaged over p2) values of the average number of points
are slightly higher for the p1 = 0.4 cases. This is so
because when both p1 and p2 are low, e.g., in the case of
p1 = 0.4 and p2 = 0.38 ~ 0.39, serves are expected to
change hands more frequently as the server is more likely
to lose the point than win it, thereby leading to a longer,
see-saw type of game. If both p1 and p2 are high, on the
other hand, as in the case of p1 = 0.6 and p2 = 0.59 for
example, servers are expected to retain their serve longer,
making it more likely to be able to string together
consecutive points and leading to shorter games. The
standard deviation of the number of points played in a
game is displayed in the lower portion of Figures 3(a) and
3(b), respectively, for the three p1 values. Note that the
standard deviation curve does not fluctuate much with p2
for all three p1 cases under both formats, remaining in the
2 ~ 3 and 4 ~ 5 ranges, respectively, for the most part,
which represent only a small fraction of the average
number of points in a game.
Next, the behavior of the average number of points in
a match is displayed in the upper portion of Figures 4(a)
and 4(b) for various combinations of p1 value and scoring
format. It is seen that the average number of points per
match is considerably lower under the 511 format
compared to the 321 results across the board. The
average number of points for a match ranges from 62 ~ 78
for the 511 format and from 75 ~ 97 for the 321
format, considering only the 0.4 ~ 0.6 range for p2.
Finally, the standard deviation curves are shown in the
lower portion of Figures 4(a) and 4(b). The curves exhibit
a broad peak region in the 15 ~ 16 range for the 511
format and a substantially narrower peak region -
indicating less sensitivity to p2 variation - in the 19 ~ 20
range for the 321 format, respectively.
Figure 3.
The average and standard deviation of the numbe
r
points played in a game (a) under the 5
11
format and (b) under the 3
21 format. They are
shown as a function of the opponent’s point-winnin
g
probability p
2
for three choices of p
1
(solid lines
are for p
1
= 0.4, dashed lines for p
1
= 0.5,
dotted lines for
p
1
= 0.6
)
.
Analysis of the best of five games of 11 points scoring system in singles badminton matches 231
Figure 4.
The average and standard deviation of the numbe
r
points played in a match (a) under the 5
11
format and (b) under the 3
21 format. They are
shown as a function of the opponent’s point-winnin
g
probability p
2
for three choices of p
1
(solid lines
are for p
1
= 0.4, dashed lines for p
1
= 0.5,
dotted lines for
p
1
= 0.6
)
.
Our model, as mentioned earlier, is very simple, and as
such, it is imperative to check the predicted results against
actual data of relevance in order to gain a measure of
validation. In order to compare our calculation results
against actual badminton matches, we analyzed a sample
of tournament data available from a website (Tournament
Software (http://www.tournament software.com)). While
the tournament data cannot provide a direct means of
verifying the predictions of game- and match-winning
probabilities calculated from our model, it may still be
possible to make some comparisons regarding the game-
and match-length statistics under a reasonable set of
assumptions.
Over the period of August 2014 to November 2014, 21
international tournaments (including 12 junior events)
sanctioned by BWF were held using the 511 format
(BWF, 2014b). Of these, men’s singles (MS) and women’s
singles (WS) match results from four selected events
representing various competition levels, geographical areas
and calendar dates were used as sample data. The data
from 264 MS and 163 WS match results were used for
comparison against the results from our calculation. We
calculated the average and the standard deviation for the
number of games per match, number of points per match,
and the match duration (in minutes). For comparison, we
also selected four tournaments with similar attributes that
employed the conventional 321 format, and the statistics
of 273 MS and 138 WS matches played in those
tournaments were analyzed.
The statistics regarding the match duration in minutes
cannot be directly compared against our model, as the
number of strokes or the time required to complete a rally
is not incorporated in the model. However, it may still be
possible to make a comparison between the tournament
and model data regarding the statistics of the number of
games per match and the number of points played per
match under the following assumptions. One, the skill
levels of the players that participated in the aforementioned
tournaments span a certain range, which corresponds to the
point-winning probability range of 0.3 ~ 0.7 in our model,
and two, the probability distribution is uniformly
distributed within that range. The range of 0.3 ~ 0.7 seems
reasonable since it is expected that completely lop-sided
matches are rather unlikely in competitive international
matches. Under these assumptions, calculations can be
232 Hyunsuk Yang et al.
made within our model for all cases within the probability
grid of 0.3 < p1, p2 < 0.7 and the results averaged, which
can then be compared against the tournament statistics.
The results for the 511 and 321 formats are
summarized in Tables 1 and 2, respectively. Under the
511 format, the average number of games per match
shows a range of 3.61 ~ 3.74 for MS matches and 3.29 ~
3.57 for WS matches (with the standard deviation in the
0.63 ~ 0.75 range) compared to 3.78 ± 0.72 for our
calculation result. The corresponding ranges are 2.15 ~
2.35 for MS matches and 2.30 ~ 2.38 for WS matches
(with the standard deviation in the 0.36 ~ 0.49 range)
under the 321 format, respectively, compared to 2.30 ±
0.42 of our calculation. The average number of points per
match spans the range of 62.20 ~ 66.79 points for MS
matches and 54.42 ~ 64.26 for WS matches (with the
standard deviation in the 13.12 ~ 16.90 range) under the
511 format and 73.64 ~ 83.14 for MS matches and
79.06 ~ 86.04 for WS matches (with the standard deviation
in the 16.60 ~ 21.44 range) under 321 format. The
corresponding theoretical results, on the other hand, are
67.11 ± 14.22 and 81.95 ± 16.23, respectively. Thus, it
appears that there is a fairly good agreement between the
tournament and the analysis data. Also, note that the
average match time is considerably shorter - by more than
several minutes in most cases - for the 511 tournaments
for both MS and WS matches, whereas the difference in
the match time fluctuation between the two sets of
tournaments is generally only a couple of minutes or less.
The fact that the match-durations are significantly shorter
in the 511 tournaments may be of paramount interest
from a tournament organizer standpoint as there should be
more flexibility and margin of error in scheduling the
matches and managing the tournament.
Yonex Dutch Open
(Grand Prix)
Brazil International
Badminton Cup
(Int. Challenge)
Fernbaby Auckland
International
(Int. Series)
Bulgaria Eurasia Open
(Future Series) Our
Calculation
<MS > < WS >< MS >< WS >< MS >< WS >< MS >< WS >
No. of games 3.73
±0.75 3.57
±0.74 3.72
±0.73 3.29
±0.64 3.61
±0.72 3.52
±0.68 3.74
±0.75 3.38
±0.63 3.78
±0.72
No. of points 66.45
±15.55 64.26
±14.97 64.99
±16.27 54.42
±15.92 62.20
±16.52 59.00
±16.90 66.79
±15.56 59.78
±13.12 67.11
±14.22
Match length
(min.) 30.52
±9.96 29.40
±10.14 34.10
±11.64 27.04
±10.72 26.82
±10.89 24.10
±10.21 29.62
±9.78 26.20
±8.13
Table 1.
Summary of match length statistics under the 5
11 format
Scottish Open
(Grand Prix) Lagos International
(Int. Challenge)
OUE Singapore
International Series
(Int. Series)
Yonex Riga
International
(Future Series)
Our
Calculation
< MS >< WS >< MS >< WS >< MS >< WS >< MS >< WS >
No. of games 2.35
±0.48 2.32
±0.47 2.15
±0.36 2.30
±0.47 2.26
±0.44 2.30
±0.46 2.29
±0.46 2.38
±0.49 2.30
±0.42
No. of points 83.14
±20.08 82.27
±18.96 73.64
±16.60 79.06
±21.44 78.35
±20.22 79.60
±19.67 79.96
±20.36 86.04
±20.83 81.95
±16.23
Match length
(min.) 38.61
±14.00 36.12
±10.84 30.63
±13.02 27.78
±10.15 32.67
±11.95 33.58
±12.35 35.98
±11.10 36.43
±9.76
Table 2.
Summary of match length statistics under the 3
21 format
Analysis of the best of five games of 11 points scoring system in singles badminton matches 233
At this point, we would like to address the issue of the
‘first-serve’ effect, namely whether and if so when it is
advantageous to be the first server in the game. Although
the results are not included here, it can be shown that the
game-winning probability is greater for the first server,
provided pj > 1- pi, where pi and pj are the point-winning
probabilities of the first server and first receiver,
respectively. The first server is also at an advantage when
two players of identical skill-levels with p1 (= p2) > 0.5 are
facing each other, which might require a counter-measure
of some sort to offset such bias. These first-serve effects,
though inherent in both scoring formats on game and
match levels, are generally more pronounced for the 511
cases due to the fewer number of points involved.
The experimental 511 scoring system appears to offer
an attractive alternative to the current 321 counterpart
based on the analysis presented in this paper. Results were
generated based on the probabilistic analysis of a
two-parameter model and partially validated by a statistical
analysis of data from eight tournament results. The
findings suggest that singles matches would tend to be
completed in less number of points and time under the
511 format, with the characteristics of the match
outcome hardly changed from those of the current 321
format. To wit, the new rule is more forgiving - less
sensitive - to the player’s skill-level difference insofar as a
single game’s outcome is concerned, but the eventual
match winner is highly unlikely to change, even under the
new rule. The variation of the match length, on the other
hand, is not expected to decrease noticeably under the
511 system. At least from the quantitative standpoint
then, these preliminary findings imply that singles matches
in the trial format might perhaps be more exciting to watch
from the viewers' perspective and more appealing to
tournament organizers and broadcasting partners. Shorter
matches would mean that the viewers would be able to
concentrate on the matches more while the tournament
organizers would be able to schedule more matches in a
given time duration and/or with more room to cope with
late-running matches. We conclude with a remark that the
analysis presented here represents only a first attempt at
predicting the potential consequences of the scoring system
change, and possible impact on other aspects of the game
need to be examined as well for a more complete
assessment.
This work was supported by the Hongik University
Research Fund.
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Wright, M., (2014). OR analysis of sporting rules - a survey.
European Journal of Operational Research, 232(1), 1-8.
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Article
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The goal of this study was to analyze, through a longitudinal study, the Olympic Badminton Men’s singles finals from the Barcelona Games (1992) to the London Games (2012) to assess some changes of the Badminton game characteristics. Six Olympic finals have been analyzed based on the official video of the Olympic Games (OG) through the temporal structure and with a notational approach. In total, 537 rallies and 5537 strokes have been analyzed. The results show a change in the game’s temporal structure: a significant difference in the rally time, rest time and number of shots per rally (all p < 0.0001; 0.09 < Ƞ² < 0.16). Moreover, the shot frequency shows a 34.0% increase (p < 0.000001; Ƞ² = 0.17), whereas the work density revealed a 58.2% decrease (from 78% to 30.8%) as well as the effective playing time (-34.5% from 34.7±1.4% to 22.7±1.4%). This argues for an increase in the intensity of the game and a necessity for the player to use a longer resting time to recover. Lastly, the strokes distribution and the percentage of unforced and forced mistakes did not show any differences throughout the OG analysis, except for the use of the clear. This results impact on the way the training of Badminton players should be designed, especially in the temporal structure and intensity.
Article
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The purpose of this study was to investigate and compare the time motion and notational variables of 21 point singles' badminton play and of the old scoring system (15 points for males and 11 for females). Sixteen (8 males and 8 females) state-level badminton players with a mean age of 15.7 ± 1.2 years participated in this study. They were initially tested using incremental treadmill test following Bruce protocol to obtain individual maximum oxygen consumption (VO2max) value. VO2max of the male and female participants were 47.1 ± 5.2 ml·kg-1·min-1 and 39.8 ± 6.2 ml·kg-1·min-1 respectively. On a separate day, they played a simulated badminton match using 21 points (Trial 1) and 15 / 11 points (Trial 2) scoring system. During the trials, a video camera was used for time-motion and notational analysis throughout the match. The statistical analysis showed that total number of shots and rallies in a match were the only variables which were significantly higher in the 15 points compared to 21 points in men's singles match play (331.2 ± 51.6 vs 463.5 ± 24.7 (total shots) and 70.2 ± 1.2 vs 97 ± 6.6 (total rallies) respectively). Even though female players had a greater point difference (10 points) in the new scoring system compared to the male counterparts, there were no significant differences in all parameters measured. The patterns of play which were analyzed on the basis of notational variables were also similar in both scoring systems. However, some differences in the time motion and notational analysis were found between genders suggesting that there should be different training regimens for men and women in their respective disciplines due to greater intensity, speed of play and the longer rally lengths in men's singles. Therefore, it is recommended that players should impart more emphasis in the development and improvement of the skills/techniques rather than making any drastic changes to the training programme to develop their physical fitness to meet the demands of the match with the 21 point scoring system.
Conference Paper
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In tennis the serve can be a most powerful weapon. However in badminton, the serve holds a much lower advantage in comparison to tennis, and for many players, yields a net disadvantage. Badminton"s most common service used is a short serve requiring accuracy, as opposed to a long serve requiring power. This is because badminton does not allow for the advantage of a second serve on fault of the first, someway explaining the conservative nature of serving, and low success probabilities. The short serve allows the receiver to gain the advantage, putting the server under pressure on the third shot. In this work, we develop a model to ascertain whether a player should be taking a high or low risk serve. Using Bayesian models, we hypothesize how a player"s performance could be optimized conditional on the state of the match in progress. Practical implications for players are discussed, given that the rules of badminton allow for coach intervention during a match in progress.
Article
This paper surveys the academic OR/analytics literature describing research into the laws and rules of sports and sporting competitions. The literature is divided into post hoc analyses and proposals for future changes, and is also divided into laws/rules of sports themselves and rules/organisation of tournaments or competitions. The survey outlines a large number of studies covering 21 sports in many parts of the world. The analytical approaches most commonly used are found to be various forms of regression analysis and simulation. Issues highlighted by this survey include the different views of what constitutes fairness and the frequency with which changes produce unintended consequences.
Article
Probability models on games involving two opposing players or teams are discussed with particular emphasis on the relative probability of a server in a play. Two examples (i.e. the tennis and badminton games) are presented. Several comments and suggestions are made regarding their game rules.
Article
The goal of this qualitative review was to analyze the state of the bibliography about rule modification in sport. In the literature reviewed, there are few studies of rule modification and related aspects. Most studies omit mentioning the purpose of the modifications, but they do refer to the goals of their analysis (improving players' performance, attracting spectators and athletes, attending to commercial pressure, adapting the sport to children's needs and interests, preventing injuries). Eighty percent of the studies did not report the outcome of the previous modifications they analyzed. More than half of the studies (60%) achieved the proposed goals. Nearly two-thirds (63.83%) analyzed the effect of rule modification on game actions occurring during the game or through a test. Most of the studies (91.5%) did not consult the participants. Three-fourths of the studies (74.46%) examined the effect of rule modification without any knowledge of a previous analysis or without any previous analysis, and 74.47% studied rule modification related to internal logic. Modifications to be introduced in a sport should be analyzed through a reflective process before their final introduction. The following points should be considered: establishing goals, respecting the basic rules without modifying them, becoming familiar with players' and coaches' opinions, determining the effect of the modification on a wide spectrum of variables, elaborating useful proposals for the organizations that are responsible for competitions, using more than one type of data, modifying the internal logic and, preferably, the functional rules, and following some basic stages to consolidate rule modification.
Article
The International Badminton Federation recently introduced rule changes to make the game faster and more entertaining, by influencing how players score points and win games. We assess the fairness of both systems by applying combinatorics, probability theory and simulation to extrapolate known probabilities of winning individual rallies into probabilities of winning games and matches. We also measure how effective the rule changes are by comparing the numbers of rallies per game and the scoring patterns within each game, using data from the 2006 Commonwealth Games to demonstrate our results. We then develop subjective Bayesian methods for specifying the probabilities of winning. Finally, we describe how to propagate this information with observed data to determine posterior predictive distributions that enable us to predict match outcomes before and during play.Journal of the Operational Research Society (2009) 60, 63-71. doi:10.1057/palgrave.jors.2602528 Published online 7 November 2007
BWF members forum: Scoring system
Badminton World Federation (2014a). BWF members forum: Scoring system. Retrieved from http://bwfbadminton. org/file.aspx?id = 555962&dl = 1.
Badminton win probability -from points to games
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BadmintonCentral.com (2010). Badminton win probability -from points to games. Retrieved from http://www. badmintoncentral.com/forums/showthread.php/88211-Badminton-Win-Probability-From-Points-to-Games.