=Paper=
{{Paper
|id=Vol-1971/paper-08
|storemode=property
|title=Honest Mirror: Quantitative Assessment of Player Performance in an ODI Cricket Match
|pdfUrl=https://ceur-ws.org/Vol-1971/paper-08.pdf
|volume=Vol-1971
|authors=Madan Gopal Jhawar,Vikram Pudi
|dblpUrl=https://dblp.org/rec/conf/pkdd/JhawarP17
}}
==Honest Mirror: Quantitative Assessment of Player Performance in an ODI Cricket Match==
https://ceur-ws.org/Vol-1971/paper-08.pdf
Honest Mirror: Quantitative Assessment of
Player Performances in an ODI Cricket Match
Madan Gopal Jhawar1? and Vikram Pudi2
1
Microsoft, India
majhawar@microsoft.com
2
IIIT Hyderabad, India
vikram@iiit.ac.in
Abstract. Cricket is one of the most popular team sports in the world.
Players have multiple roles in a game of cricket, predominantly as bats-
men and bowlers. Over the generations, statistics such as batting and
bowling averages, and strike and economy rates have been used to judge
the performance of individual players. These measures, however, do not
take into consideration the context of the game in which a player per-
formed. Furthermore, these types of statistics are incapable of comparing
the performance of players across different roles. In this paper, we present
an approach to quantitatively assess the performances of individual play-
ers in single match of One Day International (ODI) cricket. For this, we
have developed a new measure, called the Work Index, which represents
the amount of work that is yet to be done by a team to achieve its tar-
get. Our approach incorporates game situations and the team strengths
to measure the player contributions. This not only helps us in evaluat-
ing the individual performances, but also enables us to compare players
within and across various roles on a common scale. Using the player
performances in a match, we predict the player of the match award for
the ODI matches played between 2006 and 2016. We have achieved an
accuracy of 86.80% for the top-3 positions, which is superior to baseline
models and previous works, to the best of our knowledge.
Keywords: Cricket Analytics, Player Performances, Player of the Match
1 Introduction
Cricket is majorly played in three formats – Test, ODI and Twenty20 (T20),
with ODI being one of the most followed formats. An ODI is a form of limited
overs cricket, played between two teams where each team has a combination of
batsmen and bowlers making up to 11 players in total. Each team bats for a
maximum of 50 overs where an over is defined as a set of six deliveries bowled
by the bowlers of the opponent team. An ODI cricket match starts with a coin
toss and the Captain of the side winning the toss chooses to either bat or bowl
first. The team batting first sets the target score in a single innings, where the
?
This work was done when the author was a student at IIIT-Hyderabad.
2 Quantitative Assessment of Player Performances in ODI Cricket
innings lasts until the batting side loses all the 10 wickets, where a wicket refers
to a player getting out, or the batting side’s quota of 50 overs is completed. The
team batting second tries to score more runs than the target score in order to
win the match. Similarly, the side bowling second tries to take all the 10 wickets
of the opponent team or make them exhaust their overs before they reach the
target score in order to win.
In a game of cricket, the batsmen of one team play against the bowlers of
the other team, and vice-versa, in order to win the match. Therefore, evaluat-
ing the performances of individual players in a game of cricket becomes very
critical. It helps in segregating the players who are contributing to the team
from the ones who are failing to deliver on the ground. However, evaluating the
performances of players is not a straight-forward task. Traditionally, statistics
such as batting and bowling averages, and strike and economy rates have been
used to assess the performance of individual players. However, these statistics
fail to incorporate several important aspects of the game. Runs scored or wick-
ets taken under pressure at crucial stages are of more value as compared to
scoring more number of runs or taking more number of wickets. Furthermore,
assessing the overall performance of an individual cricketer requires a compre-
hensive evaluation of his contributions to the team, both in terms of his batting
and bowling contributions. However, combining and comparing the batting and
bowling performances of a player, on a common scale, is a challenging task and
often becomes a subjective decision.
Therefore, in this paper, we propose a methodology to quantitatively assess
the performances of individual players in a single game of ODI cricket match. We
introduce a new measure, called the Work Index, which represents the amount
of work yet to be done by a team to reach their expected target score. Work
Index incorporates several important aspects of a game, including the current
stage of the match, the progress so far as compared to the initial estimations,
the two competing teams’ strengths, etc. We measure the Work Index for both
the batting as well as bowling teams, namely, the Batting Work Index and the
Bowling Work Index. The former denotes the amount of work to be done by
the batting team to reach the target, while the latter represents the amount of
work to be done by the bowling team to restrict the batting team from reaching
the target. Using these two work indices, we calculate a contribution-score for
each player which incorporates his batting and bowling contributions towards
achieving the team’s overall goal.
Furthermore, akin to many other sports, the player of the match title is
awarded to the player who played the most significant role in a match of cricket.
Today, it is chosen by the match committee and the commentators which makes
it a subjective decision. Therefore, we propose a methodology to determine the
player of the match using the player contribution-scores calculated by our ap-
proach. We compare our model with previous works and other baseline models,
and the superiority of our model over others further proves the validity of our
approach.
Quantitative Assessment of Player Performances in ODI Cricket 3
2 Related Work
In literature, Duckworth and Lewis proposed a real-time measure to estimate
the amount of resources remaining with a team, called as D/L resources, as a
function of number of balls and wickets remaining. They further used the D/L
resources to reset targets in rain interrupted matches [1]. It is said to be one of the
most pioneering works in cricket analytics and was adopted by the International
Cricket Council (ICC) in 1998.
Pertaining to assessing player performance, Johnston et al. [4] used dynamic
programming formulation to develop a method of calculating the contribution,
in runs, made by each player to the team’s score in a game of one-day cricket.
Lewis [2] used Duckworth/Lewis methodology to create alternative measures of
player performances in a game of cricket. These measures take into account the
stages of innings when runs are scored or conceded and wickets are taken or lost.
Recently, Bhattacharjee et al. [5] proposed a measure of quantifying the pres-
sure, named as Pressure Index, on the teams batting or bowling in limited overs
cricket matches. They use D/L resources, as proposed in [1], ratio of the wick-
ets lost and the current as well as the initial required run rates to quantify the
pressure on a team. Further, they use the pressure index to access the individual
player performances in a specific match. However, the method could be used to
quantify the pressure on a team only for the second innings of a match, where
the batting team has a fixed target to chase. Also, their approach takes into
account the ratio of the wickets fell down instead of incorporating the varying
strengths of individual players. This is a very critical factor because teams do
not play with a fixed number of specialized batsmen. Losing 6 wickets has a
different impact on a team playing with 6 specialized batsmen as compared to a
team playing with 7 specialized batsmen. Furthermore, no quantitative method,
in any form, of validating the approach has been discussed.
Therefore, in this paper, we propose a new dynamic measure, called the
Work Index. Apart from the runs scored and balls bowled, the work index also
incorporates the potentials of the batsmen and bowlers who are remaining to
perform. In addition to this, with the use of D/L resources, we propose a method
which enables us to calculate the work index in the first innings also, where a
team does not have a fixed target to chase. We further use the work index to
quantitatively assess the player performances in a match and predict the player
of the match.
3 Methodology
Our methodology to assess the player performances for a given ODI cricket
match involves estimating a new measure, called the Work Index. Work Index
incorporates several crucial qualitative and quantitative aspects of the game.
The three parameters considered in calculating the work index are as follows:
– The progress, in terms of runs scored, towards chasing the set target.
4 Quantitative Assessment of Player Performances in ODI Cricket
– The current stand, in terms of scoring rate, of the batting team relative to
the initial estimations.
– The remaining batting and bowling potentials of the batting and bowling
teams, respectively.
The first and second parameters capture the quantitative aspects of the game
situation in terms of the runs scored and the required run rate as compared to
the initial required run rate for the batting team. On the other hand, the third
measure captures the quality of the batsmen and bowlers remaining for the
batting and bowling teams, respectively. Therefore, work index, a blend of these
features, captures the context at a given stage of the match.
3.1 Target Estimation in First Innings
Calculating the first and second parameters requires us to know the target score
the batting team is trying to achieve. In an ODI cricket match, the team batting
second has a predefined target, set by the opponent team, to chase in order to
win the match. On the other hand, the team batting first does not have a fixed
target to score. Ideally, the team would try to score as many runs as possible,
but there are limited resources in terms of the number of overs and wickets.
Therefore, at the start of the first innings, we estimate the target score to be the
average number of runs scored in the first innings of all the matches played in the
same country in the past, where the team batting first was able to successfully
defend their score. This estimated target score is further improved after every
ball is bowled as per Equation 1, depending upon the actual situation of the
match.
newT arget ← runsScored + DLrem ∗ initT arget (1)
where runsScored is the number of runs scored by the batting team at the
current stage of the game, DLrem is the ratio of the D/L resources remaining
with the team [1][7], and initT arget is the target estimated at the start of the
innings.
With a defined target score to achieve for both the innings, Equations 2 and
3 represent the mathematical formulation of the first and second parameters of
Work Index (as mentioned at the start of Section 3), respectively.
k ← runsRemaining/T arget (2)
r ← reqRunRate/initRunRate (3)
where runsRemaining, reqRunRate and initRunRate represent the number of
runs yet to be scored, the average number of runs required per over from the
current stage and the average number of runs require per over at the start of the
match, respectively, by the batting team to achieve its target score. The higher
values of k and r intuitively tell us that the batting team has a lot of work to
do to reach the target score, and vice-versa.
Quantitative Assessment of Player Performances in ODI Cricket 5
3.2 Modeling Players and Teams
Calculating the third parameter requires us to model the player and team poten-
tials for a given match. Therefore, as proposed in [3], we use the Batting Strike
Rate and Batting Average to calculate a player’s batting score, and Bowling
Strike Rate and Bowl Economy to calculate his bowling score, where Batting
Strike Rate is the average number of runs scored per 100 balls faced, Batting
Average is the average number of runs scored per innings, Bowling Strike Rate
is the average number of balls bowled per wicket taken, and Bowling Economy
is the average number of runs conceded per over by the player.
Further, we define the total batting score of a team to be the summation of
the batting scores of all of it’s players. And similarly for the total bowling score
of a team. However, at a given state of the match, some of the players from
the batting team would have got out and some of the players from the bowling
team would have bowled a part of their quota of maximum 10 overs (60 balls).
Therefore, we define the remaining batting score of the batting team as the sum
of the batting scores of only those players who haven’t got out yet. Similarly,
the remaining bowling score of the bowling team is calculated as the sum of all
the individual bowlers’ bowling scores, weighed by the ratio of number of balls
he has remaining to bowl in this match to the maximum number of balls he can
bowl in an ODI cricket match, i.e., 60.
Hence, with a defined method to estimate the total and remaining batting
and bowling potentials of the batting and bowling teams, respectively, Equations
4 and 5 represent the mathematical formulation of the third parameter.
b ← remBatScore/totalBatScore (4)
w ← remBowlScore/totalBowlScore (5)
Where totalBatScore and remBatScore represent the total and remaining
batting potentials of the batting team. And similarly for the totalBowlScore
and remBowlScore. The higher values of b and w tell us that the batting and
bowling teams have got good players to perform who can win the match for
them, respectively.
3.3 Work Index
Having formalized all the three parameters of work index, we will now explain
the Work Index in detail. Work Index is a dynamic measure which is updated as
the innings progresses and takes into account the current state of the match to
estimate the work yet to be done. With the help of variables defined in Equations
2, 3, 4 and 5, the batting and bowling work indices are calculated as per the
Equations 6 and 7, respectively.
battingWorkIndex ← 100 ∗ k ∗ (r + α ∗ (1 − b) + β ∗ w) (6)
bowlingWorkIndex ← 100 ∗ k ∗ (1/r + α ∗ b + β ∗ (1 − w)) (7)
6 Quantitative Assessment of Player Performances in ODI Cricket
600
500
400
Number of wickets
300
200
100
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Over
Fig. 1. Total number of wickets fell in each over in our dataset. As a game reaches its
final stages, the batsmen adopt a riskier strategy to score runs at a higher rate, with
less concern about losing wickets.
Variable k (defined in Equation 2), defined as the ratio of the runs remaining
to score with respect to the target, is used as a bias in calculating the work
index. The lower values of k, generally found at the end of the innings, directly
reduces the impact of the other factors in determining the work index. As it can
be seen from Figure 1, as a game reaches its final stages, the batsmen adopt
a riskier strategy to score runs at a higher rate, with less concern about losing
wickets. The value of a wicket reduces as scoring runs becomes the sole purpose.
Similarly, higher values of k, found at the start of the innings, boosts the impact
of other factors. This is because, at the initial stages of the innings, the wickets
of the batsmen carry a lot more importance. Losing early wickets at the start
of an innings puts the batting team into tremendous pressure, as they lose their
key batsmen and face the threat of getting all-out, before even completing the
quota of 50 overs. Variable r (Equation 3) captures how well is the batting team
scoring as compared to the initial estimations. It is directly proportional to the
batting work index, as increased required run rate, increases the amount of work
to be done, and similarly it is inversely propotional to the bowling work index.
Variables b and w (Equations 4 and 5) represent for the remaining batting
and bowling potentials of the corresponding teams. They account for the amount
of batting and bowling resources remaining with the batting and bowling teams,
respectively. Incorporating individual player’s skills into these variables enables
us to assess the current game scenario in a detailed way. They enable us to
capture those scenarios where a team has lost several wickets yet still has good
players remaining in the batting line-up, who can potentially change the game’s
Quantitative Assessment of Player Performances in ODI Cricket 7
direction. The parameters, α and β, represent the relative weightage of the re-
maining batting potential and the remaining bowling potential, respectively.
Also, bowlers have 300 balls to possibly get the batsmen out, whereas the bat-
ting team possesses only 10 wickets to score runs. Therefore, losing wickets has
significant impacts on the batting team. The values of the parameters, α and β,
have been discussed in the experiments Section 4.
In all, work index is a combination of many important aspects of the game
that enables it to capture the overall game scenario.
3.4 Player of the Match
Cricket is a game of bat and ball. Bowlers from the bowling team take turns in
overs to bowl their quota of 50 overs, where, in an over, one of the players from
the bowling team bowls 6 deliveries to the batsman at strike. We calculate the
Batting Work Index and the Bowling Work Index after each ball is bowled. The
difference between the two consecutive batting work indices is contributed to the
batsman who played the corresponding ball. Similarly, the difference between the
two consecutive bowling work indices is contributed to the bowler who bowled
the ball. We repeat this process for each ball bowled in the entire match. At
the end of the match, the scores attributed to an individual player represents
his all-round performance in the entire match. This score not only captures the
quantitative amount of runs scored or wickets taken by a player, but also the
context in which he made the contributions. Phrases like “Catches win Matches”
are very popular in the game of cricket and therefore, the fielding efforts of
players could also be integrated to capture the players’ overall contribution to
the match. However, we have tabled it for the future work as of now.
Furthermore, Player of the Match title is awarded to the player who played
the most significant role in a particular match. At first, it seems that the player
who has the maximum score at the end of the match should be awarded the player
of the match. However, player of the match award is almost always (95.83% of
the times) given to a player from the winning side. A player from the losing
side bags the player of the match award only if his performance is significantly
better than the others and has contributed to an almost win for the losing side.
Therefore, as of now, we choose the players from the winning side only as the
potential candidates for the player of match award. We rank them directly based
on their scores and the player with the maximum score is awarded the player
of the match. Note that some heuristics can be used to capture the very rare
player of the match awards from the losing side also. However, for now, we have
tabled it for future work.
4 Experiments and Results
We have studied all the ODI cricket matches played between 1st of January, 2006
and 30th June, 2016. Ball-by-ball data for each match has been taken from the
cricsheet database [8]. We have focused our study to only the top 9 ODI-playing
8 Quantitative Assessment of Player Performances in ODI Cricket
teams, namely, India, Australia, South Africa, England, Sri Lanka, Pakistan,
New Zealand, Bangladesh and West Indies. Since the impact of nature on the
game cannot be foreseen, a total of 216 matches which were either interrupted
by rain or ended up in a draw/tie, have been removed from the dataset. Finally,
we studied a total of 786 ODI cricket matches.
For the potential player of the match candidates, as discussed in Section
3.4, we consider only the players from the winning team. For a given match of
cricket, our model outputs a list of player ranked in the descending order of their
contribution in the match. Hence, to measure the efficiency of our model, we use
an exponential-ranking metric. For a given match, the match score is calculated
to be 1/2R−1 , where 1 ≤ R ≤ 11 is the rank at which the player of the match
has been predicted by our model. Therefore, the exponential-rank of our model
is calculated as the summation of the match scores for all matches. The choice of
an exponentially decaying metric over existing metrics such as Mean Reciprocal
Rank has been made to increase the penalty for wrong predictions, as there is
only one player of the match as compared to top-k relevant outputs.
With the defined accuracy metric, we use a validation set containing all the
matches played between January, 2006 and December, 2012 to find the most
suitable values of the parameters α and β, defined in Equations 4 and 5. Table
1 tabulates the exponential-rank of our model on the validation set for multiple
values of the parameters. As it can be seen, α = 2.0 and β = 1.5 yields the best
results. Therefore, these values will be considered for the further discussions.
Table 1. Exponential rank of Honest Mirror for multiple values of the parameters, α
and β, on the validation set. α = 2.0 and β = 1.5 yields the best results.
αβ 0.5 1.0 1.5 2.0 2.5
0.5 362.1 357.9 346.2 334.3 330.1
1.0 369.9 371.2 367.8 354.7 344.2
1.5 349.8 379.6 375.9 373.1 360.8
2.0 328.7 363.7 384.8 378.7 371.9
2.5 306.1 344.7 372.6 379.8 377.5
Accuracy (in %) for player of the match for the first 5 ranks are shown in
Figure 2. A decreasing curve proves that the players who are performing better
are placed higher in the rankings than the others. We have achieved 59.14%
accuracy for the first rank and an accuracy of 77.79% and 86.80% for the top
two and top three ranks respectively.
In literature, to the best of our knowledge, we could not find any previous
work on predicting the player of the match for ODI cricket matches. However,
Bhattacharjee et al. [5] proposed a model, the PI Model, to assess player per-
formances in a game of limited overs cricket match using pressure index, but
only for the second innings of a match. We extended their method for the first
Quantitative Assessment of Player Performances in ODI Cricket 9
innings by estimating the target score using the same approach as discussed in
Section 3, and add up the player’s batting and bowling contributions for both
the innings to calculate a player’s overall performance in a match. The players
from the winning team are considered to be the potential player of the match
in the order of their overall contribution in the match. We implemented their
work, to the best of our abilities, to compare their approach against our model.
70
60 59.14%
50
40
% Hits
30
20 18.65%
10 9.01%
3.81%
0 1.02%
1 2 3 4 5
Ranks
Fig. 2. Accuracy (in %) for player of the match for the first 5 ranks. A decreasing curve
proves that the players who are performing better are placed higher in the rankings
than the others.
Apart from that, in a game of cricket, the number of runs scored by a player
and the number of wickets taken by him are the two major criterion to judge a
player’s performance. Therefore, we further compared our approach with the two
following baseline models which take into account a player’s overall contribution
in a match–
– Model 1: The overall contribution of a player is the summation of the ratio
of the runs he has contributed to the teams total batting score and the ratio
of the wickets he has taken to the total of wickets taken by his team.
– Model 2: To be able to combine the runs scored and wickets taken by
a player, we map one of these into another, i.e., we calculate the weight
of a wicket taken by a bowler in terms of the runs scored by a batsman.
The weight of a wicket, denoted by ω, is calculated as the total number of
runs scored in the match divided by the total number of wickets fell down.
Therefore, the total contribution of a player in a match is the summation of
the number of runs scored by him and ω times the number of wickets taken
by him.
10 Quantitative Assessment of Player Performances in ODI Cricket
Figure 3 demonstrates the exponential-rank comparison for the top-5 po-
sitions for the four models. The number of right predictions, i.e., at the first
position, is higher by our model as compared to the others. Hence, the superi-
ority of our model against the others validates our approach.
0.9 Honest Mirror
Model_2
Model_1
0.8 PI Model
0.71% 0.71% 0.71%
0.7 0.69%
0.67% 0.68% 0.68%
Exponential Rank (%)
0.64%
0.6 0.59%
0.54% 0.54%
0.52% 0.53%
0.5 0.48%
0.4 0.38%
0.31% 0.31%
0.3 0.29%
0.25%
0.2 0.18%
1 2 3 4 5
Positions
Fig. 3. Exponential-rank for the the top 5 positions for all the four models. Higher
value for Honest Mirror at the first rank proves that our model is able to pick the
player of the match by taking the game situations into account.
References
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target in interrupted one-day cricket matches.” Journal of the Operational Research
Society 49.3 (1998): 220-227.
2. Lewis, A. J. “Towards fairer measures of player performance in one-day cricket.”
Journal of the Operational Research Society 56.7 (2005): 804-815.
3. Barr, G. D. I., and B. S. Kantor. “A criterion for comparing and selecting batsmen
in limited overs cricket.” Journal of the Operational Research Society 55.12 (2004):
1266-1274.
4. Johnston, Mark I., Stephen R. Clarke, and David H. Noble. “Assessing player per-
formance in one-day cricket using dynamic programming.” (1993).
5. Bhattacharjee, Dibyojyoti, and Hermanus H. Lemmer. “Quantifying the pressure on
the teams batting or bowling in the second innings of limited overs cricket matches.”
International journal of Sports Science Coaching 11.5 (2016): 683-692.
Quantitative Assessment of Player Performances in ODI Cricket 11
6. Bailey, Michael, and Stephen R. Clarke. “Predicting the match outcome in one day
international cricket matches, while the game is in progress.” Journal of Sports
Science Medicine 5.4 (2006): 480.
7. DL Table http://www.tcuandsa.org/Doc/dldocs/DLResourceChartNew.pdf
8. Cricsheet http://cricsheet.org/