Developed a simulator for 100 ball cricket which is based upon a binary logistic model. Particular attention is given to second innings batting where the state of the match (e.g., score, wickets, balls) affects the aggressiveness of batsmen. Also, demonstrated how the simulator can be used to address questions of interest

1. Comparison of 100 ball and 120 ball tournament using the
predictive modelling method keeping the structure of
tournament same
Introduction
Cricket, a game meant for social entertainment of the early Englishmen, is now popular in more
than half the world and is one of the most attractive platform.The game spreads across 5
continents and 10 countries are continuously competing for the top spot. It has a core following
of more than 2.5 billion which makes is second most popular sport in the world (Kimber, 2008).
Since the arrival of T20 cricket in 2003, the game has reached a new height of popularity and a
there are many top T20 leagues that have been setup across the globe. With high viewership
the game has been attracting a lot of money with an always increasing number of players
wages, sponsorship money and betting of both legal and illegal nature. And so that all this
money doesn’t end up in disappointment, every game have to have a winner and in case there
is none, a fair practice have to be used to declare one.
England is planning to disrupt this by launching a format that is even shorter, can be enjoyed by
core fans enjoy and garner more casual eyeballs. When England and Wales Cricket Board
proposed for a 100 ball cricket format instead of T20, it was received with both excitement and
suspicion.Dubbed 'The Hundred', the new format could feature 20 five-ball overs per side, with
the eight-team tournament to begin in 2020. With each match 40 balls shorter than a T20, the
action will be cut to around two and a half hours. It is hoped families with younger children will
be attracted to attend evening games.
But can the reduced length of the match will affect the match result? Can a lower ranked team
will have more chances of beating a higher ranked team? Will there be an increase in number of
the boundaries? And many more question like these are in the spotlight in this discussion.
Models of sports performance are produced by analysing previous cases where key variables of
interest and outcomes are known. Once the model is produced, future performances can be
simulated where the key variables for these matches are known providing predictions for
outcomes. We also need to be aware of the limitations of simulations and the assumptions that
they make.
This does not invalidate such a simulation study but we do need to be aware of the limitations.
The most important thing to understand about simulation studies is that they do not actually
predict match outcomes!
In the pre-computer days, Philip (2011) fit the geometric distribution to individual runs scored
based on results from test cricket. probabilities for selected ranges of individual scores in test
cricket using product-limit estimators. More recently, Sirsai (2016) simulates batting outcomes

2. between a specified test batsman and bowler using career batting and bowling averages as the
key inputs without regard to the state of the match (e.g., the score, the number of wickets lost,
the number of overs completed).
In this article, we develop a simulator for 100 BALL cricket matches. The approach extends the
work of Swartz et al. (2006) who investigate the Modelling and Simulator in ODI cricket. In
addition, we now provide a method of generating runs in the second innings. Given that only a
finite number of outcomes can occur on each ball that is bowled, a discrete generator on a finite
set is developed where the outcome probabilities are estimated from historical data involving
T20 cricket matches. The probabilities depend on the batsman, the bowler, the number of
wickets lost, the number of balls bowled and the current score of the match.
In Section 2, we develop a simulator for 100 ball cricket which is based upon a Binary logistic
model. Particular attention is given to second innings batting where the state of the match (e.g.,
score, wickets, balls) affects the aggressiveness of batsmen. In Section 3, we consider the
adequacy of the approach by comparing simulated results against actual data. The simulator is
constructed using data from recent T20 matches. In Section 4, we demonstrate how the
simulator can be used to address questions of interest. We conclude with a short discussion in
Section 5.
Methods
There are many factors that influence performance in sport; these factors have varying degrees
of complexity and validity. The computer-based predictions modeled the relationship between
the result of a match and three relevant factors in the 120 matches of the previous 2 cricket T20
World Cup and the matches in between(2104-2016). There are 3 different factors, one for each
innings.
The three factors used were for 1st innings:
1. World ranking points
2. Balls remaining
3. Wickets left
The three factors used were for 2nd innings:
1. World ranking points
2. Balls remaining
3. Wickets left
4. Runs remaining to win
These data were chosen because the reliable data for other factors were not available and once
consider constant. Here we chose the Ranking points instead of the rank to get more sensitive
to data. It is because the difference between the consecutively ranked team doesn’t justify the
actual gap. Sri Lanka is ranked 1 with 135 points and India is ranked 2 with 124 points. Here the

3. difference is of 11 points whereas New Zealand and South Africa is ranked 6 and 7 but the
difference between them is of 0 points. That’s why the ranking points difference was chosen
instead of the rank difference.
The next variable is the balls remaining which is the total balls left after the x balls are bowled;
120-x, Wickets remaining is also calculated in the same way. It is the wicket remaining after the
x batsman are out; 10-x
The variable used in the second innings Is the runs remaining. The pattern of play of the chasing
team largely depends on how many runs to chase. They adjust their attacking and defensive
strategy accordingly.
Models
First innings model (A teams bat first)
Independent Variables
This model used 3 independent variables which were all determined with respect to the higher
ranked of the two teams within matches according to the ICC World Rankings at the time
matches were played:
* The difference in World Ranking Points, Rankδ: higher ranked team’s value – lower’ranked
team’s value.
* Number of balls remaining: 120 - balls bowled
* Number of wickets remaining: 10-wickets out
Second innings model
Independent Variables
* The difference in World Ranking Points, Rankδ: higher ranked team’s value – lower’ranked
team’s value.
* Number of balls remaining: 120- balls bowled
* Number of wickets remaining: 10-wickets out
* Runs remaining to win: this is calculated as Runs scored by team A - the current run scored by
team B.
Dependent Variable
Dependent variable is the event that can happen on each ball. This can be either run scored
{0,1,2,4,6,} or a wicket is a fallen
Tournament Prediction
The 2016 ICC World T-20 was the sixth edition of the world championship of Twenty20
International cricket. Participating teams were 16; the number of teams being for the second
time in its history of the championship. Ten teams already qualified through their full status
from the ICC (International Cricket Council) and six qualified through 2015 edition qualifiers.

4. Tournament was of 3 stages; first stage being of eight lowest ranking teams playing out of
which two qualifying and joining the eight highest ranked teams to become the Super 10 stage.
Finally, the top four teams made it to the knockout stage.
Fig. 1 Tournament structure of the T20 world cup in 2016
There is a role for the simulation to determine the chances of different squads reaching
different stages of tournaments and simulations studies have highlighted factors influencing
success.
In this case, the structure of the tournament is not altered instead the format of the game is
changed to a 100 ball tournament and see if there are changes in the team qualifying or even
winning the tournament.
The 2016 T20 World Cup is used as an example because its the latest tournament conducted.
Therefore, we are dealing with latest progression the matches as well as the ranking
Modelling
We consider the simulation of runs in the first innings for predetermined batting and bowling
orders. We initially investigate the first innings runs since second innings strategies are affected
by the number of runs scored in the first innings. By a predetermined batting and bowling order,
we mean that a set of rules has been put in place which dictates the batsman and bowler at any
given point in the match. These rules could be simple such as maintaining a fixed batting and
bowling order. The rules for determining batting and bowling orders could also be very complex.
For example, the rules could be Markovian in nature where a specified bowler may be
substituted at a state in the match dependent upon the number of wickets lost, the number of
overs, the number of runs and the current batsmen. The key point is that they need to be
specified in advance for the purpose of simulation.
In 100 ball cricket, there are a finite number of outcomes arising from each ball bowled.
Suppose that the first innings terminate on the mth ball bowled where m ≤ 100. Ignoring certain
rare events (such as scoring 5 runs), and temporarily ignoring wide-balls and no-balls,

5.
Fig 2. Showing the event that can happen on each ball
These ​includes the possibility of scoring due to byes and leg byes. Byes and leg byes occur
when the batsman has not hit the ball with his bat but decides to run.
Modelling assumptions
The runs scored on each ball depend on many factors including
the batsman;
the bowler;
the number of wickets left;
the number of balls left;
the current score of the match; the opposing team;
the location of the match;
the coach’s advice;
the condition of the pitch, etc.
Since, we don't have the quality data for other events we are considering them constant. Hence
only the following factors were taken.
For the first innings, we consider three factors
● Balls left
● Wickets left
● Ranking points difference of each team
The three factors used were for 2nd innings:

6. ● World ranking points
● Balls remaining
● Wickets left
● Runs remaining to win
Our data are based on 84 T20 matches from January 2014 until July 2016 amongst the 10 full
member nations of the International Cricket Council (ICC). These matches are those for which
ball by ball commentary is available on the Cricinfo website (www.cricinfo.com) and include
almost all matches amongst the 10 nations during the specified time period. In the 84 matches,
20,012 balls were bowled involving I = 435 batsman and J = 360 bowlers. In the first innings,
10000 balls were bowled. Over these matches, we calculate vˆ = 895/20012 = 0.044 as the total
number of wide- balls and no-balls divided by the total number of balls bowled hence ignored.
Table 1: ICC T20 rankings of team as per 2016
Modelling stage
The first stage is to identify the type of model that can be applied to the dependent and
independent variable. We will try to find a relationship between the dependent and independent
variable individually first and then all together. The significant value helps in determining
whether there is a relationship between the variables exist or not.
The model being used here is a binary logistic model. This is an extension of the commonly
used linear regression model. In the binary logistic model, the probability of the dependent
variable is taken out in terms of independent variable. For each probable outcome of a x0, x1,
x2, x3, x4, x6, xW, a function is formed. For the first innings, the function is based on the balls
remaining, wickets remaining and the rank difference of both the teams and for the second
innings an additional independent variable of runs remaining is added. Probability is calculated
on each ball for each of the possible outcomes.

7.
For 1st Inning
1. x0 = - 0.00007*Rank_diff + 0.01856*Ball_remaining - 0.215148*Wicket_remainig - 0.05479
2. x1 = 0.00057*Rank_diff - 0.00838*Ball_remaining + 0.055152*Wicket_remainig - 0.34979
3. x2 = 0.00099*Rank_diff - 0.01164*Ball_remaining + 0.080700*Wicket_remainig - 2.44566
4. x4 = - 0.00107*Rank_diff - 0.00387*Ball_remaining + 0.160612*Wicket_remainig - 3.13587
5. x6 = - 0.00165*Rank_diff - 0.02436*Ball_remaining + 0.314123*Wicket_remainig - 4.15646
6. xW = - 0.00199*Rank_diff - 0.01238*Ball_remaining + 0.014393*Wicket_remainig - 2.31583
For 2nd Inning
1. x0 = - 0.000257*rank_diff + 0.018408*Ball_remaining - 0.004386*Runs_remaining -
0.125313*Wktremain -0.34237
2. x1 = 0.00018*rank_diff - 0.011771*Ball_remaining + 0.002616*Runs_remaining +
0.053257*WktRemain - 0.397337
3. x2 = 0.000994*rank_diff - 0.007598*Ball_remaining + 0.000396*Runs_remaining +
0.024646*Wktremain -2.238433
4. x4 = -0.000979*rank_diff - 0.0024*Ball_remaining + 0.002929*Runs_remaining +
0.098909*Wktremain - 2.95531
5. x6 = 0.000733*rank_diff - 0.023353*Ball_remaining + 0.005015*Runs_remaining +
0.152199*Wktremain - 3.29799
6. xW = -0.003198*rank_diff - 0.011384*Ball_remaining + 0.003907*Runs_remaining -
0.018718*Wktremain -2.507615
Formula to calculate the probability of event happening on each ball
P: probability of Y occuring
e: natural logarithm base
b0: interception at y-axis
b1: line gradient
bn: regression coefficient of Xn
X1: predictor variable

8. The X1 predicts the probability of Y. The difference between the linear model and the logistics is
that the linear regression predicts the value of Y whereas in the Logistic model it predicts the
probability of Y by taking a specific value. In this case x1, x2...xW is calculated. Then those
values were put in the above equation and the probability is calculated. The final probability is
normalized so that it doesn’t exceed one.
These equations are formed by the binary logistic model. The rank_diff was not significant but
still, we took as it is better if to have one more variable.
Results :
A simulator was implemented in Matlab to run the 2016 T20 Cricket world cup. For the
tournament each version i.e. 120 balls tournament and 100 ball tournament were run for 10000
times. There are 23 matches with 20 league and 3 knockout including the finals. 10 teams were
distributed in 2 groups of 5.
From the simulation results, we can see the probability of winning for the lower ranked team has
increased in the knockout stage compare to the higher ranked team whereas it has decreased in
the league stage. It implies that the clearing group stage is more difficult than winning the
knockout matches. The striking feature is Pakistan and New Zealand decrease in the chances
of qualifying to -4.62%. 3rd in pool implies that they won’t be finishing 3rd and hence more
chances of qualifying in the knockout stages or lower in pool. Whereas Higher ranked team like
india and Sri Lanka has ~3.6% higher chance to finish 3rd.
Stage Sri Lanka India Australia West Indies Pakistan
New
Zealand
South
Africa England Bangladesh Afghanistan
Winners -52 -87 -49 -37 64 74 50 12 13 12
Finalists -215 -98 -87 -49 18 47 149 89 148 -2
Losing SF -265 -286 -25 -42 156 56 147 149 37 73
3rd in pool 369 331 -99 -58 -462 -462 -65 -119 281 284
4th in pool -45 -65 213 152 195 264 -93 -40 -307 -274
5th in pool 208 205 47 34 29 21 -188 -91 -172 -93
Table 2. Shows the difference of team winning in 100 and 120 ball tournament. (Number of times winning in
100 minus the number of times winning in 120 ball)
Another feature is the increase in the Average number of boundaries and decrease in the zeros
and ones. There are increase in the percentage of 4s more in compare to 6s. More the number
of boundaries scored throughout match demands more power hitter and an aggressive
approach

9.
Table 3. Shows the average percentage changes in occuring of each event. (Percentage in 100 minus the
percentage in 120 ball)
Fig 3. Graphical representation of average percentage changes in occuring of each event. (Percentage in
100 minus the percentage in 120 ball)
Conclusion​:
It is clearly seen from the results that the shorter the format higher the chances of winning a
team in knockout stages though in the league format the higher ranked has more chances of
qualifying. The scoring pattern demands for more batsman who can hit boundaries than who
can take 1s and 2s. More boundaries mean more entertainment which is good for game and the
money.

10.
Bibliography
Alan C. Kimber and Alan R. Hansford, Journal of the Royal Statistical Society. Series A
(Statistics in Society), Vol. 156, No. 3 (1993), pp. 443-455
Philip Scarf, Xin Shi and Sohail Akhtar, Journal of the Royal Statistical Society. Series A
(Statistics in Society), Vol. 174, No. 2 (APRIL 2011), pp. 471-497
Sirsai, ​A Bayesian stochastic model for team performance evaluation in T20 cricket:
Effectiveness of Power Hitting & Consistency, ​July 20, 2016
Tim B. SWARTZ, Paramjit S. GILL and Saman MUTHUKUMARANA, The Canadian Journal of
Statistics / La Revue Canadienne de Statistique, Vol. 37, No. 2 (June/juin 2009), pp. 143-160