Saturday, May 15, 2010

Duckworth-Lewis Calculation Graphs for Different Duration Matches

I think one the best things to have happened to cricket in 1990s was the development of a rule to update the target score should there be an interruption and team batting cannot have full set of overs. Even more remarkable was that ICC who has a reputation for choosing wrong options always, accepted this rule. This rule was devised by two statisticians Frank Duckworth and Tony Lewis and appropriately named after them.

According to Duckworth and Lewis, cricket is about using resources (overs and wickets) to achieve a target set by an opposition who batted first. Therefore, in case of an interruption, both overs and wickets should be considered. 

Exact D-L calculations often become very cumbersome. Thus, in absence of sophisticated computer, most teams in small league and friendly matches devise some ad-hoc rule. Here I show the graphs that can be used to estimate the modified target after an interruption. Originally the D-L method was developed for 50 overs matches, but usually in small leagues and friendly games, matches are shorter, therefore I estimated the D-L calculations for 20,30,40 and 50 over games.

How to read and use the graphs
x-axis is number of over remaining. The different colors of the lines refer to number of wickets fallen. So estimate the scaling factor to update the target, you need to know how many overs have been bowled (i.e. x-axis), how many wickets of the team batting second have fallen, color of the line. Corresponding to the number of wickets fallen and over bowled, y-axis give a fraction, by which you have multiply the original target to get the updated target.


Imagine, you are playing a 40 over game and set a target of 220, and rain stops the play at 25 over and the team chasing has lost 6 wickets. What should be D-L score of the team batting second to win the game? So we draw a vertical line at 15 over, and find out where does it cross the green line, from that crossing draw a horizontal line and find out what value it corresponds to on the y-axis. In this example we get 43.6 on y-axis. This means that the opposition should have scored 56.4 % runs i.e.  220 *(100 - 43.6) = 123 runs. This number would go up if they had lost one more wicket, to 142 and so on.

Enjoy your own simplified graphical D-L update rule, but I do wish that your games go on uninterrupted...

right arm over
Arvind

Tuesday, May 11, 2010

juggling with cricket balls

Two new players, Tilo and Matthews, of the Freiburg Nomads Cricket Club have found this new way to set their eyes on the ball...
Juggling with cricket balls

Saturday, May 1, 2010

How random was IPL2010: Effect of a wicket, six and four on scoring

Fall of a wicket is random process. Very best of the deliveries from the masters of the art of bowling, fail to claim a wicket while some novice can on his day (as they say) can claim wicket of a settled batsman of highest class. Similarly, there is no apparent pattern to scoring of a boundary (six or four).
But is this randomness just a hunch or experience. Is there data to support this claims of randomness in cricket. Because most of our experience is based on Limited over and TEST matches. If there is randomness in such longer version, perhaps there will be more randomness in T20 where everyone seems to be in a hurry.
The beauty of cricket is that it generates data and now equipped with technology, cricket.org is storing ball-by-ball commentary and other relevant data (e.g. ball speed, trajectory and so on)... cricket is wonderful and so is cricket.org.
The ball by ball commentary data is most accessible (also most systematic) for the recently concluded IPL2010. So I decided to check the  randomness hypothesis.

I focused on three events in the progression of a match. A wicket, four and six. These three events have most influence not only on the progress of the match but on the psyche of the bowler. A wicket in most cases brings a new batsman on strike. A four or a six is very effective way to get into the head of a bowler and unsettle him.
EFFECT of FALL of a WICKET
So lets see what happened when a wicket fell in T20 matches during the IPL2010. From the ball-by-ball commentary I extracted all the wickets that fell between second and 18th over. I also separated the analysis inning-wise. 

Once I knew when the wicket fell I extracted how many runs were scored just before and just after the wicket fell. This is plotted in the top panel (a) of the figure below. On the X-axis 'zero' marks the ball on which the wicket fell. Negative numbers on the x-axis marks the balls just before the wicket fell. Similarly, positive numbers on the x-axis marks the balls just after the wicket fell. On y-axis I plot average runs scored per ball. The two horizontal lines show average runs per ball in the two innings.

The plot shows that at least 6 balls before the fall of wicket, there was nothing unusual going on. Just out of blue the wicket fell. So indeed fall of a wicket is a random process in T20 matches of the IPL2010. There is no strategy that bowlers follow and weave a web to get the batsman out.

Once the wicket fell and new batsman came in and team perhaps went in some sort of safety mode. For about four balls after the fall of a wicket the effect can be felt (shaded in blue) and run rate dropped by at least 30%. The analysis also seem to suggest that the recovery from the fall of wicket was faster in second inning (the red line catches up faster).
Panels b and c show the actual distribution on runs scored on each ball before and after the fall of wicket (FOW). These distributions show that the reduction in the scoring rate for about 4 balls after the FOW, is due to reduced probability of fours and sixes on the post-wicket deliveries.


EFFECT of a SIX or FOUR
Similar to the analysis of the wickets, I estimated the number of runs scored just before a boundary shot of six (panel a in figure below) or four (panel b in figure below. In these figures '0' is ball on which a SIX or FOUR was hit, but I have set that value to 'zero'. The analysis suggests that a six is hit when run rate is slightly is higher than average run rate. This could be and effect of increase in the number of boundary shots. Perhaps, sixes are hit when bowlers are already down and because runs are coming easy, batsmen take risk and hence the aerial route. But the fact that the run rate does not differ much from just before the six, suggests that both bowler and batsman forget about proceeding of the previous ball.
The four is a pure random event. Unlike the six, a four is hit when run rate is higher than average. A four is not associated with an pre-four or post-four change in the game. Thus in T20 matches of IPL2010 a four was just another shot.

A quick summary
  1. Fall of wicket is a random process and post-wicket there is a lull in scoring that lasts about 4 deliveries. Second inning team recover faster from the jolt of a wicket.
  2. A six is hit (on average) when runs are coming easy and batsmen feel comfortable in playing risky shots.
  3. In the IPL-2010 matches a four was scored just as any run, of course probability of a four was smaller than that of TWO, ONE and a dot-ball.
Now if these results hold in longer matches, needs to be checked. cricket.org has the necessary data for both TEST and 50over games. Beyond sixes and fours, I would be very interested in the post-wicket effect. I would imagine that after a wicket teams would go in slow safety mode for longer that four balls. It would be the longest for TEST matches.

It was very frustrating to know that fall of a wicket is random process. I hope that at least some great master of the art of bowling, e.g. Shane Warne, Glenn McGrath, Anil Kumble, Murali do set up their wickets. This analysis is on my to do. Just that it is going to take a while to write a semi-smart routine to extract the relevant information. Wait for the next Saturday...


PS: I have to thank my lab mate Christian Garbers for extracting the commentary data from cricket.org.

PPS: The guys at cricket.org, if yo read this blog, could you devise a rule to automatically download the commentary data....

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