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

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

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....

This is blog is now listed on http://cricket.superblogroll.com/

Question of Loyalties in IPL-- My Cricket Zen Moment

It is obvious to all those who know me that I do not approve the IPL in general, and the Twenty20 format cricket games, in particular. But it is the beauty of cricket that despite this absurdly reduced format, it still remains cricket. There are some differences, of course, for instance, (1) the balance between the ball and bat has further shifted in the favor of the bat, (2) chance plays far greater role than in longer forms, (3) there are no real ups and downs in a match and a couple of good overs for a team are enough to turn the flow of the game irreversibly.

Because IPL games are still cricket matches, because, cricket season in Germany is still few week away, (finally) because youtube offers free webcast of the IPL matches, I could not help watching the IPL matches over weekend.

While watching the matches I realized another change that IPL has brought in for me, which I might share with the Cricket purists.

I still follow all the international cricket [cricinfo is so generous and informative and updated] and I follow cricket with a clear bias, I always have a favorite team -- for all combinations of countries I have a favorite pre-decided e.g. India takes the precedence over all, and I do not like to see the Aussies win yet again.

But IPLis different, I do not have a favorite team, even though its in its third season -- maybe its a bit too early and I should wait until all the superstars of the longer forms of cricket retire. It is true that because I have my favorite players scattered in all the teams I cannot support any team in particular. I assume that most fans have same problem. Perhaps more teams in IPL-4 with 94 odd matches, fans will finally have to decide to follow one or two teams -- even an ardent fan cannot keep track of 94 games happening in less than two weeks.

Watching cricket, without loyalties was something new, and despite buffering issues on youtube webcast, I enjoyed it far more. There was no adrenaline flowing, thus, my head remained still on shoulders (like it should be in execution of a good drive) and I was able to appreciate the effort and skills of the players. My opinions about the game proceedings were more objective and even my predictions were more correct (have you tried the predictor feature on cricinfo -- its adds so much fun in following game over internet).

Overall it was my cricket Zen moment. And I have more clear plans for my weekends as long as the IPL3 runs. After that, our own cricket season starts...

In the meantime thank you very much cricinfo and youtube

The mongoose bat: Further unbalancing the contest between bat and ball

There is lot of talk going on about Matthew Hayden unveiling the so called 'Revolutionary Mongoose Bat' .

I remember, as a school boy, playing with such a bat for my village team. That was not a technological innovation for us, rather it was an improvisation -- a very good bat broke at the bottom and we did not have much money that we could discard the broken bat, so we chipped away the broken part, shaped the shoulders of the bat a bit to balance the weight and were left with a slightly shorter bat. And in retrospect, we had our own ingenious Mongoose bat. That bat became quite a favorite among the hard hitters in the team. However, even at the village level cricket it was clear that the shortened bat was not the best equipment to play the fast bowler bowling with new ball.

In our times anything that favors batsmen and in particular hard hitting batsmen is always welcome so in that sense it is not surprising that such a bat has been approved for use in the international cricket.

In his first match of IPL-2010 Hayden was supposed to use it. As I read form the commentary on cricinfo that he wanted to start with conventional bat and then once settled, would bring on the 'revolutionary bat'.

I do not want to argue with such a strategy, but I have a couple of questions for the administrators of cricket.

Would they allow a bowler to pick up a ball in the middle of the match because the bowler thinks that with a slightly worn out ball he can get better spin (a spin bowler) or get more reverse swing (fast bowler) and so on... Hayden intending to change his bat to a different one in the middle of his inning is similar. But it is clear from the outset that bowlers will not be allowed to go for such a 'strategy'.

On related note, Hayden wants to use a bat that gives him a better hitting power, are we willing to give the bowlers a choice to chose a ball of his choice for instance one with slightly oval shape because that would swing more, or one with raised seam to get better movement off the seam...

Cricket is a contest between bat and ball and the rule makers and administrators of the game should be aware of this basic fact and follow it while making any policy decision.

There is lot of apprehension among the cricket fraternity about the survival of the game. If there is anything threatening cricket right now then it is biased approach of the rule makers and administrators, which is favors the batsmen more than the bowlers.

The Mongoose bat is yet another instance that reminds us of our bias against bowler and reminds that we should strive for equality of contest between bowler and batsmen else a batmen dominated game would no longer remain 'Cricket' as we have known it.