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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