July 27, 2008

How much do wickets matter in Twenty20 cricket?

A new approach to calculation of economy rates in Twenty20 matches

In Test cricket, using the bowling average to judge how good a bowler is makes a lot of sense. The economy rate (or strike rate) is not important — an attack comprised of bowlers who average 30 will, on average, dismiss opposition teams for 300, regardless of what their economy rates are.

In 50-over cricket, it's more complicated. Taking wickets is still useful, especially early on — you force the batsmen to bat more slowly until later in the innings.

But in Twenty20 cricket, the bowling average isn't important at all. The bowling average is based on wickets, and wickets don't mean much in T20. This fact doesn't seem to be widely recognised, but the whole concept of the 20-over game relies on it. If wickets were important, then batsmen wouldn't blaze away at 8 or 9 an over. So, in T20, the most important simple stat for measuring bowlers is the economy rate.

But of course wickets do help the bowling side a little bit (well, maybe not if Jacques Kallis is on strike), and so in this blog entry I'll try to work out just how much they're worth, and use these to adjust economy rates and give a useful measure of T20 bowling.

***** Before starting, I'd like to thank commenter Russ, who gave useful criticism and suggestions on an earlier version of this analysis.

There are two ways in which wickets reduce the number of runs scored by the batting side. First, batting teams with less wickets in hand have to bat more slowly — this is a long-term effect over the rest of the innings. Second, the new batsman has to get his eye in, causing a short-term drop in run rate.

To begin, let's look at that first effect. Each scorecard contains the over and ball at which each wicket fell. We also know the score at the fall of the wicket, and the final score made by that team. Collect this data for all the scorecards, and you can plot graphs of runs remaining against balls remaining at each wicket. You can see these graphs, along with other technical details, here. All of the data used is from the IPL.

When you do this, you find that early wickets are worth about two and a half runs each. That's not very much. Wickets only become really important when a team loses lots of them and has the tail exposed early (for example, a seventh wicket with 12 overs left is worth about 14 runs).

A simple method to adjust economy rates would be to work out how many runs each wicket is worth, and give the bowler credit for that. But that's not always fair. Suppose the opening bowlers each take three wickets in their opening spell. They get credited 6 or 7 runs each. Then the change bowlers come on and, bowling at the tail, pick up wickets that are worth over 10 runs each! The opening bowlers surely deserve some of that.

So, what I did was to ignore which number the wicket was, and consider only the number of balls remaining. Doing some graphing and regression gives a pleasantly round result: a wicket is worth (in runs) the number of overs remaining, divided by 6. Keep that in the back of your mind, as we'll come back to it later.

Now let's look at the temporary run-rate drop after a wicket. From the ball-by-ball records, we can find the average run rate in each over, and compare it to the average run rate in each over given that a wicket fell recently.

A couple of features emerge from the results. For most of the innings, a wicket results in a dip of about 2.2 runs, and the dip lasts a couple of overs. After 15 overs, this changes — the dip being smaller and smaller, until there's none at all in the last over.

We now have pretty much all the ingredients necessary to tweak economy rates in T20. There are a couple of subtleties that I go into in the details page.

Now let's look at bowlers in the IPL. In the table below are the top bowlers according to the adjusted economy rate. The columns are balls bowled, runs conceded, wickets taken, average, usual economy rate, the runs credited from the wickets, and lastly the adjusted economy rate. The adjusted economy rate is the runs conceded, minus the runs credited from the wickets, divided by the number of overs bowled.

There is a bit of variation in the runs credited — Tanvir has more wickets than runs credited, whereas Pollock's runs credited is almost twice the number of wickets that he took. This tells us that Pollock's wickets came mostly early in innings, whereas Tanvir picked up many of his wickets near the end of the innings.

name           b    r    w   avg   econ  cred  adj econ
Sohail Tanvir  247  266  22  12.1  6.46  18.4  6.01
SM Pollock     276  301  11  27.4  6.54  20.1  6.11
IK Pathan      318  350  15  23.3  6.60  21.6  6.20
GD McGrath     324  357  12  29.8  6.61  17.9  6.28
AB Dinda       234  260  9   28.9  6.67  15.0  6.28
DW Steyn       228  252  10  25.2  6.63  10.7  6.35
MF Maharoof    216  249  15  16.6  6.92  14.9  6.50
M Ntini        210  242  7   34.6  6.91  11.0  6.60
SR Watson      325  383  17  22.5  7.07  21.1  6.68
M Muralidaran  348  404  11  36.7  6.97  11.7  6.76
Tanvir was the stand-out bowler of the tournament, but his spectacular wicket-taking made him look further ahead of the rest than he really was. Ashok Dinda was a bit of a quiet achiever through the tournament. For those interested, Shane Warne had an adjusted economy rate of 7.32.

Details of the methods and calculations can be found here.

Comments have now been closed for this article

  • testli5504537 on September 1, 2008, 16:36 GMT

    Further to 'bowling average being the measure of greatness'.... it was mentioned that the batting department does not have a yardstick to measure greatness by. i wish to differ. in my opinion, the batting average is a valid statistical figure by which we can assess the greatness of batsmen. here's why: if we were to pick the most important quantifiable qualities of a batsman, they would be: 1-runs per dismissal 2-balls per dismissal 3-runs per balls a high numerical value for each of these aspects indicates a good batsman. product of these three figures gives

    (runs/dismissal) x (balls/dismissal) x (runs/balls) = (runs/dismissals)^2.... i.e square of the batting average!!!!!!!!!!!! how cool is that?

  • testli5504537 on August 13, 2008, 23:24 GMT

    Marcus, http://pappubahry.blogspot.com/2008/06/accuracy-of-averages.html

    I don't think that the formula is precise enough for there to be any difference between innings and (innings - not outs).

    I've already started doing stuff on adjusting economy rates by the average economy rate of the over.

    Jacques, batting in T20 is a much harder thing to evaluate. Strike rate is certainly important, but there has to be some allowance for average - scoring 4 runs off 2 balls every innings is only going to be useful if the rest of the batsmen are guaranteed to bat out the overs. Whatever metric is best, our old G division side would probably do badly.

  • testli5504537 on August 13, 2008, 21:38 GMT

    Good stuff David. The same analysis probably applies to batting as well in 20-20 where strike rate is particularly important. Sadly, no matter how much bowling analysis we do into our Oman G division side, I don't think any bowlers will come out with an adjusted economy rate under 10. I still have our old score book from which I dug out a few interesting facts for your records: Our opening batsman, Saim Qidwai, scored a duck of 18 balls against Al Habib at DGPM ground on 24th Oct 1997 thus effectively reducing our innings to 22 overs as opposed to 25 (Nevertheless we still won the match, a rare feat!). David Barry scored a 67 of 54 balls against ISG at OAC 3 on 9th Nov 2000, though despite this high strike rate this innings only included one boundary.

  • testli5504537 on August 13, 2008, 13:04 GMT

    I wasn't aware of that, very cool. I'm a little confused however; for the batting average, is inns just innings, or (innings - not outs)? Do you have a blog where this past research has been published? I haven't put very much thought into this idea, so it may not make much sense: have you tried adjusting economy rate for the average economy rate in that over? For example, if a bowler concedes 6 in an over where 6 runs are conceded on average, that is worse than a bowler who concedes 7 in an over where 9 are conceded on average. This could maybe be combined with the above research. I think this makes sense but I'm not sure how useful it would actually be predictively.

  • testli5504537 on August 4, 2008, 11:34 GMT

    That is a good idea, Marcus. I'm not sure if you're aware of it, but I've done a similar study on Test match batting and bowling averages, with a 95% confidence interval being roughly [avg - 1.8*avg/sqrt(inns), avg + 1.8*avg/sqrt(inns)] for batsmen, and [avg - 1.8*avg/sqrt(wkts), avg + 1.8*avg/sqrt(wkts)] for bowlers.

    My guess is that bowlers have a good deal of control over their economy rates - Pollock and McGrath were near the top, just as you'd expect from their ODI stats.

  • testli5504537 on August 4, 2008, 11:25 GMT

    Perhaps for a new article you could see how much control over their economy rate a bowler holds? eg, how consistent a bowler's economy rate is over matches/overs. With this done you could then work out confidence levels for how good the bowlers are, as the sample sizes you're working with aren't particularly voluminous. I have a suspicion that variance is a greater factor than most suspect. With that as well as the work here, you would have an extremely good methodology for evaluating bowlers, which could then be used by IPL franchises. Though, in likelihood, the IPL franchises would ignore any stats like this.

  • testli5504537 on July 31, 2008, 21:12 GMT

    Well to be honest I don't believe they matter a great deal because they can be very deceptive if a bowler primarily bowls at the end of the innings like Tyron Henderson where wickets are more likely to come with batsman having a swipe at nearly everything, this proves as Henderson has the most wickets ever in Twenty20 Cricket. Somebody once told me that with 20 - 20 its not the bowlers average per wicket, or amount of wickets, its their economy. With the batsman it's more about strike rates rather than averages and career runs. 20 - 20 is such a different game where just about anything can happen. Look at Essex's Graham Napier, Essex sent him in at 3 as a pinch hitter to get the score ticking, but instead he batted the whole innings smashing everything having a strike rate of about 270 I believe. I also feel that so much pressure is released in 20 - 20, David Lloyd, now commentator consistently says that he just takes 20 - 20 as entertainment.With that I conclude statistics dont matter

  • testli5504537 on July 30, 2008, 8:18 GMT

    I think its a bit of a mistake generalizing all T20 cricket to be as per the IPL. Th batting conditions were really flat, and even tailenders could play their shots. If you use data for T20 internationals, and England county cricket, I suspect you'll get different results.

  • testli5504537 on July 29, 2008, 20:49 GMT

    I think you'll find that many of the big scores in the IPL came when the batting team formed decent top order partnerships allowing a platform for the middle and lower order to launch from. However, if the batting side lost early wickets, the innings often stagnated and required rebuilding and the launch would occur a lot later on in the innings. I think you are underestimating the importance of wickets in Twenty20. Wickets bring pressure at the start of an innings in Twenty20. That is the beauty of Twenty20, you can't actually come out and slog from ball one. There is an art to building a Twenty20 innings and it's a fine line between chancing your arm and setting a platform. A lot of the basics still apply, like playing well technically. The same applies with wickets, they bring pressure early. That slows the scoring rate. Giving points to the fielding side is ludicrous, it doesn't even follow any practical logic. The game is good as is.

  • testli5504537 on July 29, 2008, 13:55 GMT

    I disagree. Wickets have a huge play in T20. T20s are very hard for the bowler. Look at it from a bowlers perspective. The bowler has two tasks, get wickets and be economical. You NEED wickets. Think about it. If Sanath Jaisuriya is batting, he is not going to rest with his big shots. Every one has seen him bat. Bowlers need to get him out of the game or he is going to do damage early on. Top six batsmen could do the same. It does not just have to be the openers who hit. And its even harder for the bowler when he is getting bashed. Again, think like you are bowling. It would kill your confidence in your bowling when you see the batsmen take it up and down the ground easily. Wickets at that moment will bring confidence and will help put pressure on the batting side. New batsmen would also take few balls to settle down. Now for the economy rate, you need that. You have to be a clean bowler. Get wickets, keep run rate low and don't lose confidence when getting your balls smashed. :D

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