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.