Twenty20 cricket gives us a whole new set of problems when it comes to assessing batting performance. Upper order batsmen are much more likely to achieve ‘not out’ scores in Twenty20 and we have seen in the previous post how that can render the traditional Average score (Ave) close to useless.

In Twenty20 scoring rate is of critical importance, a batsman who scores 30 runs off 10 balls, than one who scores 31 off 30. So to accurately reflect the quality of a batting performance we need a measure that takes in both runs scored and the rate at which they are scored.

To further complicate matters, runs are scored at very different rates under very different conditions. It is much easier to score runs quickly on a track with true and predictable bounce under a bright blue sky, than on a green strip in Manchester, or a dead track in Nagpur. So if possible we need the measure to take into account conditions on the day.

**Croucher (2000)** was the first researcher I have found to deal with the first of these problems. He proposed something he called the “Batting Index” (BI). Which was found by simply multiplying the conventional average by the strike rate per 100 balls faced.

BI = AVE X SR

Where

AVE = R/out

R= runs scored

Out = times out

SR = 100 X R/B

B = balls faced.

**Basevi & Binoy (2007)** used a very similar measure, which they called CALC

CALC = R^{2}/(out X B)

Now if you work this out (bear with me here, I only just scraped a low grade ‘A’ level in maths and that was a long time ago), you get

CALC = (R/out) X (R/B)

In other words this is just AVE X SR again, the difference between that this is runs per ball rather than runs/100 balls, or to put it another way CALC = BI/100.

The general feeling among researchers was that this method of simply multiplying average by strike rate over-emphasized the value of strike rate in Twenty/20 games. Secondly it did not take into account different batting conditions. So how do we account for differing playing conditions when we are assessing a batsman’s performance? One suggestion (Lemmer 2008) is to take the average scoring rate fro all batsmen and compare with that figure. For example if the average run-rate at one particular ground or in one tournament was 124, we could assess an individual players performance against that figure. This would then give us a good idea of how that individual was performing. The formula for BP (Batting Performance) is as follows;

BP_{26} = e_{26}XRP=e_{26}X(SR/AVSR)^{0.5}

^{ }

Where

E26 = (e2 + e6)/2

E2 = (sumout + 2Xsumno)/n

E6 = (sumout + f6 X sumno)/n

F6 = 2.2-0.01Xavno

AVSR = average strike-rate

SR = Strike Rate

In international Twenty20 matches AVSR = 124.03, so that figure can be substituted in to the formula.

It is clearly unfair to compare batting performance in differing batting conditions. So by comparing his performance with the average strike rate of all batsmen playing in those conditions are fairer assessment can be made.

Again, Excel is your friend here, it is an initially daunting looking formula, but once you have the formula set up in your spreadsheet, the inputs can be added quickly and the result attained satisfyingly quickly.

o0o

**Bibliography**

** **

Croucher, J.S. (2000) ‘Player Ratings In One Day Cricket’. *Proceedings of the Fifth Australian Conference on Mathematics and Computers in Sport Eds. Cohen G. & Langtry, T. Sydney University of Technology, NSW. 95-106*

* *

Basevi, T. & Binoy, G. (2007) ‘The World’s Best Twenty20 Players’ Cricinfo* cricinfo.com/columns/content/story/311962.html*

* *

Lemmer, H.H. (2008) ‘An Analysis of Players’ Performances in the first Cricket Twenty20 World Cup’. *South African Journal For Research In Sport, Physical education and recreation 2008, 3092): 71-77*

* *

Lemmer, H.H. (2011) ‘The Single Match Approach to Strike Rate Adjustments in Batting Performance Measures in Cricket’ *Journal of Sports Science and Medicine 10, 630-634*

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