August 9, 2013

# A measure for the strength of a Test team

Introducing a method of boiling a team's prowess down to a numerical value

Cricket is notoriously conservative when it comes to measuring performance. Batting average, bowling average, and less frequently bowling strike rate, are possibly the only commonly used measures of cricketing performance. In this post, I describe a measure of team strength in Test cricket. I will describe the basic structure of this measure but hope you will see that more specialised measures can be derived using this basic idea. I have calculated these proposed strength measures for all Test matches since 1877. After describing these measures, I look at how these strength measures perform as predictors of results. I hope this basic idea will help some of you to develop better measures, either by building on this, or by using this as an example of what not to do!

The strength of a Test team is given by batting strength divided by bowling strength. The batting strength is the total that a given XI is expected to score based on their career batting averages at the start of the game. The bowling strength is the total an XI is expected to concede based on two things - the bowlers' career records at the start of the game, and the share of the bowling of individual bowlers in that game. Higher batting strength is better, while lower bowling strength is better.

I will start with an example. India's XI for its recent Test against Australia in Mohali was: Shikhar Dhawan, M Vijay, Cheteshwar Pujara, Virat Kohli, MS Dhoni, Bhuvneshwar Kumar, Ravindra Jadeja, Sachin Tendulkar, R Ashwin, Pragyan Ojha and Ishant Sharma.

Batting strength

The batting strength of a team for a given Test match is the total it would produce in a completed innings if its 11 batsmen made the exact number of runs indicated by their respective batting averages at the start of the match. In other words, it is the average of the 11 batting averages multiplied by 10 (since a completed innings involves ten wickets). The Indian team in my example would have a batting strength of 306.

It would have a "batting experience" figure of 528. This is the total number of dismissals that the 11 batsmen in the team have been in. It is calculated as shown in the following table. "Average" gives each player's batting average at the start of the Test Match. "Ave-Sum" gives the sum of the batting averages for the 11 players:

 Player Aggregate Dismissal Average Ave-Sum Batting strength Bhuvneshwar Kumar 48 2 24.0 24.0 306 Cheteshwar Pujara 1017 15 67.8 91.8 Batting experience Ishant Sharma 450 44 10.2 102 528 MS Dhoni 4151 104 39.9 141.9 M Vijay 792 23 34.4 176.4 Pragyan Ojha 86 7 12.3 188.7 Ravindra Jadeja 38 3 12.7 201.3 R Ashwin 600 15 40.0 241.3 Shikhar Dhawan 0 0 0.0 241.3 Sachin Tendulkar 15746 290 54.3 295.6 Virat Kohli 1032 25 41.3 336.9

Bowling strength

Bowling strength is trickier to measure because there is no fixed quota for each bowler, like there is for batsmen. A bowler can bowl as many overs as the captain would like him to, whereas a batsman can only bat twice in a Test. Not all 11 players are required to bowl, while all 11 players bat. The bowling strength of a team is measured by weighing two bowling statistics - runs conceded in career and wickets taken in career - for each player in the XI at the start of a Test match against that player's bowling share in the Test match. Bowling experience is the weighted sum of wickets taken by the 11 players. For example, the bowling strength of the Indian team, or the number of runs they will concede in taking ten wickets, in my example is 327 (the sum of the weighted runs conceded, divided by the sum of the weighted wickets, multiplied by 10). The bowling experience figure is 73.

At the start of the Mohali Test, Ishant Sharma had bowled 9519 deliveries in his Test career, conceded 5317 runs and taken 138 wickets. The first three columns, "BB", "RC" and "W" give Ishant's bowling in the Mohali Test. This is used to calculate his share of the bowling. In Mohali, Ishant bowled 16.9% of the deliveries bowled by India. This is shown by "B-Share". The next two columns, "W-RC" and "W-W", give a weighted score for runs conceded by Ishant in his career and wickets taken by him in his career.

 Player BB RC W Career BB Career RC Career W B-share W-RC W-W Bowling strength Ishant Sharma 234 106 3 9519 5317 138 0.169 897.0 23.3 327 Pragyan Ojha 294 144 4 6718 3004 95 0.212 636.8 20.1 Experience R Ashwin 449 169 4 4687 2344 81 0.324 758.8 26.2 73 Sachin Tendulkar 12 2 0 4186 2459 45 0.009 21.3 0.4 Ravindra Jadeja 284 112 6 1026 326 14 0.205 66.8 2.9 Bhuvneshwar Kumar 114 75 3 204 112 3 0.082 9.2 0.2 MS Dhoni 0 0 0 78 58 0 0 0 0 Virat Kohli 0 0 0 66 35 0 0 0 0 Cheteshwar Pujara 0 0 0 0 0 0 0 0 0 M Vijay 0 0 0 0 0 0 0 0 0 Shikhar Dhawan 0 0 0 0 0 0 0 0 0

Strength

The strength of a Test team for a given Test can only be calculated at the end of the Test, even though it does not include any runs or wickets scored or taken during the Test. It can, however, be estimated if one can surmise how the bowling will be shared among the team's bowlers. This can be done by looking up scorecards for Tests played by the same bowling combination in similar conditions.

The strength of the Indian team in my example is 306 divided by 327, which is 0.937. Having a strength figure greater than 1 is significant. It means that a team is expected to score more runs than it conceded.

Historically the team with the higher strength has won 67% of Tests that did not end in a draw. When a team with strength greater than 1 has played a team with strength less than 1, the former has won 71% of Tests that didn't end in a draw. The charts that follow are based on calculating these measures for all Tests since 1877. They provide a picture of how the three strength measures relate to the results of Test matches.

Kartikeya Date writes at A Cricketing View and tweets here