The amazing symmetry of Tests, ODIs, and Twenty20s

Man cannot have deliberately designed three forms of the game of cricket with more symmetry in their relative run rates than he has done so.

With the first international Twenty20 match being played in February, 2005, the three forms of the game have co-existed together since then, challenging batsmen to adapt to the vastly different conditions that each brings to the contest.

Since that time, Test cricket, with no limit on the length of an innings, has produced runs at the rate of 3.34 runs per over, (compared with a run rate of 2.74 runs per over in all Tests to that point).

One-day internationals, played for the most part over 50 overs per innings, have an overall scoring rate of 5.01 runs per over since 2005, (compared to a rate of 4.57 runs per over in the first 34 years of their existence).

Twenty20 cricket, played over 20 overs per innings, has offered runs at the furious rate of 7.53 runs per over in the first 140 matches.

What is remarkably symmetrical about these run rates since 2005 is this: the run rate in ODIs has been almost exactly 50 per cent higher than the run rate in Tests. Not 49 percent, not 51 percent, but 50 percent.

As if this is not remarkable enough, when we do a similar calculation between the run rates of ODI and T20 matches, we find again that the run rate in T20 matches is almost exactly 50 percent higher than that for ODIs. 50.3 percent, to be precise.

This symmetry in the run rates between the three forms of the game is so perfect that is appears to have been deliberately engineered. We know, of course, that it wasn't.

These 50 percent increments can be used as a benchmark to track the adaptability of individual batsmen who have played the three forms of the game.

I then became interested in finding ways to measure how individual batsmen fared against these benchmarks. I looked at six Australians who played extensively in all three since 2005, Ricky Ponting, Mike Hussey, Adam Gilchrist, Andrew Symonds, Michael Clarke and Matthew Hayden.

The most adaptable of this group appears to be Mike Hussey, whose respective scoring rates in Tests, ODIs and T20s since 2005 have been 2.90, 5.30 and 8.32 runs per over. That gives him an overall increase from Tests to T20s of 287 percent, well above the 225 percent that would be achieved if he had just managed 50 percent increases up the line.

The lowest overall gain, 171 percent, was achieved by Adam Gilchrist (4.96, 6.16, 8.50), although he is somewhat penalised by his high Test run rate, where he tended to bat as though it was a limited overs match. The other player who has clearly had problems forcing the run rate is Michael Clarke (3.14, 4.55, 6.28). His figures show that he has only managed to double his Test run rate when playing T20 cricket, well below par.

As an alternative, and to overcome the penalty suffered by Gilchrist in particular for scoring so quickly at Test level, I then calculated three ratios for each player, and then multiplied those ratios together. The three ratios were the degree each player exceeded, or failed to exceed, the overall scoring rate for each class of cricket.

Ponting, for example, had a ratio of 1.10 for Test cricket, 1.11 for ODIs and 1.06 for T20s. The product of those three ratios is 1.29.

Doing this for the six batsmen provides the following:

This method confirms Gilchrist's position as a premier run-scoring batsman, and consigns Michael Clarke to where he should be.

I hope this initial foray into analysing scoring rates over different classes of cricket might lead to some more sophisticated and extensive work by others!