Recently, there has been a great deal of talk regarding the limitations of the batting average, particularly in one-day cricket. In Test cricket, the batting average is a sound indicator of the batsman's ability: the rate at which runs are scored, while becoming more important, is still nowhere near as important as the amount which are scored and not-outs rarely distort the averages of top order batsmen. However in one-day cricket, a 25-ball fifty is often worth much more than a laboured 150-ball hundred. Due to teams being less likely to be bowled out in fifty overs, there is a large number of not-outs among the top order batsmen. This has led to the strike rate being considered almost as important by some pundits as the average itself.
In baseball, there have been similar problems. The basic batting average did not give enough detail about the player's true value to the team and failed to show his style of play: was he the classic slogger or the dasher that enabled other players to move around the diamond. Therefore statisticans have developed a number of formulae to demonstrate different aspects of the player numerically, the study of which came to be known as sabermetrics. Rather than just concentrate on a couple of factors to find a value, some sabermetrics use large formulae, some complex, others basic.
Therefore, with a bit of time on my hands, I decided to see how I could manipulate the figures of leading ODI batsmen to find several values that, used either in conjunction or alone, would paint a better numerical picture of the type of ODI batsman the player in question is.
Please note that as yet my formulae have only had a few hours work on them and there is definite scope for improvement (which is why I'm posting them here).
I took the career ODI batting statistics from 53 leading batsmen from the leading eight nations. The cut-off point for what defines a batsman was roughly 50 completed innings with an average in excess of 25, though exceptions were made for the likes of Pietersen, Afridi, Dhoni and Hamish Marshall. These stats were taken from The Cricinfo Guide to International Cricket 2007 and only include ODIs up to mid-September 2006.
If the basic batting average was no longer the most useful statistic, then I needed something to replace it, showing the true value of a batsman to his team. Therefore I introduce the total batting value or TBV.
To begin with, a few terms I made up need explaining:
Regular average - the standard batting average (runs divided by times out).
Raw average - runs scored divided by innings batted, hence removing the not-outs.
100s per innings - the number of hundreds scored divided by innings batted.
50s per innings - the number of fifties scored divided by innings batted.
The sum of the raw average multiplied by four and the regular average multiplied by one is divided by five to give the weighted average.
(raw*4 + reg)/5
The 100s per innings (100/I) is multiplied by 450, to give the weighted 100/I.
The 50s per innings (50/I) is multiplied by 150 to give the weighted 50/I.
Matches played is also factored into the formula to reduce the anomalies caused by players with short careers (e.g. Pietersen, Dhoni).
Strike rate (SR) is divided by two to give the weighted SR
The TBV is composed as follows:
0.65 - weighted average
0.20 - weighted SR
0.09 - weighted 100/I
0.04 - weighted 50/I
0.02 - matches played
The entire formula is therefore:
(0.65*weighted average)+(0.20*weighted SR)+(0.09*weighted 100/I)+(0.04*weighted 50/I)+(0.02*matches played).
My spreadsheet shows players' performances over their entire career, so Tendulkar therefore tops the pile. Pietersen is second. While the differences in the players' ratings may seem very small, they are unlikely to fluctuate as drastically as a batting average. At the moment the only problem is trying to strike a balance between removing the anomalies caused by a short career by making experience more important (which puts Tendulkar, Jayasuriya, Inzamam to high) and removing too much emphasis on experience (which puts Dhoni to high). It tends to work best with top order players who have played over 100 ODI (Nico Boje, for example, is too high, as is Shaun Pollock).
I'd appreciate some feedback here - if you can try making subtle adjustments to the formula. I've already realised that it fails to take in the match conditions (e.g. runs scored on Asian flattracks are worth as much as those in New Zealand), but I think it is difficult to do so without a huge formula and lots of time. It looks like an improvement on the simple batting average anyhow. It is not an effort to show how 'good' a batsman is, but how useful he is to his team.
I've also been working on a 'slog coefficient', but that requires a bit more work.
Thanks to Hakon to his help and suggestions.