Who is the greatest test batsman of all time? In a follow up to a recent paper I created a media furore by suggesting that India’s Sachin Tendulkar had eclipsed Australian great Sir Donald Bradman in terms of career performance.

The spirited reaction to my research is perhaps not surprising. As the Little Master prepares to step into the crease for his final Boxing Day Test against a much-diminished Australian opposition, it’s inevitable his remarkable legacy will begin to be dissected by fanatics of the game. Never mind the fact he’s chasing an elusive hundredth hundred.

That said, it seems the mainstream media has not fully understood the significance of my result, so I’m writing here to explain what it does and does not mean.

Batting averages: just not cricket

The most common way to assess a batsman’s career is to look at their average, which is simply the ratio of runs scored to the number of times the player has been dismissed.

Bradman, who is widely regarded as the greatest batsman ever, has an average of 99.94 runs per dismissal. This is phenomenally high, as an average of 50 is generally considered to be a world class performance. Sachin Tendulkar, on the other hand, has a relatively low (albeit still exceptional) average of 56.02.

But the batting average has problems. Cricket fans will often point to factors such as the quality of opposition, as well variations in playing conditions and equipment over time as reasons not to completely trust a player’s average as a measure of performance.

These concerns are reasonable, but they can be incorporated into a statistical analysis quite easily by comparing batting performance relative to historical means. One factor that is not so easily modelled is the issue of player longevity – some players simply play more cricket than others. This issue is actually implicitly accounted for when people cite Bradman as the greatest ever.

While Bradman’s average is exceptional, it is actually not the highest in test cricket. That honour belongs to little-known West Indian cricketer Andy Ganteaume, who played only one test innings and was dismissed for 112, leaving this as his career average.

Cricket fans are correct in noting that Ganteaume is not better than Bradman, and to ensure cases such as his do not appear in rankings of performance, a “qualification” is usually used to filter out extreme results. In a list of great batting averages it is required that a batter plays 20 tests before their name can be included. Such a system ensures that all players have had ample time to demonstrate their quality at test level.

Better than average

To an economist such as me, the above system looks rather odd. A batsman who plays 19 tests does not get included in the rankings, but a batter who is selected for 150 tests gets treated no differently than one that only just makes the cut. As sustained success is surely better than transitory success, there is a need to alter such a system to account for longevity in performance more effectively.

If we look at it like this, the question becomes, “how much weight should be given to a batter’s longevity versus his average in assessing his career performance?”

This question can be answered with a little economic theory. A batsman is only of use to his team if he averages more than his replacement player could have; a value known as the player’s “opportunity cost”. For test cricketers this value is approximately 40, although it changes from season to season. This means a batsman is contributing to his team when he scores above this, and detracting from his team’s performance – and risks being dropped – when he scores below this.

The opportunity cost may be plugged into an index to provide the correct weighting between these two facets of performance. Such players may be ranked by the extent to which they exceeded a “benchmark” player of their generation over the course of their career. This gives a sense of the total value of their career performance.

It is on this basis that Tendulkar (who has sustained his average for 184 tests so far) has slightly eclipsed Bradman who played only 52. Both players are miles ahead of the rest of the pack.

Mastering the stats

Bradman fans need not be too dismayed by my result, however. While it is fair to say that Tendulkar has been slightly more valuable than Bradman in aggregate, it is equally correct to say that what took Tendulkar 184 tests, Bradman achieved in only 52.

Perhaps the best way to think about the result is this: innings for innings, Bradman is vastly superior to Tendulkar, just as Ganteaume is slightly ahead of Bradman.

But if the Australian selectors could unearth another Bradman (restricted to playing just 52 tests) or another Tendulkar, they would be wise to opt for a local version of India’s Little Master. Just.