Last weekend Bruce Chapman sent me another of his little bits of econometrics about Don Bradman. Bruce calcualted how much the Don increased gate takings and concluded that the ACB got a pretty good deal when he batted!
In any event, with due acknowledgement, here is Bruce’s latest insight into the state of the world more than half a century or so ago.
The Centre for Economic Policy Research, in the ANUs Research School of Social Sciences, has been involved in research related to the economics of Australian Test cricket for over 13 years. In 1987, for example, we estimated the extent to which the Australian Cricket Board (then known as the Board of Control) benefited in revenue terms from the presence of Don Bradman at the batting crease.
When Bradman batted we found that the crowd was around 20 per cent higher. Our technique controlled for a host of other variables that affected crowd size, such as the price of the ticket, the venue, the unemployment rate, the state of the series, the state of the game, rain and the opposition. This increase in the size of the crowd had considerable implications for gate takings: just for Tests played against England in Australia, for example, we found that as a result of Bradman ACB revenue was about $X million higher (in 2000 dollars).
Recently we have turned our attention to a series of counter-factual questions, such as how much did World War II affect the ACBs revenue, given that the war meant that no Test cricket was played from 1939 to 1945?. Yvonne Dunlop, a part-time research assistant and PhD student in the Economics Program at RSSS has calculated that with the three additional series that would have been played in Australia in the absence of the war, the ACB would have raised around $12 million (in 2000 terms).
Hearing of our research, Frank Castles, a Professor of Politics at RSSS, suggested that there would be great interest in asking the related counter-factual question: What would Don Bradmans batting average have been if there had been no war? After all, we all know that his actual average of 99.94 is the most quoted, extraordinary, and exasperating statistic in Australian sport, given that it is so agonisingly close to the magic figure of a century.
It turns out to be very straightforward to address the issue. The idea we came up with was recognising that over time, as batsmen become both older and more experienced, it is likely that their performance changes. Thus if there is a relationship between Bradmans scores and when he batted, we can use this information to recalculate his hypothetical, war-less, new average.
There were four steps in the process:
(i) work out the extent to which his performances changed over the period of his career, 1928 to 1948;
(ii) impose some assumptions concerning when Test cricket would have been played if the war hadnt happened, and when Bradman would have batted;
(iii) estimate Bradmans hypothetical scores in each of these new innings, given the results of step (i); and
(iv) recalculate his Test average given these additional scores.
For step (i) we used regression analysis in which the association between each actual Bradman score and the month and year in which he made it was estimated. We did find a relationship but, to put it bluntly, as far as regression analysis is concerned the results were poor. Yvonne and I arent holding our breath for next years Nobel Prize in Economics for the power of this econometric exercise.
Nevertheless, the best approximation of the extent to which Bradmans scores changed over the period is that they increased by about 0.04 each month, or about half a run a year. That is, the statistics suggested that his 1948 average would be about 10 runs higher than his 1928 average (it was in fact about 7 runs higher).
For step (ii) we imposed the pre and post-war Test cricket experience, which suggested that if there hadnt been a war, there would have been four additional Test series, three in Australia (in 1939/40, 1941/42 and 1944/45) and one in England (in 1943). On the basis of Bradmans actual experience, we then worked out that the most likely scenario would have been that over 1939-45 he would have completed 28 additional innings from the extra Tests.
From our regression analysis we then estimated his likely score for each of these innings. In total this would have given him an additional 2,877 runs.
The exercise is completed by adding these scores to his actual total of 6,996, which gives him a war-free total over 1928 to 1948of 9,873 runs. Since he would now have been dismissed a total of 98 times, we divide 9,873 by 98. This gives us his new average of 100.74.
We repeated the analysis for a range of other regression models, and in all cases the hypothetical average exceeded a century, although never by much. Thus the conclusion: without WWII our best approximation of what Bradmans batting average would have been is just over 100.
This should be put in some perspective. It is apposite to note that the Bodyline series, designed by Douglas Jardine to curb Bradmans extraordinary prowess, had a bigger effect. Don Bradmans batting average not including the 1932/33 series was just over101.