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The most remarkable graph in the history of sport

by Michael Nielsen on October 19, 2008

The following graph is a histogram of the cricket batting average of all the people who’ve played cricket for their country [1]. It may not be obvious at first glance, but it’s a remarkable graph, even if you don’t give a fig about cricket, or even about sport.


cricket
(credit)

What makes it remarkable is the barely noticeable bump at the far right of the graph, which I’ve indicated by a blue arrow. It shows the cricket batting average, 99.94, of one Donald Bradman, an Australian batsman who you could plausibly argue was the most outsized talent in any area of human achievement.

To understand how Bradman’s 99.94 average compares with other batsmen, consider that a typical topflight batsman has an average in the range 45 to 55. Batsmen with averages above 55 are once-in-a-generation phenomena who dominate the entire game. After Bradman, the second highest average in history [2] belongs to South African Graeme Pollock, with 60.97, and the third highest to West Indian George Headley, with 60.83.

It’s tempting to think that the greats of other sports, people like Michael Jordan, Wayne Gretsky, and so on, must stand out just as far as Bradman. But a look at the statistics doesn’t back this up. For example, Jordan scored an average of 30.12 points per game, a monumental achievement, but only a fraction ahead of Wilt Chamberlain’s 30.07, with a somewhat larger gap to Allen Iverson, with 27.73. Following Iverson there are many others with averages of around 26 or 27 points per game.

For comparison, Bradman could have deliberately thrown his innings away for zero (a “duck” in cricket parlance) one time in every three innings, and he’d still have a career average of nearly 67; he’d still be far and away the greatest batsman ever to live. Even if Bradman had deliberately thrown his innings away one time in two, his average would be about 50, and he’d have been a topflight batsman.

Why yes, I am a cricket fan!

[1] Technically, it’s a graph of batting averages in test cricket, the oldest form of the game played internationally. Until the 1970s, it was also the only form of the game played internationally, and so its the only graph relevant to this post. Note that only players with at least 20 innings are included.

[2] Current Australian batsman Michael Hussey has an average of about 70. It remains to be seen if he can keep this up.

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13 Comments
  1. Reading the Wikipedia biography that you link to, it seems that the life of Donald Bradman supports the theory that genius is the product of passion and hard work. But it also seems that starting young may be important, at least for cricket.

  2. As I believe Ken Regan would confirm, a checkers grandmaster and mathematician named Marion Tinsley was perhaps an equally remarkable talent … Dr. Tinsely lost only nine checkers games in a 45 year career.

    It will be a long time before cognitive science and complexity theory can explain talents like Dr. Tinsley’s.

  3. Alejandro Rivero permalink

    The wikipedia article hints of a popularising way to explain three sigmas and five sigmas: 3sigma is Michael Jordan, 4 sigma is Pele, 5 sigma is Donald Bradman.

  4. John – Yeah, Tinsley was pretty amazing. Bob Beamon’s unbelievable long jump at the 1968 Olympics comes to mind as well.

  5. chris y permalink

    Bradman was famously interviewed in 1980, and asked how he thought he’d perform against contempoary opposition.

    “Oh, I reckon I’d average 50 or 60″, he replied.

    “But you averaged nearly a hundred in your career, and you played against some of the best bowlers in history!” said the reporter.

    “Yeah,” said Bradman, “But you’ve got to remember I’m 72 years old now.”

    Absolute self belief is also a key to making a great sportsman or woman.

  6. Chuk permalink

    It will be a long time before cognitive science and complexity theory can explain talents like Dr. Tinsley’s.

    Checkers was solved last year: http://www.sciencemag.org/cgi/content/abstract/1144079

  7. christine permalink

    Similar analysis by Justin Wolfers at Freakonomics, with comparisons to Usain Bolt (conclusion: misleading chart) and Joe DiMaggio (conclusion: “DiMaggio is okay, but he’s no Don Bradman”) recently:

    http://freakonomics.blogs.nytimes.com/2008/08/21/usain-bolt-its-just-not-normal/#more-2986

    Not coincidentally Wolfers is also Australian :)

  8. Christine – That’s very interesting, and some great graphs. I’ll add it to my linklog.

  9. christine permalink

    More contributions from economists (this time, Bruce Chapman, at ANU):

    The effect of the war and bodyline on Bradman’s batting average (without those would have been over 100; I think there was a formal paper, but can’t find it now):
    http://blogs.mbs.edu/fishing-in-the-bay/wp-content/uploads/2007/08/bradman1.pdf

    Don Bradman’s effect on revenue: http://econrsss.anu.edu.au/pdf/DP480.pdf

  10. Christine – How entertaining! I especially liked the comment about the authors’ relationship in the second paper. I imagine the effect of people like Jordan-Woods-Federer must run into hundreds of millions or billions of dollars today.

  11. Jack permalink

    HERE IS ANOTHER EXAMPLE. In the 1930’s the Australian team went to New York and Bill Woodfull the Australian captain was invited to have a swing with a baseball bat.
    He hit 9 out of 10 pitches for home runs. When he was asked by an Australian how he missed one, he said he felt sorry for the pitcher.
    At that time one of the Hall of Fame hitters was averaging 4 hits per pitch.
    Woodfull refused a contract.
    That is how good Bradman was by comparison.

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