Hundreds, ducks, averages and #RootMaths

Dennis Freedman Roar Guru

By Dennis Freedman, Dennis Freedman is a Roar Guru

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    Joe Root led England to victory over South Africa. (AFP PHOTO / CARL COURT)

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    During the latest Ashes series in Australia, a gentleman by the name of Dave Ticknor came up with the term #RootMaths.

    If I interpreted correctly, he was defending the age old use of cricket averages and why, in his view, it was nonsensical to remove Joe Root’s highest Test score of 180 from any evaluation of him as that is not how averages work…or something like that.

    In any case, it got me thinking about how the cricketing world uses maths.

    However, there is a counter argument to #RootMaths and it goes something like this:

    Averages are a poor predictor of a batman’s likely score as it allows for outlying scores (e.g. Root’s 180 and his one duck) to skew what may be his predicted score.

    In another sense, would you prefer Marcus North in your team who is perceived to score either 0 or 100 only, or Ed Cowan, who will make you 35 every time? Depending on your team makeup and strategy, this could be very important data.

    So, I applied standard deviation theory to the batting career’s of Root (29 innings @ 36), North (35 @ 35.5) and Cowan (32 @ 31) who all have similar records and here is what I have found.

    Let’s start with Root. Firstly, when plotted on a chart, his innings are clearly skewed to the left.


    That is to say, he is more likely to make less than his mean, than more on any given innings, with 72% of his scores falling less than 32 (his mean).

    Note also that for this purpose, not outs receive no special treatment unlike in cricketing averages. This exercise will only predict Root’s likely scoring range irrespective of the not out or game situation. It is an innings score predictor, not an average per wicket lost predictor.

    However, if the principle is applied equally across all players, it should not matter.

    Next, using standard deviation mathematics and plotting those points, we get a standard deviation of 38 on a mean of 32.


    In simple language, probability maths says that 66.6% of the time, Joe Root will score between 0 and 70.

    95% of the time, he will score between 0 and 108.

    99% of the time, he will score between 0 and 146.

    His highest score of 180 is therefore a 1% or even <1% event. Does that mean you can exclude it from his average? In a cricketing convention sense, probably not. However, in a Moneyball sense, I let maths do the speaking. North’s numbers
    66.6% of the time, North will score between 0 and 76.

    95% of the time, he will score between 0 and 117.

    99% of the time, he will score between 0 and 159

    71.5% of his scores fall below his mean of 33.4

    Cowan’s numbers
    66.6% of the time, Cowan will score between 0 and 60

    95% of the time, he will score between 0 and 89

    99% of the time, he will score between 0 and 118

    72.5% of his scores fall below his mean of 31.2

    Of these three players with similar records, North was the one more likely to score higher on any given day, even though his average was less than Root’s.

    I’m still developing my theories, and considering the strengths and weaknesses of this type of analysis, but welcome your thoughts. Let’s hear your comments!

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    The Crowd Says (61)

    • Roar Guru

      January 12th 2014 @ 8:11am
      Dennis Freedman said | January 12th 2014 @ 8:11am | ! Report

      If you are reading this, please disregard the article.

      As the author, not only are the images not showing properly, but 1/4 of the article was not published making the analysis nonsensical.

      • January 12th 2014 @ 9:30am
        up in the north said | January 12th 2014 @ 9:30am | ! Report

        Cheers Dennis, I thought for a while there that I was particularly dense this morning.

        • Roar Guru

          January 12th 2014 @ 9:50am
          Dennis Freedman said | January 12th 2014 @ 9:50am | ! Report

          The worst thing is that the article was groundbreaking. : )

          • Roar Guru

            January 12th 2014 @ 10:10am
            JGK said | January 12th 2014 @ 10:10am | ! Report

            From groundbreaking to heart breaking.

            Curse you The Roar.

      • January 12th 2014 @ 9:47am
        Shand said | January 12th 2014 @ 9:47am | ! Report

        Hi Dennis, that’s a shame- I hope the full article gets published- the analysis so far was quite interesting.

      • Roar Guru

        January 12th 2014 @ 12:09pm
        Dennis Freedman said | January 12th 2014 @ 12:09pm | ! Report

        Ok. Article fixed

    • January 12th 2014 @ 9:59am
      twodogs said | January 12th 2014 @ 9:59am | ! Report

      Can you do one for Watson?

      • Roar Guru

        January 12th 2014 @ 10:17am
        SuperEel22 said | January 12th 2014 @ 10:17am | ! Report

        He’s 100% likely to make a good start before inventing a way to get out.

    • January 12th 2014 @ 10:00am
      Jack said | January 12th 2014 @ 10:00am | ! Report

      Hi Dennis, that looks like a really interesting analysis. I for one would be keen to read the rest of it, and I know a few others who would be interested too so I think it would be great if you could find a way to post all of it.

    • January 12th 2014 @ 10:06am
      Timmuh said | January 12th 2014 @ 10:06am | ! Report

      That is unfortunate. I guess the editors will release part 2 at some point.

    • Roar Guru

      January 12th 2014 @ 10:16am
      Pom in Oz said | January 12th 2014 @ 10:16am | ! Report

      If we used medians instead of means (as we often do to compare house prices or salaries), I suppose we would get a more realistic figure for the most likely outcome of a player’s innings.

      • January 12th 2014 @ 2:34pm
        Straight Ball said | January 12th 2014 @ 2:34pm | ! Report

        ditto, even though he’s a Pom.

    • Roar Guru

      January 12th 2014 @ 10:18am
      JGK said | January 12th 2014 @ 10:18am | ! Report

      For what it’s worth, all this data (means, medians) etc can be found pretty easily on Ric Finlay’s stats software.

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