When Numbers Count

Part I: Statistics and the Law

Statistics and judicial notice

In Multi-Sports Holdings, the Court considered whether the operator of an indoor cricket facility had been negligent in failing to warn a player of the risk of injury, or failing to provide protective equipment.  In concluding that there had been negligence, McHugh J (in a dissenting judgment) referred to statistics on injuries in sport, published by the Australian Bureau of Statistics and other bodies.  His Honour considered that such facts fell into the class of “legislative” facts that a court may judicially notice and use, at least for the purpose of defining the scope or validity of a principle or rule of law². 

Callinan J took a narrower view of the doctrine of judicial notice, concluding that resort to the statistics was not only unhelpful, but impermissible³.  His Honour appeared to accept that resort to more notorious statistics, such as the Consumer Price Index, may be permissible⁴. 

Life expectancy tables

In Golden Eagle International Trading Pty Ltd v Zhang,⁵ the High Court agreed that, in determining life expectancy, tables that projected future life expectancy on the basis of current trends, were to be preferred to those based on historical information.  The difference between the two was said to be some 5.6 years — a particularly significant increase for a judge approaching the age of statutory senility.

Long odds for special leave

Each of the above appeals resulted from the grant of special leave by the High Court.  A quick look at the number of unsuccessful applications shows that a grant of leave is truly special.  Once through this threshold, however, an appellant has an even money chance of being vindicated in the High Court, as the following table shows:

Short odds for mediation

The Supreme Court does not (to my knowledge) publish similar statistics on the number of successful and unsuccessful appeals.  However, it does publish statistics on alternative dispute resolution orders, which reveal a strong preference for mediation over case appraisal, and a high success rate for mediation.  Some of these figures are tabled below:

Part II: Statistics and Sport

On 9 September 2007, Jamaican sprinter Asafa Powell broke the world record for the 100 metres.  Powell’s time of 9.74 seconds was 0.03 seconds lower than his previous world record.  It had been almost a decade since the world mark had been lowered by so substantial a margin.  Upon hearing the news, I (like most Australians) wondered whether this kid from Kingston was as good as the boy from Bowral.

Attempts to compare achievements across different sports and different times face a number of difficulties.  One method (the “daylight” method) ranks the top eight or ten achievers in each sport, according to a leading statistic for that sport.  It then compares the statistical difference between the first and second ranked athlete, and the second and lowest ranked athlete.  If the first ranked athlete is truly ahead of the field, then there should be daylight between him and everybody else. 

Cricket

The ten highest test cricket batting averages of all-time are tabled below:¹⁵

The above table shows a cluster of averages approaching 60.  It is almost an insuperable barrier for any mere mortal.  However, Bradman’s average of 99.94 runs per innings is 38.97 runs better than Pollock’s, whose average is only 3.19 runs better than Sobers’.  In statistical terms, the distance between first and second is 12 times the distance between second and tenth.  It is clearly a case of Bradman first, daylight second, the rest of the field third.

Sprinting

When one looks at other sports, the position is quite different.  The differences between the achievements of top athletes are miniscule, and statistics cluster together.  For example, the fastest 100 metre runners of all-time are tabled below:¹⁶

Powell’s world record is 0.03 seconds faster than Gatlin’s time, whose time was 0.18 seconds faster than that of Hines.  This means that (ignoring the final entry) the distance between first and second is only one-sixth the distance between second and last.¹⁷  Were Powell as far ahead of the field as Bradman, the gap between first and second would be 2.16 seconds (twelve times 0.18 seconds).  In other words, if Powell were as good as Bradman, he would have run the 100 metres in a time of 7.61 seconds.

High-jump

Although breaking the eight-second barrier is quite an achievement for a person of diminutive stature, it is perhaps not as impressive as the Don’s high-jumping record of almost 4 metres, as is evident below:¹⁸

Basketball

Another popular candidate for the greatest sportsman of all time is Michael Jordan.  Jordan averaged 31.5 points a game during his illustrious career.  However, had he been as good as Bradman, his career average would have been 93.7 points:²⁰

Marathon running

Finally, as impressive as the above stats appear, they pale into insignificance compared to Bradman’s marathon achievement in running 42.195 km in 36 minutes:²² 

Two competing hypotheses, to be derived from the above use of statistics, are that:

(a) Bradman was a cut above every other sportsman that has ever lived;

(b) statistics are to be treated with extreme caution, since 63.7% of them are made up on the spot.

Finally, in order to understand the relevance of Bradman to the law, it is worthwhile recalling that, as stated in Cricket and the Law:

“… it is time to take law and popular culture seriously, and there is nothing more serious than cricket.”.²⁴

 
Peter Franco