Cricket is one of the world's most statistical sports, and
mathematicians in cricket-loving nations love nothing more than delving
into the minutiae of the numbers and diving into averages, strike-rates
and custom-made measures of batting and bowling effectiveness.
For many people, including me, cricket isn't just a sport, it is a way of life.
These words could easily have come from me, but are actually the words of Rob Eastaway, a cricket-loving mathematician from the UK, and originator of the official International Cricket Council cricket-ratings which rank not only teams, but players within each team.
Ranking individual batsmen and bowlers is no small task. A common
method of comparing batsmen is their average, which is the average
score the batsman compiles each time he comes in to bat. This method,
however, has a number of issues as it does not take into consideration
the opposition, playing conditions and how recently the runs were
scored. How can you compare a score of 60 against a world-class
opponent on a dodgy pitch with a score of 150 against a lowly rated
team in easy batting conditions? This is what Eastaway's ranking system
attempts to do - and the maths is quite difficult (far more difficult,
in Rob's words, than the Duckworth-Lewis method
of determining the winner in a rain-effected game!) As well as taking
into consideration the strength of the opposition and playing
conditions, the ranking system places a greater emphasis on recent
performances. The overall system has a number of feed-back loops - the
individual player ratings contribute to a team's rating, which effects
how many rating points an opposition player can earn against that team
- remember, a score of 50 against tough opposition will be worth more
than 50 against low-class opponents. Similarly, how each player in a
match performs influences how many points are on offer. For example, a
score of 45 out of an overall team score of 100 will be more highly
valued than a score of 45 out of 450. As such, large amounts of
historical data are used to come up with the final numbers. Limited
overs cricket has the additional dimension of strike-rate - a batsman
who scores his runs quickly will be rated more highly than a slow
scorer.
The system was first developed in 1987 by Eastaway with former English cricketer Ted Dexter
and colleague Gordon Vince, and at first the system was greeted with
scepticism by many cricket lovers. Nowadays, however, it has gained
credibility and has even been used by international cricketers to help
negotiate their contracts - for example, Michael Bevan
was for a long time rated number one in the One Day International
version of the rankings and used this in contract negotiations, however
he could not secure a Test spot. Known originally as the Deloittes
Ratings and in later years the PwC Ratings, the system was officially
adopted by the International Cricket Council in January 2005.
With a background in Operations Research and a love of cricket, Eastaway is essentially my idol!
As
many of the equations used in this system are now copyrighted, you
can't find the exact algorithms published anywhere. However, if you are
a big nerd like me, you might like the book Deloitte Ratings: The Complete Guide to Test Cricket in the Eighties by Marcus Berkmann.
The book details the ratings changes after each Test series in the 80s,
and the appendix contains many of the equations which underpin the
system. I was given this book when I was 10 and didn't much understand
it back then, but I was very happy to find it in storage when I
returned from the UK, and I now find it a maths-cricket-nerd's delight!
I'm fascinated to know if they come up with something for Twenty 20.
The ultra-shortened form of the game brings in loads more complexities,
not least of which is that unless you are an opening batsman, you may
not even get a bat! Here's hoping Australia can win the World Twenty20 - oh and The Ashes! If only I was in the UK this summer!
