Tuesday, 28 April 2009

The duck and the case of misleading statistics

A duck is the lowest score you can get in cricket - it means nought or zero.

No runs whatsoever.

If you get out for a duck you have 'failed to trouble the scorer'. If you get out first ball that is known as a 'golden duck'.

All cricketers fear the duck. Every batsman feels better when they 'get off the mark' and score a run. But every cricketer will, at some point have got a duck. Indeed, a duck is the most common score in cricket.

Why is this?

Why is it, indeed, that even the most successful batsmen of all score far more ducks than you would expect? Indeed, a duck is often the modescore for a batasman, even if they average over 50. One might reasonably expect a batsman's average score to be the same as his mode score. But that is not the case. Ducks are extraordinarily common.

All cricketers think they know why this is. They believe that it is easy to get out 'before you get your eye in'. They believe that the bowler has the advantage of surprise. What's more the bowlers' tails are up and they are feeling confident after dismissing a previous batsman. Batsman therefore seek to start cautiously and defensively.

But in fact this theory doesn't explain it. The answer lies in simple statistics. Every batsman starts on zero. However, as batsmen can score in singles, twos, threes, fours and sixes they do not always alight on other scores. Every innings starts at zero but far fewer innings ever hit 12 or 27 or 31. Or 99.

This is an example of how common views of behaviour and life are in fact false. And how our misunderstanding of statistics hinders our view of the world, and colours our decision making.


danosirra said...

Let's take a batsman that has enjoyed 99 innings.

If, as you suggest, his/her median score is zero, then he must have had at least 50 innings in which (s)he got a duck. To protect your assumptions, let's assume (s)he got exactly 50 ducks.

And if his average score (mean, I assume), is 50+ (let's say it's 51, again to protect your assumptions), then the average score of their 49 scoring visits to the crease would have to be 103 to give them 5,049 runs overall, or an overall average of 51.

If 20% of their scoring outings ended with sub-50 scores (averaging 30, say), then the average needed for the remaining 39 outings increases to 121.

Doable, but I'd argue that it's unlikely. Did you mean mode, not median? Mode would make sense.

Bloom Blog: said...

Thank you Danosirra. I did indeed mean mode - but will leave the post unedited as a monument to a lack of care and attention.