Monday, August 03, 2009

Poisson processes and motorsport accidents

Mark Hughes argues in Autosport this week that there was no link between the F2 accident in which Henry Surtees was killed by a flying wheel, and the accident 6 days later in which F1 driver Felipe Massa suffered a fractured skull. By way of comparison, Hughes points out that there was barely any link between the five serious accidents which occurred over the Imola 1994 weekend, leaving two drivers, including Ayrton Senna, dead. "A full appreciation of randomness," writes Hughes, "means it would be bizarre if such clumps did not occasionally occur."

Mark is quite right about the Surtees and Massa accidents. In fact, this type of randomness can be mathematically characterised as a Poisson process. If a certain class of events occur randomly and independently of each other, at an average rate which is constant over time, then the number of such events which occur within a length of time will have a Poisson distribution, and the time intervals which elapse between successive events will have an exponential distribution.

In a Poisson process, the inter-event times have a tendency to cluster because short inter-event times have a relatively high probability under the exponential distribution. The clustering of accidents in motorsport is just one particular case of this statistical phenomenon.

There is, however, an extra ingredient at play in the case of motorsport: anxiety. The presence of anxiety creates a degree of clustering which exceeds that which would be explicable by Poisson statistics alone. For example, the series of fatal or near-fatal F1 accidents which occurred in early 1994, after an eight-year hiatus, is a peak too great to be attributable to randomness. Recall that, not only were there five serious accidents over the Imola weekend itself, but two weeks later Karl Wendlinger had a near-fatal accident at Monaco, and shortly thereafter, Pedro Lamy was fortunate to escape with broken legs after cartwheeling into the spectator enclosure during private testing at Silverstone.

It is well-known that certain types of anxiety inhibit effective decision-making, hence it can be hypothesized that after the first fatalities of 1994, some of the drivers, and even their teams, entered a state of anxiety, which in itself provoked further errors and serious accidents. The anxiety hypothesized here is not of the overt variety, but rather a suppressed and hidden type, which only manifests itself in split-second judgements. The presence of accident clusters in motorsport is therefore the consequence of both randomness and human psychology.


Sean said...

Better example might be cricket where wickets tend to fall in clusters.

the next batsman in is always anxious to see what the ball and wicket are doing before they start playing there better or more natural shots.

Gordon McCabe said...

Excellent point! We can say, therefore, that an England batting collapse is simply part of an anxiety-aggravated Poisson process!

Sean said...

and for your next trick you can explain the physics of reverse swing bowling, this is surly something that should not happen in a rational world?