Safe Speed Forums

I am outside of your model (which I acknowledge probably fits perhaps 80 - 90% of people).

The randomness was mentioned in a mathematics journal article by a female mathematician last year or the year before. She mentioned that a driver could expect to be banned on average once every 15 years and that it made little difference whether they were trying to stick to limits or not as you only need to make the slip up in the wrong place and you end up with 3 points.

I'll see if I can find a copy of it....

I broadly agree with your assumptions, but that is for the first four years of speed cameras.

Or you hope you are. Or perhaps it's a good job that LTI20.20s are dodgy, eh?

Possibly - but it was my spotting of the bloke in the lay-by a good half mile away that enabled me - with conviction <pun ironical> to confirm absolutely that my speedo was within the thickness of the needle on 70 when at 576m (the recorded distance). That one should never have been - but it could be that a person with similar habits and observation would have accepted the points (to maintain justice was very inconveninet on my time).

Sorry Roger, my last post no longer seems to read the way it was intended.

There's something I haven't got working properly yet - at the daft end of the scale where only 10% of drivers are speeders - the massive probability of multiple endorsements isn't calculated correctly. (Actually I was finding it hard to find a way to do it at all.)

3) Those who now cast eyes upward and pay deference to the cameras, either bychecking and if necessary gently slowing and checking in AMPLE time (I tend to fit in to that category) or by anchoring up.

There's potential for any number of other variables, of course. Drivers might modify their behaviour after being caught (a common theory, but not a very good one I think).

Many drivers are now well aware of the threat from cameras and carry out a kind of risk assessment before each journey. I scan the AA atlas for camera sites and look at the cameras on the online route-planner.

The Trouble With Speed Cameras


Rose Baker demonstrates the effect of proposed new Government policy.

Under a simple model of speeding offences, the probability distribution of time to being banned from driving as a result of speeding offences being caught on camera is studied, under the existing '4 strikes in 3 years and you're out' policy, and also under the Government's proposed new policy where banning follows 6 minor speeding offences or two major ones. The trouble with speed cameras (apart from the intractability of the mathematics) is that the time to banning for identical drivers is extremely variable. It is shown how far the proposed new policy ameliorates this problem. The analytic solution for the distribution of time to banning for major speeding offences is derived and shows a rich structure.

The number of speed cameras in the UK has increased to around 4500 at the time of writing, and many roads in my area now sport them. I found this out the hard way by getting flashed whilst driving too fast through the outskirts of Manchester. This prompted some mathematical reflections, which is ironical as it was making mathematical reflections while driving that was my downfall. I began wondering, this time at my desk, how one might model the events of being caught speeding, and the subsequent unhappy possibility of being banned from driving for a year after 4 speeding offenses within a 3-year period. The question is: what is the distribution of the time to getting banned, starting with a clean license, under a simple model of the occurrence of speeding offenses. Is the problem mathematically trivial, or not? The answer would seem to be that no analytic solution can be obtained (by me anyway) in general, but that for the simpler case when only two offenses cause banning, as is the case for serious speeding violations under the Government's proposed new scheme, an analytic solution can be obtained very simply.I can find no previous work on the mathematical modelling of speeding, although there are quite a few papers discussing the empirical effect of speeding cameras (e.g. Pilkington, 2003 and Redelmeier et al 2003) and driver attitudes to them e.g. Lawton et al (1997). The obvious point-process model for speeding offences is a Poisson process, which means that there is always a constant hazard of the next event, and that the interval between offences is therefore a random variate from an exponential distribution.
Clearly
=kN
where N is the number of speed cameras in use.
The process (and the car) stops when the driver is banned, which must eventually occur for any >0. For practical purposes however, being banned after 3000 years of driving is hardly a worry, and only the probability of being banned in a driving life span of say 50 years is of interest.
This is a problem of the absorption of a random walk, that stops when the total length of 3 consecutive steps is less than 3 years. This stopping criterion is resistant to mathematical analysis, but a Monte-Carlo computation is easy and yields quick results. Analytical results are later derived for the simpler case where only 2 offences within a period are required for banning: the resulting distribution of time to banning is sufficiently strange to suggest that an analytical solution of the general problem would be very interesting.

From Times on-line (and print edition) today...


December 12, 2004

One day soon we’ll all get a speed ban

IT IS a formula to infuriate. A leading statistician has warned there are now enough speed cameras to ensure the average driver can expect to face three driving bans in their motoring career, writes Jonathan Leake.

The study found that a typical driver — someone who normally obeys the rules but occasionally lapses — should now see occasional bans as almost inevitable.

In a research paper published in Mathematics Today, Rose Baker, professor of statistics at Salford University, says that with 4,500 cameras in Britain “the average driver will face a driving ban every 15 years”.

Baker also says that, far from habitual speeders being singled out by the cameras, being caught is “a lottery”.

According to her formula, the average driver can expect to clock up a speeding offence every two years. However, no driver will accumulate offences at exactly the average. Some will be caught for several offences in a short time, others may go for years without speeding near a camera.

This random variation means a quarter of drivers will get enough points to be banned every seven years. At the other end of the scale the randomness means about 9% will get through their motoring lives without a ban at all.

“All these motorists would be driving in an identical way, perhaps breaking the speed limit a bit but not often,” said Baker. “The reason for this effect is simply the growing number of speed cameras.”


Copyright 2004 Times Newspapers Ltd.
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I don't agree that the spread is purely random but I would suggest it is highly random.