Safe Speed Forums

I'd like to postulate as follows:


Where:
exposure is the total vehicle mileage
driver quality is the average ability of drivers to avoid crashes
environment quality is the inbuilt tolerance of the whole environment (vehicles, roads etc)

Comments?

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

I agree in principle - except of course that since none are linear operators (or, put another way, all are dynamic), I think it is better expressed as:




Where:
exposure is the vehicle mileage travelled for a given set of conditions
driver quality is the average ability of drivers to avoid crashes in such conditions
environment quality is the inbuilt tolerance of the whole environment (vehicles, roads etc) aka "given conditions" for a scenario

In general terms, that's fine - i.e. higher exposure = more crashes, lower driver quality and lower environment quality = more crashes.

However attempting to put it in a mathematical formula is somewhat nonsensical , as it implies the existence of some form of scale to measure each thing, and that environment quality is exactly equally important to driver quality, etc... I agree that exposure is linearly related to number of crashes, but whether 1/quality is linearly related to it is harder to say - what are we measuring quality by?

I think it's better to say it in broader terms:-

The number of crashes is directly proportional to the time spent driving
Lower driver quality and lower environment quality will increase the number of crashes

If a way of measuring quality was found, then we could attempt to put that into a formula, but otherwise it doesn't make much sense.

I think...!

(Edit: I don't know the difference between the words 'driver' and 'environment')

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-mike[F]
Caught in the rush of the crowd, lost in a wall of sound..

I guess that's the next step.

A good unit of average driver quality would be 'miles per crash' then we could stick it in directly. A good unit of environment quality would be 2005 = 1. And a good measure of exposure would be total miles.

_________________
Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

Ignoring environment for a sec, I agree with 'miles per crash', as then we have miles * crashes/mile = crashes, as intended. I'm not sure how useful this is, though, as 'miles per crash' is calculated from knowing the number of miles and the number of crashes, so you're in effect saying number of crashes = number of crashes...

And then there's the fact that 'miles per crash' is affected by environment quality, so trying to incorporate environment into the formula isn't going to work out, as far as I can tell.

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-mike[F]
Caught in the rush of the crowd, lost in a wall of sound..

The useful bit (as I see it presently) is establishing driver quality as a major road safety input factor. At present it's generally disregarded, but it's important. I also not that this is now converging on the work at the end of this Safe Speed page:
http://www.safespeed.org.uk/smeed.html
(I had no idea I was coming towards the same point from a different direction.)

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

But 'miles per crash' isn't a reliable measure of driver quality, as it varies with the safety of the environment. So the formula with the units chosen isn't actually showing anything about driver quality per se.

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-mike[F]
Caught in the rush of the crowd, lost in a wall of sound..

From a technical prespective you're absolutely correct. But I wasn't trying to offer measures - I was trying to describe the main relationships.

If we were going to be rigorous we'd have to refer driver quality to a specific environment we could say 'at 2005 levels' or 'in a reference environment' something like that.

But I still have to convince the road safety industry that driver quality is important. If we leave them (the road safety industry) alone, they will soon have made us as crash prone as the Belgians (four times more crash prone on Motorways).

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

Heh, sorry to be pedantic, comes with being a maths undergraduate I presume! Your modification makes more sense, although whether someone else would be able to pick a hole in it I don't know (I'm sure I could waffle about how it quite clearly isn't right if I tried, but I'd quite probably be making it up!)

Anyway, /me removes statistics hat and goes to get a mug of tea.

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-mike[F]
Caught in the rush of the crowd, lost in a wall of sound..

Yeah. You'e doing maths. I'm doing engineering. I don't care if the straight lines are slightly curved. If the answer is within 10 or 15% I'm happy. I'm looking for the factors that drive the system, and if the sums don't quite add up then that isn't important. What is important is that we understand the system well enough to manage its behaviour.

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Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

I don't see the environment as a constant. I make a very conscious decision to drive at safer times and on safer roads for my journeys. Thus if you used the same number for the environment for me and a driver who drives at more dangerous times you would skew the results. Or you could absorb my choice of times/roads into my personal skill level, treating that as part of driver skill, then it would be okay I guess.

I was more thinking about the national picture. It's be a national average environment and a national average driver quality. I think it's leads us in the right direction. We have to look for opportunities to improve average driver quality. One way is to chop out the most dangerous. Another is to educate the masses little by little. I think we should do both.

_________________
Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

I suspect that if you were to 'chop out the most dangerous' group it would be relatively unrewarding as they are likely to be a smallish group anyhow - at least I hope they are.

Surely a very large proportion of accidents involve the mass of ordinary drivers, so the greatest benefit would accrue from dealing with that group, which means practically all of us!

Anyhow I'm not into statistics so I can't prove that.

Best wishes all,
Dave.

I'm pretty sure we're looking a graph like this:



Note that the graph does not have scale numbers. I'm pretty sure that 60% of crashes are caused by the bottom 10% of drivers and that 80% of crashes are caused by the bottom 20% of drivers.

I'm also pretty sure that the high crash risk assocoiated with young drivers really comes from 20% of the young drivers. (i.e. 1 in 5 of them have a very high risk which reflects on the whole group.)

And in one very real way 90% of drivers (who say they are better than average) really do have less than the average crash risk.

_________________
Paul Smith
Our scrap speed cameras petition got over 28,000 sigs
The Safe Speed campaign demands a return to intelligent road safety

Ah, I see - makes sense, I thought you were thinking of using it to judge an individual's driving skills.

Another thing to consider is that the situation might be very different for different severities of crash. I know someone who used to have a staggering number of minor bumps, typically not noticing that the car in front of her hadn't actually pulled out into a gap while she was looking to the right, seeing a gap and deciding to pull into it as well. She once crashed her car while taking it home from the garage after it had just been repaired from the previous one. However she never had an accident that resulted in more than minor damage. This is a very different type of bad driver to the sort that might be much more skilled at "racetrack" type competent driving, but the consequences when these different types of driver make a mistake are very different.

A couple of thoughts

Driver quality would perhaps better termed driver experience.
Exposure defined as total vehicle mileage does not take account of congestion.

I think what you are trying to define is risk management, and I would guess the insurance companies have modelled this quite carefully as the success of their businesses depends on it. Of course their modellling will include other things too like car value for theft purposes.

I don't agree. On a personal level my driving experience was fairly extensive, before joining the police (at 34). I took a standard driving course followed by an advanced course when I realised that my driving quality had not improved, and in fact had probably peaked some years earlier after which bad habit and familiarity had cause a decline in quality.



It'd be interesting to get some inside info from an insurance underwriter to see if there's any correlation whatsoever between speeding convictions and mileage travelled against claim risk (both quantity and cost of claim).
Or as I expect we generally suspect, the cumulation of points on your licence gives the insurance companies the opportunity to load a premium for no added risk, or offers a get out if convictions are not notified.

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Fixed ideas are like cramp, for instance in the foot, yet the best remedy is to step on them.

Ian