Statistical chances of crashing

[dpex]

Unless my understanding of basic math is way off, then it seems to me that the statistical chance of being involved in a crash of any sort is, in fact, infinitesimal.

To save head-space, I wish to limit the following to collisions between two vehicles (of any type and size).

Therefore, to become involved in a collision at least three things are required.

1. Two vehicles.

2. Velocity.

3. A time-window.

It is item 3 which suggests the chances of being involved in a collision is, in fact, infinitesimal. And so it is upon the time-window which I ask you to dwell.

Consider this. A collision time-window can be reasonably limited to four seconds, but let's extend that to ten seconds. Hell's teeth, surely even the most brain-dead driver/rider can avoid a collision with 10 seconds warning.

Stop right now and count off ten seconds, just to get a feeling for exactly how big the time-window really is.

For those with a really fetid imagination, imagine yourself standing in front of a firing squad counting off your last ten seconds. It's a bloody long time.

And so, if you accept that 10 seconds is a reasonable window of opportunity to become involved in an unavoidable crash, it follows that during any minute while driving/riding you live through six crash-opportunity windows. During any hour you live through 360 crash-opportunities.

But it's not just you. There are something to the order of 1.7 million vehicles registered in NZ.

Let's fairly assert that during any average daylight-day, the 1.7 million vehicles each (averagely) complete a half hour journey. It follows that during any average day-light day, throughout NZ drivers/riders complete 850,000 hours of travel.

850,000 hours provides 306 million collision time-windows, per average daylight day.

Now let's assume that during an average year there are say, 20,000 collisions of all types. That's roughly 55 per day.

Now divide 306 million collision time-windows, per day, by the average daily crash-rate and you find the statistical chances of you being involved in 'any' sort of collision is 5,563,636-to-1. That's about the same statistical chance of winning Lotto.

If you then use the math to determine the probability of becoming involved in a death accident, the statistical probability is mind-boggling.

Granted, the foregoing is cold-comfort to those who have been involved, but it does make one wonder what all the fuss is about.

[McDuck]

But crashig isnt random like lotto, crashing is caused by sombody doing somthing wrong.

[Motu]

You need to factor in target fixation - possibly the biggest factor in vehicle/vehicle crashes.

[98tls]

You need to factor in target fixation - possibly the biggest factor in vehicle/vehicle crashes. Possibly the same thing but factor in that it seems many motorcyclists when faced with a collision do simply nothing.

[Jantar]

Sorry, Wrong Number. The true probability is (1 - Pr(n)) where Pr(n) is the probability of NOT having an accident.

However to take your methodology one step further, lets assume that you are unlucky enough to have an accident, What are the chances that you will be injured?

The average motorcyclist travels around 17000 km per year. There are 8766 hours in an average year (including leap years), so your average speed on your bike is just under 2 kph. If you hit another vehicle head on then your combined average speed will be just under 4 kph.

According to the police the chance of being killed or injured in an accident is 50% at 50kph (the legal speed limit in tows) and this reduces by 2% for every 1 kph reduction in speed. So that at an average speed of 4 kph there is absolutely no chance of being injured in an accident.

So by using averaging, not only have you proved that its almost impossible to have an accident, but if you do have one then the most that can happen would be a light bruise.

[98tls]

:doh:Wheres Katman?

[Skyryder]

so where does the law of averages fit into the equation??


Skyryder

[dpex]

Sorry, Wrong Number. The true probability is (1 - Pr(n)) where Pr(n) is the probability of NOT having an accident.

However to take your methodology one step further, lets assume that you are unlucky enough to have an accident, What are the chances that you will be injured?

The average motorcyclist travels around 17000 km per year. There are 8766 hours in an average year (including leap years), so your average speed on your bike is just under 2 kph. If you hit another vehicle head on then your combined average speed will be just under 4 kph.

According to the police the chance of being killed or injured in an accident is 50% at 50kph (the legal speed limit in tows) and this reduces by 2% for every 1 kph reduction in speed. So that at an average speed of 4 kph there is absolutely no chance of being injured in an accident.

So by using averaging, not only have you proved that its almost impossible to have an accident, but if you do have one then the most that can happen would be a light bruise.

You are probably not aware of the fact that there was a glider, a V-Tailed job, named the Jantar, which crashed a lot due to poor design.

It seems you are carrying on the 'family' name.

Your analysis has nothing to do with the statistical probability of becoming involved in a collision.

And it wasn't really even vaguely humorous from an ironic view.

[dpex]

But crashig isnt random like lotto, crashing is caused by sombody doing somthing wrong.

Almost right, McDuck but....Except you got things back to front. Crashing results from two drivers doing something wrong, randomly.

Although you may wish to argue that God is sitting at his desk, bored shitless, and simply arranging crashes for His entertainment.

I mean, He wouldn't have the thrill of wondering what might happen if he conditions two drivers to crash...on account of He knows all which was, all which is, and which will be....Fuck what a boring existence he must have. Imagine having absolutely nothing to look forward to on account of you know all which is going to happen anyway.

Imagine being God watching McDuck and Mrs O'Hagey traverse the byways.

McDuck is doing anal-retentive and traveling at 99.78Kph and thus is pissing God off for being such a woose. Then there's Mrs O'Hagey, who is returning from giving here key-note speech to the Sceptics Society, entitled, 'God Is An Illusion'.

One woose. One unbeliever. One bored God. He knows what will happen but at least he gets the fun from watching Mrs O'Hagey pull out in front of McDuck, and watch McDuck's bike hit Mrs O'Hagey's car and turn McDuck into a human version of Jonathon Livingston Seagull, till he hits the tree. Splat!

Yup. It's all God's fault. My math exposition cannot compete.

[Big Dave]

so where does the law of averages fit into the equation??


Skyryder

In the middle.

[NighthawkNZ]

so where does the law of averages fit into the equation??


Skyryder

UnderneathSods law which below the Murphy laws

[FJRider]

To collide, another vehicle is not always required. A tree, a power pole, a fence, a rock face ... the list goes on ...

Collisions are a minor number of "accidents" ...

[FJRider]

so where does the law of averages fit into the equation??


Skyryder

There are some ..... above average .... lucky them. Most bins win's ... apparently ...

[Katman]

You are probably not aware of the fact that there was a glider..........


Oh, how I chortled.

[yod]

And so, if you accept that 10 seconds is a reasonable window of opportunity to become involved in an unavoidable crash, it follows that during any minute while driving/riding you live through six crash-opportunity windows. During any hour you live through 360 crash-opportunities.

how many oncoming cars can you go past in a minute?

it's a fuck of a lot more than 6....and every one of those fuckers is a "crash-opportunity"

[ajturbo]

cool..... i love numbers

[awayatc]

A statistician applies for a job....
How much is 1+1?

" how much do you want it to be?" ........

[6ft5]

so where does the risk comment come from that says a biker is 17 times more likely to be involved in a crash than a cage? How does this fit your equation?

[Viscount Montgomery]

89.23% of statistics are made up on the spot

[Kirill357]

Statistics is an artificial thingy to make one comfortably certain in the uncertain world, important thing most people dont understand about statistics is its promise absolutely nothing, even though your quarter had 10 heads in a row, it doesnt mean that next one will be eagle. And tell me about crash statistics, spend last 6 weeks in a cast, just now start walking again.

[FJRider]

Statistics are a way of keeping Statistition's ... employed.


So ... they have a use. :blank:

[skidMark]

Possibly the same thing but factor in that it seems many motorcyclists when faced with a collision do simply nothing.


I usually have time for one word...

It's usually

FUCK! :laugh:

[cc rider]

So, we're conjecturing on the substantially unsubstanciated statistical probability of an infinitesimally variable entity effecting a reactive outcome of which there is no ostensibly substantive evidential material. :cool:

[YellowDog]

Interesting facts however I cannot agree with the 10 second window of opportunity to crash or avoid a crash.

IMO - I'd put it at 1-2 seconds.

[dpex]

how many oncoming cars can you go past in a minute?

it's a fuck of a lot more than 6....and every one of those fuckers is a "crash-opportunity"

Thank you Yod, you support my posit most elegantly. In fact I'd be interested to know what the national statistics have to say about car (read 'other' vehicle)-V-bike head-ons. I suspect they represent a very small proportion of total Car-V-Bike collisions....I assert this because the lateral mass of a bike is, perhaps, one-fifth of a standard car, so the bike has much more room to negotiate a passage past an on-coming because the biker has five-times the road-space to use.

My further suspicion is that the greatest proportion, by far, of 'other vehicle'-V-Bike collisions occur at intersections, local and highway.

I presume that 'other vehicles' turning left or right in front of the biker (while traveling in the same direction as the bike) would take second place to intersection collisions.

I then come back to the issue of the time-window. Ten seconds is, in fact a hell of a long time. And I reassert that any biker who gets tangled after a ten-second window of warning is 'probably' Darwin's gene-pool cleaning fodder.

In fact, reaction-time required to avoid a collision (except of wet roads) is probably closer to the order of three seconds warning...Still a long time. But let's assume five seconds. That would then presume an accident opportunity window of 720 accident opportunity windows per hour.

But, if we all come back to the 'intersection/turning in front of' main opportunity, the relative opportunity numbers related to the chances of being involved in a crash start to crawl into the 100,000s-to-1 in any given time period.

Look at it from this view. You're tooling along at 50Kph. In other words you're covering about 14 metres per second. Ahead of you and to your left is a vehicle stopped at an intersection.

From a standing start this vehicle will require nearly a second to move forward sufficiently to get into your line of travel. During that second you will have traveled 14M. If that vehicle moved out when you were 2 seconds away, the gap would have been 28 metres. Three seconds away equals 42 metres separation.

When next you get the opportunity, have a go at doing a full stoppie from 50Kph to zero. If it takes you more than 10 metres I suggest you go back to walking or catching the bus. Allow 1.5 seconds for reaction time.

Do you see what I'm getting at here? Yet we still have fatalities vehicle-V-bike on suburban roads.

The chances, based upon time-opportunity-windows, of becoming involved in a crash are infinitesimal. But, shit happens. But is the 'shit-happens', hypothesis sufficient to regulate speed?

You see, if you were doing 100Kph in the same zone the window of opportunity for a collision shrinks to half the above values.

It follows that if you take errant pedestrians out of the picture, and increased urban speeds to 100Kph, the windows of opportunity for intersection collisions diminishes by 50% on account of you get past potential danger in half the time that you would at 50Kph.

[dpex]

so where does the risk comment come from that says a biker is 17 times more likely to be involved in a crash than a cage? How does this fit your equation?


Firstly: Maybe there's seventeen more times 'other' vehicles than bikes.

Secondly: Where did the stat come from?

Thirdly: The nature of the vehicles involved in a two-vehicle collision 'can' have a value....'I didn't see you', being the most used excuse used by other-vehicle-V-bike collision.

Frankly. I dunno.

It is entirely possible that a number of 'other-vehicle' drivers resent the freedom they 'imagine' bikers to have, and at some atavistic level wish to punish bikers for obviating the 'other-vehicle' drivers lack of such freedom. Like arseholes who gun for bikers and cagers wearing L-plates.

How many of the collisions occurred between one novice rider and one distracted mother of seven?

Who knows. What I do know is. the possibility of becoming involved in a collision with another vehicle is about as likely as winning lotto.

But maybe we should wear seat-belts, anyway.

[awayatc]

So, we're conjecturing on the substantially unsubstanciated statistical probability of an infinitesimally variable entity effecting a reactive outcome of which there is no ostensibly substantive evidential material. :cool:


I have got hypothetical double.....
Swap?.....

[ntst8]

Not sure about 17 times more likely to be in an accident but obviously the outcome will likely be worse if in one. A stats comparison would also be fairer if bikes vs high performance cars - even a Goldwing way outperforms your average family car.
Being a self employed old grey head when I took out life/loss of income insurance i checked whether motorcycling came under the dangerous pastime (ie cover excluded) category - it does not. That suggests the stats people don't see a significant risk vs all the other ways i might cost them money.

[p.dath]

Ahh, but you are assumng the 10s crash window events are independent. They are not.

You could have the accident at 1s, 2s, ... , 9s, 10s, into your minute.

[p.dath]

I would also consider the formula related to availability. You need to consider the MTTR (mean time to repair). e,g. Once an accident has happened, that driver is not "available" to have another accident until they are "repaired".

[p.dath]

Oh yeah, and you are also assuming that accidents are uniformly distributed across your crash windows. I'm guessing the time of the day has a large impact on the crash rate when considered by hour of the day.

[dpex]

I would also consider the formula related to availability. You need to consider the MTTR (mean time to repair). e,g. Once an accident has happened, that driver is not "available" to have another accident until they are "repaired".

You must smoke some good shit, man. Can I get some?

[bogan]

read this http://www.transport.govt.nz/assets/NewPDFs/Motorcycle-Crash-Factsheet.pdf read that, should offer some factual insight into the actual crash distributions and reasons, beats mad up statistics any day!

30% of people cannot understand the statistics produced by 72% of the remaining 15% of the total population

[cc rider]

I have got hypothetical double.....
Swap?.....

Are you talking predictions of double displacement reactions of 2 ionic compounds that are dissolved in water as in "AB (aq) + CD (aq) ® AD + CB" or maybe just some other thingy?

Happy to swap though, yeah? :rockon:

[Big Dave]

89.23% of statistics are made up on the spot

7.0% of us always give a similar response

[dpex]

read this http://www.transport.govt.nz/assets/NewPDFs/Motorcycle-Crash-Factsheet.pdf read that, should offer some factual insight into the actual crash distributions and reasons, beats mad up statistics any day!

30% of people cannot understand the statistics produced by 72% of the remaining 15% of the total population

Yeah Yeah Yeah, the stats are great, if not subject to an amount of subjective determination.

But that still does not defy the fact that the likelihood of any driver being inside to 2/5/10 second window of opportunity, required to to become involved in a crash 'with another vehicle' is infinitesimal.

Remember, to become involved in a crash with another vehicle you have to be at precisely the same place, at precisely the same time as the other vehicle.

Before your path-crossing with any other vehicle is a billion billion years. After you pass will come another billion billion years. It's only the ten seconds between to two sets of billion years which count for a crash to occur.

And so I come back to the point. 1.7 million drivers, doing just one hour per day, average. 1.7 million hours of daily driving, which provides 612 million, ten second windows for a two vehicle crash, per day.

I mean, really! What are the statistical odds for becoming involved in a two vehicle collision?

I figure I've completed, probably, in excess of 900,000Ks in the last forty years. Take my average speed throughout as say, 60Kph. That's 17,000 hours of driving ride (on the roads). Thus 61 million, 200 thousand windows of ten-second opportunities for me to have become involved in a crash have passed.

How may crashes have I had, to date? Zero.

Therefore, my current chances of having had a crash are 61,200,000-to-1.

Better odds than Lotto.

Mind you. Should I ever become involved in such a crash, the odds resile to !-to-1.

[Jantar]

You are probably not aware of the fact that there was a glider, a V-Tailed job, named the Jantar, which crashed a lot due to poor design.

It seems you are carrying on the 'family' name.

Your analysis has nothing to do with the statistical probability of becoming involved in a collision.

And it wasn't really even vaguely humorous from an ironic view.

I am very aware that there was a glider called the Jantar (and still is). It is not a V-tail and has a very good safety record. Three were imported into New Zealand in 1979, and one was destroyed in an accident on Mt Benmore. The pilot survived in circumstances such that had he been in almost any other glider he would have been killed. The other two Jantars are still flying. One is based in Taupo and the other at Omarama.

Jantar is my username because it is my favourite type of glider. One I have flown successfully in competitions and aerobatic demonstrations.