I’m a scientist at heart, I believe in emperical evidence, research based medicine and the eradication of silly superstitions.

Unfortunately sometimes this job can throw weird things at you.

An example of this happened to me the other day.

Out of eleven jobs I went to three in the same street, lets call it ‘Gray close’. All the jobs were to diferent houses and all were for diferent illnesses. The area is not in an especially deprived part of Newham, so there is no real reason why I should have to go there more than usual – and to be honest, I can’t remember the last time I was there.

I was wondering what the chances of this happening were – so bear with me for a bit, and if my maths is a bit screwy then feel free to correct me.

There are roughly 92,382 households in Newham (I worked this out by dividing the population of Newham by the size of the average household 2.64), and while I cover more of an area than Newham, this number will do for the purposes of this example.

All numbers come from the Fire Service.Gray close has 34 households.

92,382 divided by 34 is 2,717. So the chances of a specific call being in Gray Close is 1 in 2,717.

I did 11 calls that day, and three of them were in the same close, which has the odds of something like 1 in 20,057,135,813.

At least I think that is right – it has beenyearssince I looked at statistics and probability and to be honest I didn’t understand it then. But while the maths might be wrong, the effect is still stunning.

An additional thought is that this isn’t that unusual – At least once a week I’ll find myself going to the same street, or streets that are neighbouring each other on the same day for multiple, unconnected calls..

It is this that makes me think that there might just be certain concentrations of some form of ‘bad vibe’ that hit certain areas causing illness, assaults and other ‘emergencies’. I’m sure there is some clever (and very expensive) clustering software that could work out if this sort of thing was a real effect or just my all too human mind playing pattern recognition tricks with me.

Or am I just going mad?

This is probably related to the puzzle of how many children you need in a class to be fairly certain that two of them will share the same birthday. The answer is surprisingly small less than 30 if I recall.The trick is that it is not the odds of 3 incidents in Grey close but the odds of 3 incidents in any one street.

Hope that helps or there's a statistician soon along to explain better. (what are the odds of a trained statistician reading this post?)

I refer you to http://www.numberwatch.co.ukHave a look at “the cluster fallacy” as desrcribed at

http://www.numberwatch.co.uk/Breakthrough.htm

I think that tells you all you need to know about this “phenomenon”.

mind tricks and madness!

I'm trained to a certain degree (part of my maths degree is statistics)You are indeed right, it's the chances of 3 being within any “local area”.

There's also the fact that people only notice something when it's different from what they expect. E.g. people who think that all women are bad drivers will notice any woman who drives badly, and think “There, that proves it”. They'll miss all the women driving well, or the men driving badly.

Another thing is “wouldn't it be odd of odd things never happened” – if something has odds of one thousand to one of happening any given day, you'd still expect to see one every 3 years or so. If you went 10 years without seeing any, that'd be far weirder than seeing it 3 or 4 times!

Hope some of that makes sense.

Fun times with statistics, but I believe the birthday example above moves towards the right direction.For weirdness, though, doesn't Newham General A&E pull in extra staff for nightshifts with a full moon? I think my sister may have lied to me. Again.

With all the different A&E departments I've worked in, we've never worried about full moons. (read as – your sister is telling porky pies). And in my experience the phase of the moon has little to do with patient number/disposition (and this is backed by a number of scientific studies).What

doesmake a difference is the weather…hmmm…I think that'll be tomorrow's post as it is especially relevant considering yesterday's weather around here.EMS certainly lends itself to superstitious thinking (just try saying it sure is quiet today around an ambulance station).In this case, it seems the me that the question really isn't what are the odds of getting three out of 11 calls on “gray” street, but instead what are the odds of getting three out of 11 calls on ANY given street, as that would have caught your attention in the same way.

I'm too lazy to do the math (the semester just ended after all), but I know from psychological research that people underestimate the probabilities of “unrepresentative” sequences.

For example, imagine you put two red, two green and two purple balls in a hat and shake them up. Then, one ball at a time is retrieved at random. Which of the following two sequences is more likely?

Sequence A: G,G,P,P,R,R

Sequence B: P,G,R,G,P,R

Probability theory tells us that the sequences are equally likely, yet most people say Sequence B is more likely than Sequence A, as A does not fit their idea of a “representative” random sample.

It is likely that you forget the hundreds of days where you have calls on all different streets, as they fit your idea of a representative call distribution. Likewise, you are likely to note the clustered calls as they violate your representativeness heuristic. Of course a true empiricist would document call sequences over a five year span and then do the analysis. I hope you have better things to do :-).

DJ

psychonomic.blogspot.com

That's the difference between getting three calls to the same street, and getting three calls to Grey Close specifically. Getting the first call to Grey Close was a 1 in 2717 in itself…Also, the chances of getting ONLY 3 calls to Grey Close on a day of 11 calls is 1 in 20,116,290,457

1 / (((1/2717.0)^3) * ((2716/2717.0)^8))

It's a long time since I've done stats as well, but I think you're thinking about this the wrong way.If you'd said at the start of the shift “ooh, I wonder what the odds of me going to grey close 3 times today are”, you'd be closer to the mark.

But you weren't – the first visit is nothing unusual, it's the repeats that are the coincidence.

Say the first job was at Grey close. I think the odds of 2 repeat visits to a given street is something like:

( (housesInNewham / housesInGreyClose) ^ 2 ) / (jobsInDay – 1)

Which is about 1 in 738,000. Still a big number, but a bit more believable.

Also see the law of large numbers.

“The law of truly large numbers says that with a large enough sample many odd coincidences are likely to happen.”

therefromhere.

You are of course all assuming that incidents are independent of each other. This may not be the case, as psychic ripples in space/time from incident 1 impact on the other lives in “Gray Close”. Of course, the degree to which the ripples hold true or dissolve into existential white noise depends entirely on the residents and their ability to preconceive happenings. I think it is more likely that “Gray Close” is inhabited by psychic tools, who trip over the first paradox they see and hurt themselves.=) ValhallaShoes

Someone with a much higher intellect than myself once explained this by saying it wasn't unusual – what was strange was that it didn't occur more frequently. And now I think I'll have to go and lie down.Pat

Yep. I agree with that. I work in a secure unit and the weather, particularly high wind or pre-thunderous humidity are usually the busiest times. I understand schoolteachers notice the behaviour difference in school children on windy days too. Anyone able to confirm that? I'll be interested in tomorrow's observations Reynolds.

Forget the maths, ambulances and hospitals are lights, and people are moths. Your first call just set the trend.I have been known to attend more than one call in a street in one day simply because of the fact that it is cheaper to fake chest pain and get an ambulance to hospital to visit your neighbour than it is to get a taxi there.

A teacher I know told me that kids mood was a very reliable snow-forecast tool. They apparently get over-excited a couple of hours before the first snow flakes.

Haven't the foggiest about probability or statistics (except my favourite one that 49% of all people are below average), but wondered if you'd seen the site http://www.momscancer.comYou mentioned being interested in doing some kind of comic book project with your blog, and this linky is an excellent one with a medical theme that really works.

Well, this sure beats Sudoku!

The birthday “paradox” explains this exactly. The issue isn't Gray Close. It's not three of something, its about three of anything. Imagine that there are 2717 days in a year and there are 11 people in the room, then the odds that two of them have the same birthday are about 2.4%.

If you break Newham into household zones each containing 34 households, then in any 11 calls, you would expect two to be in the same zone every 41-42 days, assuming you never got a day off.

What is the math for three people in a room having the same birthday? I have no idea, though I suppose if I weren't so addled with 1975 Bordeaux, I could work this out. Obviously, less than 2.4%, but probably not amazingly so. I'll bet that you 3 out of 11 in the same “zone” every few years. Draw your grid now.

Of course, there are an awful lot of undistinguished 34 household zones to consider.

I've got too much time on my hands and not enough mathmatical ability but the math for 2 occurances in the same space is quite well documented if a little head spinning. for 3 more cases there is less info, these two links point the way to anyone with a BIG calculatorhttp://mathforum.org/dr.math/faq/faq.birthdayprob.html

http://mathforum.org/library/drmath/view/56650.html

meanwhile if you include adjacent streets I think you reduce the odds by a half, third or even by 9

hope that helps I'd love to know the odd of three in a street if someone can do the extra maths

As well as these good corrections to the maths & hence the actual number value of the probability, it's obviously important to notice that even if the odds were 1 in 20 billion, that doesn't mean anything other than chance is necessarily at work.As a scientist friend pointed out, anything that occurs randomly can be expected to occur in clusters sometimes. What would be far more bizarre is if a random event always occurred at regular time intervals, eg if every 2,717th day you were called to Gray close, once only and never in between.

It would make it easier for the ambo service to know where to position their cars!

It would be interesting to know how serious the subsequent jobs were, if they were borderline cases, might it be that having seen an ambulance in their street gave them the idea of calling?

Isn't it like lottery numbers? Like, if you had 40 numbers, the likelyhood of getting any one is 1 in 40, and it increases slightly for each number you draw out, and kind of 'resets' each time, so that the likelyhood of getting 1,2,3,4,5,6 is the same as getting any number. In the same way, you're just as likely to get three houses in Gray Close as you are of getting any three houses out of the same size sample. It's one of those weird things where if you went to three houses in Gray Close, that's as likely as a house in White Ave, Black Street, and Orange Lane. However, if you went out before your shift and chose which houses you'd get call outs (which, strictly speaking, should be 'calls out', given that to call is the verb here, and you get 'called out') to, then got them, that'd be highly unlikely (like picking winning lotto numbers). But then again, you do get regulars, so I guess that warps the sample to some extent. That probably doesn't make sense, I'm much better at crosswords…

I don't think that visiting the same street three times is all THAT probable.Pick any combination of three journeys out of eleven. The probability of them being to the same street are 1/2717 * 1/2717 (which is not a lot, about 0.000014%). There are many combinations of three and so many chances. How may? The answer (see http://en.wikipedia.org/wiki/Combinations) is C(11, 3), or (11! / (3! * (11-3)!)), which is 165. The probability of visiting a street three or more times is therefore 165*1/2717*1/2717, which is 0.000022 or 0.0022% (1 in 44740).

For two it's rather more likely. C(11, 2) is 55 and the probability of any two journeys being the same is 1/2717 – so the probability of visiting the same street twice is 55/2717 or about 2%.

For neighbouring streets it's a little more likely. Suppose that every street has three neighbours. The probability of the second of a combination of two journeys being to the same or a neighbouring street is 4/2717. 55*4/2717 is 8.1%, which gives the probability of going to any 'neighbourhood' of four streets twice.

For three visits the corresponding result is 165*4/2717*4/2717, or 0.036%.

This all assumes a variety of things: that visit probabilities are independent, that streets are all the same size, that you always do 11 visits and so on. Breaking just about any of these puts the probabilities up. If there are 2716 one house streets and one mega-street then you'll visit Mega Street many times a day with high probability. If you're routed to streets near to your previous call with higher probability than more distant ones then it goes up. If the probability of medical emergency changes in different areas (eg, because all the old people or poor people live in one place) then it goes up. If the probability of a visit are not independent (eg, because all the people live in one place and the weather increases the risk of emergency for people more than it does for everyone else) then the chances go up. etc.

Xelah