Any experts in statistics around? Something weird happened and I'm curious if the odds could even be estimated.

[jderimig]

I don’t buy the subconscious explanation. The stimulus was going out of town, which is often the only reason I think to get my oil changed or do other maintenance, especially on my older cars. I have no idea what the mileage number on my sticker for my next oil change is, and I also have no idea what my odometer reading is on either of my cars. It’s not something I pay attention to or check unless I have a specific reason to look at it.

That is is fair.

But a long time ago there was an era when cars didn't tell you when to get an oil change. Sandy and I lived in that era. Most every vehicle had the sticker in the corner of the windshield and I would guess the majority of vehicles got the oil changed in time or not too late. For that to happen there had to be frequent glances at both the sticker and odometer consciously or unconsciously. I would bet the stimulus for all those millions of glances were not upcoming 1500 car trips.

I agree that the odds of any one individual of catching the exact mileage are high, but I do not think they are lottery level high. But lets say the odds are 100,000:1. There are 286 million cars on the road in the US. Given those odds and 286 million + trials every year, the odds of someone catching the mileage are almost 1. This time it was Sandy, probability says there are many others too.

Edit/Add: Since this event the system has become even less random. I will predict that @Sandy H. will experience this again. Sandy check back with us in about 5000 miles.....

 

[ThirstyBarbarian]

That is is fair.

But a long time ago there was an era when cars didn't tell you when to get an oil change. Sandy and I lived in that era. Most every vehicle had the sticker in the corner of the windshield and I would guess the majority of vehicles got the oil changed in time or not too late. For that to happen there had to be frequent glances at both the sticker and odometer consciously or unconsciously. I would bet the stimulus for all those millions of glances were not upcoming 1500 car trips.

I agree that the odds of any one individual of catching the exact mileage are high, but I do not think they are lottery level high. But lets say the odds are 100,000:1. There are 286 million cars on the road in the US. Given those odds and 286 million + trials every year, the odds of someone catching the mileage are almost 1. This time it was Sandy, probability says there are many others too.

Edit/Add: Since this event the system has become even less random. I will predict that @Sandy H. will experience this again. Sandy check back with us in about 5000 miles.....

4 years ago I bought a car that has a brain in it and tells me (my wife actually) when it’s due for maintenance. But every other car I’ve owned, starting with my first in 1986, which was already 20 years old at that time, I had to keep track of maintenance myself. Up through the mid ‘90s that meant I changed the oil and filter myself, no sticker to remind me. And for the past 30 years, give or take, I’ve had the little sticker from wherever I got the oil changed last time. But I never developed a habit of looking at the sticker and monitoring the odometer. I go on at least one 1,000+ mile road trip per year, usually more, so that’s when I check to see if the car needs any maintenance. When I used to have a longer commute, I might check if it was time if I thought of it and it felt like it had been awhile. The exception to that was when I had a VW with air-cooled engine, and I would check the oil level almost every time I got gas, and I’d change it if it started looking dirty.

 

[cls]

... Regarding the distribution of probability of the ABCDEF mileage:

I don't think it is anything like a binomial distribution. I mentioned Poisson distribution, but I think Benford's Law nails it.

Benford's Law says 30% chance the A is 1, 15% chance A is 2, etc.

https://en.m.wikipedia.org/wiki/Benford's_law

Zip'fs Law has a similar power law distribution.

https://en.m.wikipedia.org/wiki/Zipf's_law

Pareto distribution is the 80/20 rule. Closely related to Zipf's and Benford's rules, but not exactly right for guessing the likely mileage.


Regarding the pithy quote about damn lies and statistics: statistics is mathematically rigorous, proveable from basic principles. But it's a dangerous tool, naive users can easily mistake one of the sharp ends for a handle. Choosing the right tool for the job is an art.

Most stats classes only ever mention the binomial distribution. It's the easiest and most common, but not always appropriate.

 

[Art Upton]

Yep. But you have to start somewhere. The first assumption seems pretty reasonable. The second one, well, I have a colleague that remarks "80% of statistics are made up on the spot." It does provide a reasonable starting point.

Then you can go ahead and vary your assumptions to see how sensitive your probabilities are.

Now that you mention it it seems I look at my Oil Change Sticker about every 800-1200 miles.

 

[jderimig]

... Regarding the distribution of probability of the ABCDEF mileage:

I don't think it is anything like a binomial distribution. I mentioned Poisson distribution, but I think Benford's Law nails it.

Benford's Law says 30% chance the A is 1, 15% chance A is 2, etc.

https://en.m.wikipedia.org/wiki/Benford's_law

Zip'fs Law has a similar power law distribution.

https://en.m.wikipedia.org/wiki/Zipf's_law

Pareto distribution is the 80/20 rule. Closely related to Zipf's and Benford's rules, but not exactly right for guessing the likely mileage.


Regarding the pithy quote about damn lies and statistics: statistics is mathematically rigorous, proveable from basic principles. But it's a dangerous tool, naive users can easily mistake one of the sharp ends for a handle. Choosing the right tool for the job is an art.

Most stats classes only ever mention the binomial distribution. It's the easiest and most common, but not always appropriate.

The interval of inspections (glancing at the odometer) is best modeled by the Poisson distribution. But the number on the odometer cannot be modeled by any random distribution because that number is not random.

The probability problem would be defined as:
Once the odometer and sticker match, what is the probability of Sandy checking both within any 4 minute interval?

The Poisson fits that problem:
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

 

[Sandy H.]

[snip]

The probability problem would be defined as:
Once the odometer and sticker match, what is the probability of Sandy checking both within any 4 minute interval?

[/snip]

That helps things click in my head a bit more.

The human behavior aspect is what makes me think it isn't reasonable to get an actual number without huge bounds on uncertainty. For example, I probably spend less than 10 minutes a year 'looking for my keys' as I have a very rigid routine when I get home, to a hotel etc. There are a few times I break the routine due to outside issues, but I'm pretty rigid in following that routine.

My wife, on the other hand, spends tons of time looking for her keys, wallet, credit card etc. So, I think some people would be much more likely to observe the mileage match than others.

 

[jderimig]

For the Poisson process example. Lets say Sandy checks the sticker once every 100 hours of driving on average. Assume that when he looks at the sticker he looks at the odometer.

Mean rate of occurrence per 4 minutes: 1/100h/15 = 0.0006666

Probability Poisson calculator:
There is a 99.933% chance of missing this event.
But 0.067% chance of catching it.

 

[Ronz Rocketz]

Here’s another weird coincidence that happened to me a couple years ago. I gave a stranger begging for money a $5 bill in a Target parking lot when I was out running errands. About an hour later I was out for a walk in my neighborhood and found a $5 bill on the sidewalk.

Weird.

It might not be too uncommon to give a stranger some money, but it is pretty rare for me. I don’t live somewhere where I get asked very often — maybe a couple times a year at most — and I don’t always do it when asked. Also, it’s not unheard of to find money on the ground, but it’s rare enough I think I can remember most of the handful of times it’s happened. So what are the odds I’m going to give away $5 and then find that exact amount on the ground an hour later?

There is a philosophical belief that everything in the universe averages out. If you give away something, you’ll get something similar. If you take something, you’ll lose something similar. Therefore finding $20 isn’t that exciting because it means you’ll lose something worth $20. It adds another view on charity.

 

[ThirstyBarbarian]

There is a philosophical belief that everything in the universe averages out. If you give away something, you’ll get something similar. If you take something, you’ll lose something similar. Therefore finding $20 isn’t that exciting because it means you’ll lose something worth $20. It adds another view on charity.

I agree about things evening out, but I prefer to think this thing was more of a very mathematically precise instant karma, but the good kind: You gave five bucks, so here’s your five bucks back.

 

[Sooner Boomer]

There is a philosophical belief that everything in the universe averages out. If you give away something, you’ll get something similar. If you take something, you’ll lose something similar. Therefore finding $20 isn’t that exciting because it means you’ll lose something worth $20. It adds another view on charity.

Probably...

I was out mowing the front yard one afternoon. I looked down and saw a five dollar bill in the grass. Just as it got sucked into the mower.

 

[ThirstyBarbarian]

Probably...

I was out mowing the front yard one afternoon. I looked down and saw a five dollar bill in the grass. Just as it got sucked into the mower.

Easy come. Easy mow.

 

[Ronz Rocketz]

I’m donating double Red at the blood bank. What would be the equivalent that I might get back?