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

#### Sandy H.

##### Well-Known Member
TRF Supporter
Well, I guess the title says it all, but here is the scenario.

I'm going out of town on Wednesday and though I was probably way over due for an oil change (guessing 8-10k over). I glance down at the odometer and the mileage was ABCDEF. I looked at my oil change sticker. . . and it said ABCDEF. I couldn't believe it. It seems completely impossible (in my mind) that I looked down at the odometer at the exact minute I was driving and was at the exact mileage that the sticker said. I had totally forgotten that I got the oil changed earlier this year before a different trip, hence my thought that I was way over on mileage, so its not even like I had a bias to the number.

So, is there any reasonable way to approximate the odds of that scenario occurring?

On a completely unrelated note, I bought my first ever Powerball ticket on the way home. . .

Sandy.

#### Charles_McG

##### Ciderwright
That's not statistics, that's probability.

#### ThirstyBarbarian

##### Well-Known Member
Unfortunately, I think you used up your Powerball luck on the odometer trick. Better luck next time!

#### mikec

##### Well-Known Member
I'm going out of town on Wednesday and though I was probably way over due for an oil change (guessing 8-10k over). I glance down at the odometer and the mileage was ABCDEF. I looked at my oil change sticker. . . and it said ABCDEF.

For one thing, you are really bad at estimating how far you've driven.

If we assume you changed your oil 7K miles ago (usually the sticker tells you to do it more like 3K later so the oil change place makes more \$\$) and you could be off by that much, then I imagine the chance of this event happening is something like 1 in 14,000.

#### jderimig

##### Well-Known Member
To calculate the odds we would have to know the frequency you look at your odometer (views/mile) and the frequency you look at your oil change sticker if this is to be modeled that each view are independent random variables.

However this is probably not a random because your behavior was likely modified by your guilt of exceeding your service interval. So the random independent assumption would underestimate the probability of this event.

#### Sandy H.

##### Well-Known Member
TRF Supporter
For one thing, you are really bad at estimating how far you've driven.

If we assume you changed your oil 7K miles ago (usually the sticker tells you to do it more like 3K later so the oil change place makes more \$\$) and you could be off by that much, then I imagine the chance of this event happening is something like 1 in 14,000.
Hmm. Not sure how 14k would be the number, but ok.

To me, the odometer was changing 1 mile about every minute and 20 seconds (its a 45mph stretch and I actually don't speed!!!). I obviously don't look at my odometer that often (or the sticker) as I was thinking I was way over on mileage. So, I saw the two numbers being the exact same at a point in time that was roughly 1 minute and 20 seconds long. Any earlier and it would have been one mile short. Any longer and it would have been one mile too much. Seems way less likely than 14k, regardless of the oil change interval, but maybe I'm wrong.

Its kind-of like the saying 'a stopped clock is right 2 times a day'. That is true. But what is the chance you happen to look at that clock at the exact time it happened to be correct? If you constantly observed the clock, you would see both events, but if you looked at the clock any other time it would be wrong. That makes me think it has to do with how often you look at the clock. If I look every minute, it would happen 2 times in 1440 minutes, so that's easy. But if you only looked at the clock once an hour, it would either be 2 times or never, as we're talking minutes. If you looked every 59 minutes, it would be 1 time in (not going to figure out the math, but you get what I'm saying). . .

Sandy.

#### Grog6

##### Well-Known Member
TRF Supporter
You've seen the mileage number on the sticker for the last few months, and during the normal gauge scan we do, you saw it was the same. It speaks more to our pattern matching algorithms in our brain shaped by millenniums of evolution to pick out that predator hidden in the weeds.

#### Sandy H.

##### Well-Known Member
TRF Supporter
To calculate the odds we would have to know the frequency you look at your odometer (views/mile) and the frequency you look at your oil change sticker if this is to be modeled that each view are independent random variables.

However this is probably not a random because your behavior was likely modified by your guilt of exceeding your service interval. So the random independent assumption would underestimate the probability of this event.

I can't even guess how often I look at the odometer. Since I don't speed, I do check the speedometer often and the odometer is on the cluster as well, so some side-glances happen. I don't think my brain registers it most of the time, but when you see 112233, something clicks and you observe the number due to the pattern your brain saw and actually commit it to memory and try to take your phone out and take a pic or something stupid like that. Usually, when those events happen, I get 112234 in the pic.

But, if you had asked me how many miles I thought my truck had on it, I would have said around 117k. It was 123k. If you had asked when I got my last oil change, it would have been September, but in reality it was February and I just forgot about it (I guess humans aren't good at remembering random things they really don't care about that much. . . ).

The key point to me is that there was only a 1m20s window in which this observation was actually made and it happened to be the exact number in the 123000 range. The range does have something to do with it too, as if I bought a brand-new car with 0 miles on it and the first oil change was at 5000 miles, for the first 4999 miles there would be zero chance that I observed the two numbers being identical.

It seems to me the number would be in the 1:1e^whatever range.

#### Zeus-cat

##### Well-Known Member
Another thing to consider is can you see the odometer in your periphereal vision at any time while driving? You may subconciously see it and not really think about it. Once you got close your subconcious told you to look and bam, dead nuts on.

#### jderimig

##### Well-Known Member
I can't even guess how often I look at the odometer. Since I don't speed, I do check the speedometer often and the odometer is on the cluster as well, so some side-glances happen. I don't think my brain registers it most of the time, but when you see 112233, something clicks and you observe the number due to the pattern your brain saw and actually commit it to memory and try to take your phone out and take a pic or something stupid like that. Usually, when those events happen, I get 112234 in the pic.

But, if you had asked me how many miles I thought my truck had on it, I would have said around 117k. It was 123k. If you had asked when I got my last oil change, it would have been September, but in reality it was February and I just forgot about it (I guess humans aren't good at remembering random things they really don't care about that much. . . ).

The key point to me is that there was only a 1m20s window in which this observation was actually made and it happened to be the exact number in the 123000 range. The range does have something to do with it too, as if I bought a brand-new car with 0 miles on it and the first oil change was at 5000 miles, for the first 4999 miles there would be zero chance that I observed the two numbers being identical.

It seems to me the number would be in the 1:1e^whatever range.
You would be surprised. I think that happened to me too. Your brain is a fascinating machine. The occurence you experienced is not an alignment of random events. They are correlated. The sticker mileage was in your brain somewhere. Your brain also has your vehicle mileage stored somewhere and a predictor. Why were you thinking about your oil change? Thats not random either.

#### Sandy H.

##### Well-Known Member
TRF Supporter
OK, I see the points about subconsious things happening and I do believe it could be possible, but I would hope my active memory would be better. If you asked me the last place I got my oil changed (and I thought it was September) it would have been at Shamrock Automotive, but in reality, it was Scott Clark Toyota in February. I was suprised by that too, but could eventually work up the memory and remember why (last minute before a trip. . . ).

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
Safe to say mileage is normally below 200,000. So the odds are at last 1 in 200,000. You can reduce the number of possible values according to your particular case or what you knew beforehand. 1 in 100,000 would make sense.

(for someone in a "new" car, odds might be 1 in 10,000, because "new" could mean less than 10,000 miles).

#### Sandy H.

##### Well-Known Member
TRF Supporter
Safe to say mileage is normally below 200,000. So the odds are at last 1 in 200,000. You can reduce the number of possible values according to your particular case or what you knew beforehand. 1 in 100,000 would make sense.
But what if I only look at the odometer once every 100 hours of driving, for example. I only had 1 minute 20 seconds for that specific event to occur.

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
But what if I only look at the odometer once every 100 hours of driving, for example. I only had 1 minute 20 seconds for that specific event to occur.
Each time you look is like a lottery ticket where you get a 1 in 100,000 chance of getting it right. That's how I see it. Very crude model, but sure you can refine it with time intervals and eliminating numbers you know are impossible.

#### Art Upton

##### Well-Known Member
TRF Supporter
Ahh, ABCDF? really???

My Odometer on my crappy car and my nice Tundra Truck are all NUMBERS

#### Sandy H.

##### Well-Known Member
TRF Supporter
Ahh, ABCDF? really???

My Odometer on my crappy car and my nice Tundra Truck are all NUMBERS

I said in the initial post I bought my first PowerBall ticket tonight. . .why would I give away the winning numbers and reduce my payout!!! lol!!!

So there's a new probability to question. What are the chances I get more money back than my 'investment' (again, lol. . .) tonight? I think the drawing is in an hour.

Banking on still just flying LPR moving forward. . .

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
Ahh, ABCDF? really???

My Odometer on my crappy car and my nice Tundra Truck are all NUMBERS
Using a viriable "x" instead of a specific number "73" is like saying "some dude" instead of naming "King Kong Bundy". Math people just don't like picking favorites because the specific number doesn't really matter.

#### cls

##### Well-Known Member
Dunno what my odometer actually reads, but every time I cruise past the beach my mind says 80085 wow!

#### Sandy H.

##### Well-Known Member
TRF Supporter
Using a viriable "x" instead of a specific number "73" is like saying "some dude" instead of naming "King Kong Bundy". Math people just don't like picking favorites because the specific number doesn't really matter.

. . . And I didn't want to dilute my mega millions of dollars by sharing the number on a public forum. . .

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
First digit is likely a “1” of course. I would expect cars with more than 200,000 miles to be common but still a minority.

After that, there should be a nice weight curve from 100,000 to 199,999 with a park somewhere. Unless the peak is somewhere below 100,000. I’d like to see the curve from 0 to 200,000 (say for all cars on American roads today).

Sort of interesting … Ok, let’s go:

Average age of cars on road (US): 12.5 years
Average yearly miles driven per car (for 2022 in the US): 14,263 miles/year
Average mileage of car on road = 12.5 years * 14,263 miles/year
Average mileage of car on road = 178,287 miles

Last edited:

#### Sandy H.

##### Well-Known Member
TRF Supporter
Regretfully, I am still an LPR guy.

It was a fun conversation, though. Thanks for the laughs!

#### ThirstyBarbarian

##### Well-Known Member
You aren’t going to be able to get a mathematical probability for something like that, but it’s definitely a weird coincidence and an unlikely thing to have happen.

#### K'Tesh

##### OpenRocket Chuck Norris Lifetime Supporter
TRF Supporter
You should probably get yourself a finite probability drive, put a fresh cup of tea in it and see how things turn out.

#### Sandy H.

##### Well-Known Member
TRF Supporter
You should probably get yourself a finite probability drive, put a fresh cup of tea in it and see how things turn out.

I can say for sure the answer was not 6 12 23 27 33 or 15. . .

#### ThirstyBarbarian

##### Well-Known Member
If you want to access skills form your alternate selves in alternate universes, you need to do something really improbable, like get in a fight over an IRS trophy shaped like a… er…um…well, let’s just say it’s pretty improbable, and it could lead to many jokes about Uranus.

#### Bravo52

##### Well-Known Member
TRF Supporter
Ahh, ABCDF? really???

My Odometer on my crappy car and my nice Tundra Truck are all NUMBERS

#### Sandy H.

##### Well-Known Member
TRF Supporter
Three oh nieeeeeeeeeieeeen!

#### Funkworks

##### Low Earth Orbit, obstructing Earth's view of Venus
You could also say that there was a 1 in 100,000 chance of having ABCDEF on the odometer, and a 1 in 100,000 chance of having the same number on the sticker. If you think this better fits what you have in mind, then the probability is (1/100,000)x(1/100,000). Which is 1 in 10 billion!

#### jahall4

##### Well-Known Member
All you know for sure is the probability is something less than 1 in ABCDEF. ;-)

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