Commuting - Flats are random?

Like many bike commuters, I have a tendency to obsess over flat tires. Like many bicyclists, I'm also a nerd. As a nerd who obsesses over flat tires, one of the things that intrigues me is the problem of understanding flat tire rates, particularly as it applies to comparing various tires.

It's well known among bike commuters that flat tires are essentially random events. You'll go eight months without getting a flat tire, then you'll get three in two weeks. It's just totally random, right? Well, I'm not giving up that easily.

One of the main problems with flats being random events is that it calls into question the possibility of comparing two different models of tires without using both for a long, long time. Nevertheless, as humans we all form opinions based on small sample sizes and can't be convinced otherwise. If I try tire A and get a bunch of flats then switch to tire B and don't get a bunch of flats you won't be able to convince me that tire A wasn't significantly more flat prone than tire B.

But is that really true?

That's one of the questions to which I wanted the answer. So, being a pseudo-scientific type, I set out to collect data. For the last three years I've been compulsively recording all information that seemed relevant about my flat tires -- the date, where I was riding, what the weather was like, how many miles were on the tire, front or rear, cause of the flat, etc. Now with three years worth of data, I'm starting some analysis.

:geek:

So, I've got two tires, which I will call tire A and tire B. I used tire A for about 1900 miles and got 6 flats. I used tire B for 2000 miles and didn't get a single flat. Obviously tire B is more flat resistant, right? But how to quantify that?

What I decided is that I'd imagine a simplified probability model. I'd choose a somewhat arbitrary probability that I'd get a flat in any 10 miles of riding and then apply that probability to these two tires to see how well it would explain the data.

Let me say that I am aware of the crudity of this model. For one thing, the probability of getting a flat isn't actually consistent over time but seems to increase with tire wear. It also varies with weather and riding location. I'm ignoring these factors.

So, returning to my model, I made the guess that for any 10 miles of riding there was a 3% chance that I'd get a flat tire. Applying that (by means of the binomial formula), I find that in any given set of 200 10-mile trips, there is about a 60% chance that I'd get 6 or fewer flats, so that seems like a reasonable fit for tire A. However, with that probability, there is only a 0.2% chance that I would get zero flats in 200 10-mile trips. If both tires actually had this same probability of getting a flat, there would be about a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

Conversly, in order to get as much as a 1 in 4 chance that I could have used tire B for 2000 miles without getting a flat, I have to assign a probability of 0.7% for a flat in any given 10 mile trip. Applying that value to tire A, there would be a 99.7% chance that I'd get fewer than 6 flats. This yields less than a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

So, my conclusion is that given two tires both used for 2000 miles in similar conditions if one tires gets 6 flats while the other gets 0 flats then I can, in fact, trust my belief that the tire that got no flats has better flat protection.

The next thing I'd like to know is how many flat tires you need to get before you can conclusively say that a tire is not as flat-resistant as another tire that got no flats.

Yes, I have too much time on my hands.

Like many bike commuters, I have a tendency to obsess over flat tires. Like many bicyclists, I'm also a nerd. As a nerd who obsesses over flat tires, one of the things that intrigues me is the problem of understanding flat tire rates, particularly as it applies to comparing various tires.

Zzzzzzzzzzzzzzzzzzzzzzzzzzz.............

Yes, I have too much time on my hands.

Yup. You do Einstein :D Go for a ride.

6 flats in 1900 miles is too much for me.

Yup. You do Einstein :D Go for a ride.

:lol:

You obviously don't realize that the geeks will inherit the earth.

6 flats in 1900 miles is too much for me.

Yeah, me too. But let me attempt to pre-empt the inevitable Marathon Plus recommendations by saying that I'd rather have 6 flats in 1900 miles than ride 1900 miles on hard, heavy tires. Hence the urgency of this research. BTW, tire B was not an SMP. :innocent:

"Flats are random?"
Yes, unless someone meticulously lays out thumbtacks in a meticulous grid pattern.. :lol:

:lol:

You obviously don't realize that the geeks will inherit the earth.

Yeah, yeah, yeah, I'm surrounded by geeks all day long.


"Flats are random?"
Yes, unless someone meticulously lays out thumbtacks in a meticulous grid pattern.. http://www.bikeforums.net/images/smilies/lol.gif

Yeah, go ahead and give Andy more reasons to do his cyclescience :D

My flats are... um, not happening much at all. How about that?


I'd rather have 6 flats in 1900 miles than ride 1900 miles on hard, heavy tires.

Nah, I'm the opposite because the flats have a tendency to happen in the worst possible conditions, like early on a cold, rainy morning or that one day you're late for work. You could probably figure out, I suppose, with enough math and statistics, when and where the flats will happen and avoid them though:D

You could probably figure out, I suppose, with enough math and statistics, when and where the flats will happen and avoid them though:D

Exactly! So far I've figured out that they mostly happen between April and June on tires with more than 2000 miles on them. Tire B above just hit 2000 miles, so I'm leaving it parked until July while I ride on something else.

Way too many flats. I average one a year, which is about one every 3500 miles. Half of those are pinch flats because I don't always check my tire pressure as often as I should, and sometimes the county throws down very rough gravel on the roads including some nearly fist-sized rocks, and I might hit one of those at night. I really can't remember the last time I had an actual puncture. I think it was about 3 years ago, a sliver of wire IIRC. It was a slow enough leak that I made it the last 2 miles home after noticing it.

Like many bike commuters, I have a tendency to obsess over flat tires. Like many bicyclists, I'm also a nerd. As a nerd who obsesses over flat tires, one of the things that intrigues me is the problem of understanding flat tire rates, particularly as it applies to comparing various tires.

It's well known among bike commuters that flat tires are essentially random events. You'll go eight months without getting a flat tire, then you'll get three in two weeks. It's just totally random, right? Well, I'm not giving up that easily.

One of the main problems with flats being random events is that it calls into question the possibility of comparing two different models of tires without using both for a long, long time. Nevertheless, as humans we all form opinions based on small sample sizes and can't be convinced otherwise. If I try tire A and get a bunch of flats then switch to tire B and don't get a bunch of flats you won't be able to convince me that tire A wasn't significantly more flat prone than tire B.

But is that really true?

That's one of the questions to which I wanted the answer. So, being a pseudo-scientific type, I set out to collect data. For the last three years I've been compulsively recording all information that seemed relevant about my flat tires -- the date, where I was riding, what the weather was like, how many miles were on the tire, front or rear, cause of the flat, etc. Now with three years worth of data, I'm starting some analysis.

:geek:

So, I've got two tires, which I will call tire A and tire B. I used tire A for about 1900 miles and got 6 flats. I used tire B for 2000 miles and didn't get a single flat. Obviously tire B is more flat resistant, right? But how to quantify that?

What I decided is that I'd imagine a simplified probability model. I'd choose a somewhat arbitrary probability that I'd get a flat in any 10 miles of riding and then apply that probability to these two tires to see how well it would explain the data.

Let me say that I am aware of the crudity of this model. For one thing, the probability of getting a flat isn't actually consistent over time but seems to increase with tire wear. It also varies with weather and riding location. I'm ignoring these factors.

So, returning to my model, I made the guess that for any 10 miles of riding there was a 3% chance that I'd get a flat tire. Applying that (by means of the binomial formula), I find that in any given set of 200 10-mile trips, there is about a 60% chance that I'd get 6 or fewer flats, so that seems like a reasonable fit for tire A. However, with that probability, there is only a 0.2% chance that I would get zero flats in 200 10-mile trips. If both tires actually had this same probability of getting a flat, there would be about a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

Conversly, in order to get as much as a 1 in 4 chance that I could have used tire B for 2000 miles without getting a flat, I have to assign a probability of 0.7% for a flat in any given 10 mile trip. Applying that value to tire A, there would be a 99.7% chance that I'd get fewer than 6 flats. This yields less than a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

So, my conclusion is that given two tires both used for 2000 miles in similar conditions if one tires gets 6 flats while the other gets 0 flats then I can, in fact, trust my belief that the tire that got no flats has better flat protection.

The next thing I'd like to know is how many flat tires you need to get before you can conclusively say that a tire is not as flat-resistant as another tire that got no flats.

Yes, I have too much time on my hands.

I've concluded that the black tires get more flats than blue tires and I didn't have to work nearly has hard at it as you.

This is of course no help if your bike is red because the blue tires would clash. Imagine the horror if you did get a flat in a blue tire that was mounted on a red bike. I bet no one would stop to help you.

So, my conclusion is that given two tires both used for 2000 miles in similar conditions if one tires gets 6 flats while the other gets 0 flats then I can, in fact, trust my belief that the tire that got no flats has better flat protection.

The next thing I'd like to know is how many flat tires you need to get before you can conclusively say that a tire is not as flat-resistant as another tire that got no flats.

I believe you would want to ride several individual Tire As and several individual Tire Bs for 2k miles each to find a distribution of flats/2k miles for each model and at the end of that you would know how typical your 6/2k and 0/2k results are likely to be.

For me flats are not random, generally when a tire starts throwing too many flats in a short span I chuck it regardless of apparent wear. That has only happened to me past the 1k mark, if it was the 1st week then I might evaluate differently...

This is of course no help if your bike is red because the blue tires would clash. Imagine the horror if you did get a flat in a blue tire that was mounted on a red bike. I bet no one would stop to help you.

Clashing tire/frame is probably the equivalent of not wearing clean underwear and then winding up in the emergency room for some reason.

Way too many flats. I average one a year, which is about one every 3500 miles. Half of those are pinch flats because I don't always check my tire pressure as often as I should, and sometimes the county throws down very rough gravel on the roads including some nearly fist-sized rocks, and I might hit one of those at night. I really can't remember the last time I had an actual puncture. I think it was about 3 years ago, a sliver of wire IIRC. It was a slow enough leak that I made it the last 2 miles home after noticing it.

The trouble here is that riding location is a huge factor in flats. I'm convinced that how many flats you get on your route has essentially no numerical correlation to how many flats I would get with the same tires on my route. Only by comparing two different tires on the same route do I trust the data.

I believe you would want to ride several individual Tire As and several individual Tire Bs for 2k miles each to find a distribution of flats/2k miles for each model and at the end of that you would know how typical your 6/2k and 0/2k results are likely to be.

It's true. I could have just gotten a particularly good or bad sample of either set of tires, but I think it's a decent start given the extent of the disparity.



For me flats are not random, generally when a tire starts throwing too many flats in a short span I chuck it regardless of apparent wear. That has only happened to me past the 1k mark, if it was the 1st week then I might evaluate differently...

This is absolutely true. Four of the six flats for tire A were in the last 600 miles of use. But how do you decide how many flats grouped together are significant? One flat is obviously not meaningful. Two in a week could still be coincidence....

6 flats in 1900 miles is too much for me.

You'd have come back a broken man from my last trip to the Picketwire dinosaur trackway...63 punctures in 16 miles. I had to carry the bike the last (and worst) quarter of a mile. That's what I get for crowing about not getting a single flat on the previous trip and teasing the woman who got 20 of them.

You'd have come back a broken man from my last trip to the Picketwire dinosaur trackway...63 punctures in 16 miles. I had to carry the bike the last (and worst) quarter of a mile. That's what I get for crowing about not getting a single flat on the previous trip and teasing the woman who got 20 of them.

Holy crap! Goatheads, I assume?

Thanks for the detailed study. I see a bit of a hole that needs filling, though... you did not correct for weather, riding conditions, etc. I don't think your results are truly valid unless you had two identical bikes and riders riding through exactly the same debris on exactly the same road every day.

Although I agree with your conclusion. I am pretty lucky when it comes to flat prevention. I have been commuting to work on and off for the past six years on bad pavement and gravel, 14km each way, and never had a flat during a commute. I may have had two or three flats I discovered hours or days after I parked my bike, but I have actually never had to fix a flat on the rear of my IGH equipped bike (I would remember that).

Holy crap! Goatheads, I assume?

Acres and acres of them. 2011 was a bumper crop.

Exactly! So far I've figured out that they mostly happen between April and June on tires with more than 2000 miles on them. Tire B above just hit 2000 miles, so I'm leaving it parked until July while I ride on something else.

Make an iPhone app!

I think your sample size is too small to predict with any accuracy. You need to test about 1000 tires before you can get any assurance that your results have any validity. As I recall, a sample size of 1,000 would mean your results would be accurate to within about 3% 19 times out of 20. We need a better way of doing flat prediction. We know that if you ride on any tire long enough, there is a 100% probability that you will puncture it. I would propose n km before puncturing would be a more meaningful starting point. The idea would be that you'd have a 95% probability that the tire would go n km before going flat. That last 5% accounts for completely random behavior. But the closer you get to km n, themore likely you are to puncture! So your Tire A would have a rating of 333 miles (533 km) before puncturing. Tire B would be 2000 miles (3200 km) before puncturing. Sort of a mean time before failure rating.

Luis

MOst of my flats have been random. I've never had a planned flat. :D

Flats aren't random. They always happen at the most inopportune time. Such as 5F outside in the middle of a snow storm. That was my last flat, and it was this winter.

Wouldn't you also have to randomize your ride times to determine if flats are random?

Thanks for the detailed study. I see a bit of a hole that needs filling, though... you did not correct for weather, riding conditions, etc. I don't think your results are truly valid unless you had two identical bikes and riders riding through exactly the same debris on exactly the same road every day.

This is why I've always liked physics better than engineering. I prefer to make sweeping assumptions that simplify the calculations and then sort out the details afterward.

As it happens, tire A got all of it's flats in dry conditions while most of the use of tire B has been on wet roads, so if I include that level of analysis things get even worse for tire A. (It's intended as a racing tire, so all of this is to be expected.)

For the curious, in the three years that I've been collecting this data I've gotten 16 flats in about 12000 miles. Of those, 12 occured between April 1 and June 30. Of the 10 flats in 10000 miles that were not on tire A in the example above, 7 happened in the rain. Four of the 10 non-tire-A flats occurred on tires with more than 2000 miles on them. I believe that every one of the 16 occurred in a designated bike lane (though to be fair 75% of my commute is on designated bike lanes). Only three of the 16 were on the front tire.

I could really complicate things by introducing tire C, which got five flats in 2400 miles but 4 of which occurred at over 1880 miles.

I'm pretty sure over 35 years of riding that I have proven that new tires are much less likely to get a flat than tires with a lot of miles on them. Of course, I don't really test that theory much any more, because if I get a flat the tire is gone soon thereafter. Life is too short to nurse an older tire along to get a few more miles on it.

I think I tend to get more flats after recent heavy rains. All the water washes around debris towards the curb and leaves glass and wires pointing upwards in the pavement. That's my theory at least.

I would propose n km before puncturing would be a more meaningful starting point. The idea would be that you'd have a 95% probability that the tire would go n km before going flat. That last 5% accounts for completely random behavior. But the closer you get to km n, themore likely you are to puncture!

That's kind of what I'm getting at here, except that I don't believe that first flat is really a meaningful piece of data. I had one tire that flatted after 191 miles, but then didn't flat again for another 1691 miles. I had another tire that flatted after 580 miles and then didn't flat again in 1000 miles before I sold the bike it was on. So what I'm claiming is that zero flats and one flat are essentially indistinguishable, but zero flats and six flats are significantly different.

There seems to be some point at which a tire breaks down and the flat rate goes up exponentially, but before you approach that point I don't think a flat is any more likely in the next 10 miles than it was in the first 10 miles.

Puncture flats are caused by road debris, which is random. One day it's there, one day it's not.

I think I tend to get more flats after recent heavy rains. All the water washes around debris towards the curb and leaves glass and wires pointing upwards in the pavement. That's my theory at least.

There's definitely something to that. Wet rubber is much, much easier to cut than dry rubber, and debris absolutely accumulates on the side of the road, making designated bike lanes flat tire factories.

There's definitely something to that. Wet rubber is much, much easier to cut than dry rubber, and debris absolutely accumulates on the side of the road, making designated bike lanes flat tire factories.

Also, small shards of glass are more likely to stick to a wet tire and then slowly work their way through it. Long time members of my club say that they get more flats on rides that happen on rainy days. That would explain why flats happen at the worst times, since rainy day is one of such worst times.

The trouble here is that riding location is a huge factor in flats. I'm convinced that how many flats you get on your route has essentially no numerical correlation to how many flats I would get with the same tires on my route. Only by comparing two different tires on the same route do I trust the data.

That's certainly true. There are people who get way more flats riding Marathon Supremes on their route than I do riding the cheapest, thinnest tires I can buy on my route. There are essentially zero road hazards around here. I have over the years picked up a staple, a bit of bent metal shaving, a piece of wire, two pieces of glass and a drywall screw. But that's over 8 years of riding. For some reason I got more of them years ago than I do now. I am riding with somewhat better tires these days but I wouldn't trust that across multiple years.

maybe this is just my experience, but,
0 flats in over 3years doesnt seem random to me
maybe you need to start using armored tires? or ride further out in the lane?
last time I replaced a tire, it was because the tread was wearing thin and threads were showing, yet it had never gotten punctured in its lifespan....

...uncontrolled variables... dominate the observations reported in this thread.
When uncontrolled variables dominate, you don't have an experiment worthy of the name. Next...!

...uncontrolled variables... dominate the observations reported in this thread.
When uncontrolled variables dominate, you don't have an experiment worthy of the name. Next...!

Nonsense. Granted the variables are a bit uncontrolled, but given a large enough sample size order emerges from chaos. Besides, I never claimed there was even an experiment in progress, merely data analysis.

Like many bike commuters, I have a tendency to obsess over flat tires. Like many bicyclists, I'm also a nerd. As a nerd who obsesses over flat tires, one of the things that intrigues me is the problem of understanding flat tire rates, particularly as it applies to comparing various tires.

It's well known among bike commuters that flat tires are essentially random events. You'll go eight months without getting a flat tire, then you'll get three in two weeks. It's just totally random, right? Well, I'm not giving up that easily.

One of the main problems with flats being random events is that it calls into question the possibility of comparing two different models of tires without using both for a long, long time. Nevertheless, as humans we all form opinions based on small sample sizes and can't be convinced otherwise. If I try tire A and get a bunch of flats then switch to tire B and don't get a bunch of flats you won't be able to convince me that tire A wasn't significantly more flat prone than tire B.

But is that really true?

That's one of the questions to which I wanted the answer. So, being a pseudo-scientific type, I set out to collect data. For the last three years I've been compulsively recording all information that seemed relevant about my flat tires -- the date, where I was riding, what the weather was like, how many miles were on the tire, front or rear, cause of the flat, etc. Now with three years worth of data, I'm starting some analysis.

:geek:

So, I've got two tires, which I will call tire A and tire B. I used tire A for about 1900 miles and got 6 flats. I used tire B for 2000 miles and didn't get a single flat. Obviously tire B is more flat resistant, right? But how to quantify that?

What I decided is that I'd imagine a simplified probability model. I'd choose a somewhat arbitrary probability that I'd get a flat in any 10 miles of riding and then apply that probability to these two tires to see how well it would explain the data.

Let me say that I am aware of the crudity of this model. For one thing, the probability of getting a flat isn't actually consistent over time but seems to increase with tire wear. It also varies with weather and riding location. I'm ignoring these factors.

So, returning to my model, I made the guess that for any 10 miles of riding there was a 3% chance that I'd get a flat tire. Applying that (by means of the binomial formula), I find that in any given set of 200 10-mile trips, there is about a 60% chance that I'd get 6 or fewer flats, so that seems like a reasonable fit for tire A. However, with that probability, there is only a 0.2% chance that I would get zero flats in 200 10-mile trips. If both tires actually had this same probability of getting a flat, there would be about a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

Conversly, in order to get as much as a 1 in 4 chance that I could have used tire B for 2000 miles without getting a flat, I have to assign a probability of 0.7% for a flat in any given 10 mile trip. Applying that value to tire A, there would be a 99.7% chance that I'd get fewer than 6 flats. This yields less than a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

So, my conclusion is that given two tires both used for 2000 miles in similar conditions if one tires gets 6 flats while the other gets 0 flats then I can, in fact, trust my belief that the tire that got no flats has better flat protection.

The next thing I'd like to know is how many flat tires you need to get before you can conclusively say that a tire is not as flat-resistant as another tire that got no flats.

Yes, I have too much time on my hands.

The biggest variable is the nut behind the wheel... er... handlebars. You need a blind study; who knows what your subconscious is up to. In fact, perhaps what you've actually done here is a blind study on your own psyche. What exactly do you have against company A?

You have proven mathematically that the tire with no flats has a lower probability of getting a flat than the tire with more flats. Brilliant! (using Guiness ad voice). Seriously though, it would seem that you cannot assign any probability to getting a flat w/ tire B, since you have not had a flat with it, i.e. the current probability is simply 0 - unless you use data outside your current data set. Also, you don't mention if these tires are on the same back, or whether both tires are both being used in front or rear.

I can't assign a probability to tire B, but I can (and did) examine the probability that I would get no flats in 2000 miles if the actual probability were some value P. I didn't crunch the numbers, but I suspect that if tire A had only gotten 3 flats, for instance, then the math would have told me the results were inconclusive.

In both cases I was using the same model tire front and rear. They were used on different, but very similar bikes.

It would seem that each flat is an independent event, considering your tires don't touch the same stretch of road ever again on a ride.

Nonsense. Granted the variables are a bit uncontrolled, but given a large enough sample size order emerges from chaos.

OK, let's see your ANOVA


Besides, I never claimed there was even an experiment in progress, merely data analysis.
OK, I don't see the point of trying to draw causal correlations from "data" that is drawn from uncontrolled experiments, or non-experiments. Have fun! :)

I've concluded that the black tires get more flats than blue tires and I didn't have to work nearly has hard at it as you.

This is of course no help if your bike is red because the blue tires would clash. Imagine the horror if you did get a flat in a blue tire that was mounted on a red bike. I bet no one would stop to help you.

I got a laugh out of this, as I paid an exorbitant price to have a couple of red tires shipped to me from halfway around the world to match my red bike. Funny thing is I haven't had a flat since I changed the front tire to the red type (I'm running something different in the rear).

Flat tires have nothing to do with tubes, tires, protection, etc... they're directly attributable to the Bike Gremlins that accompany all of us
on every ride, waiting to pounce and muck up a perfectly good ride. Good relations with the bike gods, and good karma in general help
alleviate the chaos and misfortune a puncture (or several) can create...

246510

Alan :speedy:

Flat tires have nothing to do with tubes, tires, protection, etc... they're directly attributable to the Bike Gremlins that accompany all of us
on every ride, waiting to pounce and muck up a perfectly good ride. Good relations with the bike gods, and good karma in general help
alleviate the chaos and misfortune a puncture (or several) can create...

246510

Alan :speedy:

Regular offerings of ca$h to the Gear Gods, and the occasional sacrifice to N+1 help keep the Gremlins in check as well...

;)

Like many bike commuters, I have a tendency to obsess over flat tires. Like many bicyclists, I'm also a nerd. As a nerd who obsesses over flat tires, one of the things that intrigues me is the problem of understanding flat tire rates, particularly as it applies to comparing various tires.

It's well known among bike commuters that flat tires are essentially random events. You'll go eight months without getting a flat tire, then you'll get three in two weeks. It's just totally random, right? Well, I'm not giving up that easily.

One of the main problems with flats being random events is that it calls into question the possibility of comparing two different models of tires without using both for a long, long time. Nevertheless, as humans we all form opinions based on small sample sizes and can't be convinced otherwise. If I try tire A and get a bunch of flats then switch to tire B and don't get a bunch of flats you won't be able to convince me that tire A wasn't significantly more flat prone than tire B.

But is that really true?

That's one of the questions to which I wanted the answer. So, being a pseudo-scientific type, I set out to collect data. For the last three years I've been compulsively recording all information that seemed relevant about my flat tires -- the date, where I was riding, what the weather was like, how many miles were on the tire, front or rear, cause of the flat, etc. Now with three years worth of data, I'm starting some analysis.

:geek:

So, I've got two tires, which I will call tire A and tire B. I used tire A for about 1900 miles and got 6 flats. I used tire B for 2000 miles and didn't get a single flat. Obviously tire B is more flat resistant, right? But how to quantify that?

What I decided is that I'd imagine a simplified probability model. I'd choose a somewhat arbitrary probability that I'd get a flat in any 10 miles of riding and then apply that probability to these two tires to see how well it would explain the data.

Let me say that I am aware of the crudity of this model. For one thing, the probability of getting a flat isn't actually consistent over time but seems to increase with tire wear. It also varies with weather and riding location. I'm ignoring these factors.

So, returning to my model, I made the guess that for any 10 miles of riding there was a 3% chance that I'd get a flat tire. Applying that (by means of the binomial formula), I find that in any given set of 200 10-mile trips, there is about a 60% chance that I'd get 6 or fewer flats, so that seems like a reasonable fit for tire A. However, with that probability, there is only a 0.2% chance that I would get zero flats in 200 10-mile trips. If both tires actually had this same probability of getting a flat, there would be about a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

Conversly, in order to get as much as a 1 in 4 chance that I could have used tire B for 2000 miles without getting a flat, I have to assign a probability of 0.7% for a flat in any given 10 mile trip. Applying that value to tire A, there would be a 99.7% chance that I'd get fewer than 6 flats. This yields less than a 1 in 1000 chance that I would get more than 5 flats with tire A while getting no flats with tire B.

So, my conclusion is that given two tires both used for 2000 miles in similar conditions if one tires gets 6 flats while the other gets 0 flats then I can, in fact, trust my belief that the tire that got no flats has better flat protection.

The next thing I'd like to know is how many flat tires you need to get before you can conclusively say that a tire is not as flat-resistant as another tire that got no flats.

Yes, I have too much time on my hands.

Interesting.

I can't comment on your dataset since you haven't published it but I don't think the binomial model is the correct one to use. I think you should model it as a Poisson distribution as the of a flat per unit mile (or 10 miles if you want to stick with that), then you can compare the lambda of each different tire and I think that would give you a much better indication of its flat resistance.

Regular offerings of ca$h to the Gear Gods, and the occasional sacrifice to N+1 help keep the Gremlins in check as well...

;)

An excellent observation!

Some flats are random bad luck. However, there are many factors that increase the probability of getting flats, including:

- Running tires with too low pressure, which leads to pinch flats if you hit bumps, potholes, etc. I pump my tires before every ride to help avoid those.
- Riding in the "crud line" of gravel, glass, etc. that accumulates on the edge of roads and at intersections. This, I am convinced, is one of the main reasons why some cyclists get a lot of flats. They are afraid to take the lane, hug the edge of the road, and pay dearly for it.
- Fragile tires. Some tires just get a lot more flats. They are made for racing, speed and light weight. Tires like Vittoria Corsa CXs or other racing versions. I don't buy these kind of tires.
- Riding on wet roads. Unfortunately, this is hard to avoid if you commute, but it is a well-know phenomenum that you get more flats when it's raining or wet roads because glass will stick to your tires easier and debris gets washed into the roadways.
- Reinstalling tires that flat without thoroughly examining them for glass, wire, rocks that are stuck in the tread. This is the leading cause of repeated flats on the same wheel. If you keep getting flats on the same tire, turn it inside out and closely examine the inside of the tread. Run your fingers along it. Examine the outer tread real closely. Chances are very likely that something is stuck in the tread. Sometimes it's a small piece of wire or glass that is barely visible.
- Old tubes with valves that are wearing out. This is probably the most common cause of flats for me because I repair my flatted tubes and sometimes use them for years. Eventually the valves get worn out and they can't be repaired.

BTW, I don't use heavy thick tires like Schwalb Marathons. I use reasonably light but durable tires like Continental GP 4000s, Michelin Pro Races, Vittoria Rubinos. I get several flats a year but I also ride 7,000-8,000+ miles a year. I enjoy riding too much to use heavy, poor handling tires with high rolling resistance. I would much rather fix a few flats than have to slog up all the hills on heavy tires.

I enjoy riding too much to use heavy, poor handling tires with high rolling resistance. I would much rather fix a few flats than have to slog up all the hills on heavy tires.

I doubt the extra mass of "heavy" tires is holding you back as much as you seem to think, but rolling resistance certainly is a critical parameter no matter what the riding condition.

I can't comment on your dataset since you haven't published it but I don't think the binomial model is the correct one to use. I think you should model it as a Poisson distribution as the of a flat per unit mile (or 10 miles if you want to stick with that), then you can compare the lambda of each different tire and I think that would give you a much better indication of its flat resistance.

Well, statistics was never my strong suit but I don't believe the Poisson distribution works for me because I don't have enough data to know the actual probability of getting a flat for either tire with any kind of certainty at all, particularly for the tire that didn't get any flats. So what I'm actually doing is estimating the likelihood that the actual probability of getting a flat for the two tires is nearly equivalent. Of course, this doesn't tell me anything about how likely I am to get a flat in the next 10 miles with either tire, or even how many flats I would get on a second set of the same tires over 2000 miles. It just tells me that tire B probably really is more flat resistant the tire A.

- Riding in the "crud line" of gravel, glass, etc. that accumulates on the edge of roads and at intersections.

Here in Oregon we call that the bike lane. :(

I occasionally e-mail the local roads department and ask them to sweep the bike lane somewhere or other. They usually tell me they'll put in a request but that it gets done on a regular schedule anyway. The thing is, in the winter there's usually a very clearly defined line that shows you where the street sweeper stopped, and it's usually very close to the line marking the bike lane. On the plus side, they sometimes actually clean the bike lane when I ask.

I doubt the extra mass of "heavy" tires is holding you back as much as you seem to think, but rolling resistance certainly is a critical parameter no matter what the riding condition.

I have no doubt that heavy tires don't make a significant difference in the actual speed of a bike, and maybe not even its acceleration, but they feel a lot different. If the tire is also hard that's even worse. I don't really care how fast I'm going so much as I care about how much I'm enjoying the ride.

Geeks don't use iphones. Make that an Android app.