Help with calculating car crash statistics

[ShoulderThingThatGoesUp]

There have been a couple threads here about the importance of ESC and I'm trying to decide if it's worth it to replace our car. We drive 6,000 miles a year so a major risk factor is obviously lower than the general population's. Our car is a 2010 Honda Fit with 43,000 miles so it has lots of life left in it mechanically, and we really like it.

In trying to calculate our annual risk of injury for our family of three, I've run in to some sanity-check problems. I'm using Pennsylvania's 2014 crash statistics as a basis.

There were 121,317 crashes in 2014 and 98.6 billion vehicle-miles driven, so I think a simple calculation of our risk of crash is pretty straightforward:
(121,317 / 98,600,000,000) * 6000 = 0.0074 = 0.74% per year.

Crashes caused 40,882 non-minor injuries and deaths. So plugging in the same formula:
(40,882 / 98,600,000,000) * 6000 = 0.0025 = 0.25% per year.

But there's three of us in the car pretty frequently, or maybe 2 on average. Obviously your risk of somebody being injured is higher with more people in the car. But you can't just multiply by 3. These numbers make that really obvious because 0.25% * 3 = 0.75% and then you're calculating that your risk of injury is higher than your risk of crashing. Sanity check says no. (This does include some pedestrian and bicyclist injuries and deaths, which further confounds things.)

Trying to extend this over several years, since cars last longer than that, is also less simple than I'd like it to be. You can't just multiply your risk by the number of years. If I drove 30,000 miles a year for 27 years, would my risk of crashing be 100%? Clearly not. It might be really high, but it should approach 100% asymptotically.

I should be better at this - I have an engineering degree - but frankly I did a crappy job in my statistics class in college.

I think that the conclusion won't change - we hardly drive so we shouldn't replace the car - but I would like to get the numbers right. Help?

[nereo]

I see two ways of approaching this.

To begin, I believe that the non-minor injuries/deaths already INCLUDES >1 person in a car.  After all, the average number of people in per vehicle is slightly higher than 1 (i.e. there are no cars driving around with 0 drivers).  Also, if I'm understanding correctly those are crashes which resulted in injuries and deaths... meaning many of them involved two (or more) vehicles?  So some of those crashes could have had, say, 8 people involved.  It won't solve your problem but I think you can assume that your average of ~2 people/trip is close to the number of people present per crash.

Ok.  Now that we've gotten that out of the way...
you've calculated (correctly, I believe) that your odds of being in a crash each year is ~0.25%.  That means your odds of NOT being in a crash are 99.75%.  To solve for the probability of you being in a crash over a number of years it's 0.9975^n, where n = # of years. 
So in 10 years your probability of being in a crash is = 0.97527... or about 97.5% per decade.  Ergo, the odds of BEING in a crash ~=2.5% per decade

Alternatively, you could get a very similar figure by plugging in the number of miles driven over 10 years into the equation (40,882/98,600,000,000)*60,000 = 2.97%.  You'll notice they are slightly different.  That's because you'd be driving a slightly higher % of the total miles driven in the state of PA for one year, which obviously you are not.  However this is a simple ball-park method that's easy to use in spreadsheets.

Final thoughts: These calculations inherently miss aspects that are most important to personal safety.  How safe a driver you are is probably the biggest (e.g. if you speed or drive drunk).  Also it averages everywhere in the state together, so 6,000 miles around Philly is the treated the same as Harrisburg.  Ultimately I think those factors will matter more.
helpful?

[ShoulderThingThatGoesUp]

I see two ways of approaching this.

To begin, I believe that the non-minor injuries/deaths already INCLUDES >1 person in a car.  After all, the average number of people in per vehicle is slightly higher than 1 (i.e. there are no cars driving around with 0 drivers).  Also, if I'm understanding correctly those are crashes which resulted in injuries and deaths... meaning many of them involved two (or more) vehicles?  So some of those crashes could have had, say, 8 people involved.  It won't solve your problem but I think you can assume that your average of ~2 people/trip is close to the number of people present per crash.

Ok.  Now that we've gotten that out of the way...
you've calculated (correctly, I believe) that your odds of being in a crash each year is ~0.25%.  That means your odds of NOT being in a crash are 99.75%.  To solve for the probability of you being in a crash over a number of years it's 0.9975^n, where n = # of years. 
So in 10 years your probability of being in a crash is = 0.97527... or about 97.5% per decade.  Ergo, the odds of BEING in a crash ~=2.5% per decade

Alternatively, you could get a very similar figure by plugging in the number of miles driven over 10 years into the equation (40,882/98,600,000,000)*60,000 = 2.97%.  You'll notice they are slightly different.  That's because you'd be driving a slightly higher % of the total miles driven in the state of PA for one year, which obviously you are not.  However this is a simple ball-park method that's easy to use in spreadsheets.

Final thoughts: These calculations inherently miss aspects that are most important to personal safety.  How safe a driver you are is probably the biggest (e.g. if you speed or drive drunk).  Also it averages everywhere in the state together, so 6,000 miles around Philly is the treated the same as Harrisburg.  Ultimately I think those factors will matter more.
helpful?

Yes, that is helpful. I figured that my county (Lehigh) was too small to avoid wild swings in the numbers, but that it kinda looks like Pennsylvania as a whole - some dense built-up areas with narrow streets laid out in the 19th century, some suburbia, some cornfields, some forests.

I think it makes sense to look at the statistics and say they handle the average number of people in cars which as you said has to be over one. So I don't feel the need for any multipliers in particular, and I also don't feel the need for a new car.

A huge personal safety advantage we have right now is that I work at home and my wife is a SAHM with a part-time from-home job as well. So when the weather's bad we simply don't go anywhere. We don't even drive when it's raining, because why would we?

[ender]

One way to do this is simply find the odds of a crash occurring sometime in the next N years (say 30) as being equal to 100% minus the odds of it NOT happening. The odds of it not happening is 99.26% (I guess we can assume per year indefinitely?).

So in this case, 1 - (1-0.0074)^30 = 1 - 0.8 = 20% likilhood of at least 1 crash occurring during those 30 years.

. These numbers make that really obvious because 0.25% * 3 = 0.75% and then you're calculating that your risk of injury is higher than your risk of crashing. Sanity check says no

Your sanity check here is wrong. Your crash numbers is per vehicle and injuries is per person. If, on average, all vehicles had 5 people in them your risk of injury could be much higher percentage wise than the risk of a crash (since every crash could cause multiple injuries).

[seattlecyclone]

This is an interesting question. As others have pointed out, you can't directly compare the injuries to the crashes because the crash statistics measure events, and the injuries measure people affected by the events.

However these numbers become more comparable if you assume that every car only has one person in it (which probably isn't that far off from the truth). If that's the case, a crash has a roughly 1/3 probability of causing a non-minor injury to the driver.

Now, for the multiple passenger scenario we have to ask: what is the probability that a non-driver is injured in a crash where a driver is injured, and what is the probability that a non-driver is injured in a crash where the driver is not injured? My gut feeling says the first number is pretty high, and the second number is pretty low, but I have no data to support this.

The probability of getting in a crash where at least one person is injured can't be higher than the probability of getting in a crash of any sort. However the expected value of number of injuries certainly could be higher than the probability of getting in a crash if your typical passenger load is much higher than the average driver.

[ender]

It's also probably important to determine what times of day accidents are more likely to happen. And whether you are driving at those times.

[nereo]

and then there's the stat that 52% of accidents occur within 5 miles of your home.  That's why I moved :-P

[Sailor Sam]

You've obviously done your due diligence on the probability section of a risk assessment, and ender addressed the exposure section. Is there as mathematical way to address the severity? Even at 0.75%, or 2.5%, or 20% chance of the negative outcome, if that outcome is paralysis, it might change the final decision.

[tobitonic]

I feel this is one of the many attempts of folks here to use numbers in ways they aren't warranted. There's zero risk of death from not wearing seat belts if you never get into a collision. However, in a potentially fatal crash, you're 50% less likely to die if you're wearing seat belts. The level of risk reduction for ESC is the same in single-vehicle crashes. You're half as likely to die in such a crash if you're driving a vehicle with ESC compared to if you're driving one without. Naturally, the risk of dying in a single vehicle crash if you never crash is zero. Fifty percent of fatal crashes are single vehicle crashes.

If you wear seat belts, you've already made the judgment that a 50% overall risk reduction in fatal crashes is worth it. It's the same risk reduction for ESC in half of all fatal crashes. To me, it's obviously worth it. To others, it's obviously not. But there's no need to make up convoluted formulas for this unless you'd do the same to decide whether or not it's worth wearing your seat belts. Your overall risk goes down the less you drive, but the risk of what happens once a crash is imminent has nothing to do with how often you're exposed to that event.

[nereo]

I feel this is one of the many attempts of folks here to use numbers in ways they aren't warranted. There's zero risk of death from not wearing seat belts if you never get into a collision. However, in a potentially fatal crash, you're 50% less likely to die if you're wearing seat belts. The level of risk reduction for ESC is the same in single-vehicle crashes. You're half as likely to die in such a crash if you're driving a vehicle with ESC compared to if you're driving one without. Naturally, the risk of dying in a single vehicle crash if you never crash is zero. Fifty percent of fatal crashes are single vehicle crashes.

If you wear seat belts, you've already made the judgment that a 50% overall risk reduction in fatal crashes is worth it. It's the same risk reduction for ESC in half of all fatal crashes. To me, it's obviously worth it. To others, it's obviously not. But there's no need to make up convoluted formulas for this unless you'd do the same to decide whether or not it's worth wearing your seat belts. Your overall risk goes down the less you drive, but the risk of what happens once a crash is imminent has nothing to do with how often you're exposed to that event.

Ok - but all cars come with seat belts.  The OP would have to sell his/her car and buy a new one to have ESC.  Doesn't that factor into the equation?

Also, according to wikipedia, it's a reduction of 1/3 of fatal accidents.  That's still sizeable

According to Insurance Institute for Highway Safety and the U.S. National Highway Traffic Safety Administration, one-third of fatal accidents could be prevented by the use of the technology.

[tobitonic]

I feel this is one of the many attempts of folks here to use numbers in ways they aren't warranted. There's zero risk of death from not wearing seat belts if you never get into a collision. However, in a potentially fatal crash, you're 50% less likely to die if you're wearing seat belts. The level of risk reduction for ESC is the same in single-vehicle crashes. You're half as likely to die in such a crash if you're driving a vehicle with ESC compared to if you're driving one without. Naturally, the risk of dying in a single vehicle crash if you never crash is zero. Fifty percent of fatal crashes are single vehicle crashes.

If you wear seat belts, you've already made the judgment that a 50% overall risk reduction in fatal crashes is worth it. It's the same risk reduction for ESC in half of all fatal crashes. To me, it's obviously worth it. To others, it's obviously not. But there's no need to make up convoluted formulas for this unless you'd do the same to decide whether or not it's worth wearing your seat belts. Your overall risk goes down the less you drive, but the risk of what happens once a crash is imminent has nothing to do with how often you're exposed to that event.

Ok - but all cars come with seat belts.  The OP would have to sell his/her car and buy a new one to have ESC.  Doesn't that factor into the equation?

Also, according to wikipedia, it's a reduction of 1/3 of fatal accidents.  That's still sizeable

According to Insurance Institute for Highway Safety and the U.S. National Highway Traffic Safety Administration, one-third of fatal accidents could be prevented by the use of the technology.

I agree that's a factor, and definitely one to keep in mind. A few years ago, I felt the same way about ESC's importance, and still bought our family car without it because 3k was as much as we could justify spending at the time. I feel like the OP would have more success by just deciding whether he believes the technology is valuable or not, and then looking at if they can justify a vehicle swap / addition or not at the moment.

I've seen the 1/3rd figure; that refers to all fatal accidents. The 50% (or technically 49%) reduction is for just fatal single-vehicle collisions, which make up about half of all fatal crashes, IIRC: http://www.iihs.org/iihs/topics/t/crash-avoidance-technologies/qanda#electronic-stability-control

In Institute studies, ESC has been found to reduce fatal single-vehicle crash risk by 49 percent and fatal multiple-vehicle crash risk by 20 percent for cars and SUVs. Many single-vehicle crashes involve rolling over, and ESC effectiveness in preventing rollovers is even more dramatic. It reduces the risk of fatal single-vehicle rollovers by 75 percent for SUVs and by 72 percent for cars. 1 Federal studies also show large benefits. The National Highway Traffic Safety Administration (NHTSA) estimates the installation of ESC reduces single-vehicle crashes of cars by 32 percent and single-vehicle crashes of SUVs by 57 percent. NHTSA estimates that ESC has the potential to prevent 72 percent of the car rollovers and 64 percent of the SUV rollovers that would otherwise occur in single-vehicle crashes. 2 

[ShoulderThingThatGoesUp]

One way to do this is simply find the odds of a crash occurring sometime in the next N years (say 30) as being equal to 100% minus the odds of it NOT happening. The odds of it not happening is 99.26% (I guess we can assume per year indefinitely?).

So in this case, 1 - (1-0.0074)^30 = 1 - 0.8 = 20% likilhood of at least 1 crash occurring during those 30 years.

. These numbers make that really obvious because 0.25% * 3 = 0.75% and then you're calculating that your risk of injury is higher than your risk of crashing. Sanity check says no

Your sanity check here is wrong. Your crash numbers is per vehicle and injuries is per person. If, on average, all vehicles had 5 people in them your risk of injury could be much higher percentage wise than the risk of a crash (since every crash could cause multiple injuries).

No. Risk of injury from a crash can't be higher than the risk of the crash itself.

I feel this is one of the many attempts of folks here to use numbers in ways they aren't warranted. There's zero risk of death from not wearing seat belts if you never get into a collision. However, in a potentially fatal crash, you're 50% less likely to die if you're wearing seat belts. The level of risk reduction for ESC is the same in single-vehicle crashes. You're half as likely to die in such a crash if you're driving a vehicle with ESC compared to if you're driving one without. Naturally, the risk of dying in a single vehicle crash if you never crash is zero. Fifty percent of fatal crashes are single vehicle crashes.

If you wear seat belts, you've already made the judgment that a 50% overall risk reduction in fatal crashes is worth it. It's the same risk reduction for ESC in half of all fatal crashes. To me, it's obviously worth it. To others, it's obviously not. But there's no need to make up convoluted formulas for this unless you'd do the same to decide whether or not it's worth wearing your seat belts. Your overall risk goes down the less you drive, but the risk of what happens once a crash is imminent has nothing to do with how often you're exposed to that event.

Ok - but all cars come with seat belts.  The OP would have to sell his/her car and buy a new one to have ESC.  Doesn't that factor into the equation?

Also, according to wikipedia, it's a reduction of 1/3 of fatal accidents.  That's still sizeable

According to Insurance Institute for Highway Safety and the U.S. National Highway Traffic Safety Administration, one-third of fatal accidents could be prevented by the use of the technology.

I agree that's a factor, and definitely one to keep in mind. A few years ago, I felt the same way about ESC's importance, and still bought our family car without it because 3k was as much as we could justify spending at the time. I feel like the OP would have more success by just deciding whether he believes the technology is valuable or not, and then looking at if they can justify a vehicle swap / addition or not at the moment.

I've seen the 1/3rd figure; that refers to all fatal accidents. The 50% (or technically 49%) reduction is for just fatal single-vehicle collisions, which make up about half of all fatal crashes, IIRC: http://www.iihs.org/iihs/topics/t/crash-avoidance-technologies/qanda#electronic-stability-control

In Institute studies, ESC has been found to reduce fatal single-vehicle crash risk by 49 percent and fatal multiple-vehicle crash risk by 20 percent for cars and SUVs. Many single-vehicle crashes involve rolling over, and ESC effectiveness in preventing rollovers is even more dramatic. It reduces the risk of fatal single-vehicle rollovers by 75 percent for SUVs and by 72 percent for cars. 1 Federal studies also show large benefits. The National Highway Traffic Safety Administration (NHTSA) estimates the installation of ESC reduces single-vehicle crashes of cars by 32 percent and single-vehicle crashes of SUVs by 57 percent. NHTSA estimates that ESC has the potential to prevent 72 percent of the car rollovers and 64 percent of the SUV rollovers that would otherwise occur in single-vehicle crashes. 2 

It's your posts here that made me start looking at the math. The proportions I get. The money I'm honestly not even worried about if it's a reasonable thing to do - we have enormous savings, a household income over 100k a year, and we live in a pretty LCOL place. If replacing the car is the correct move, I'm even going to get an actually new one to allay my wife's concerns about used cars.

But we really do like our car, and the risks are very, very low. 1/3rd of a tiny risk (I'm not even sure about the 6000 miles per year - we bought it in fall 2010, it has just under 43,000 miles, then commuted with it for three years, then used it to bring stuff from a previous house to this one a bunch of times, and it was driven from Texas to Pennsylvania once - so I don't think we're putting much on it now) is just really, really tiny.

I don't know. It's a hard call. We don't drive in the rain. We don't drive in the snow. We do the vast majority of our driving in the daylight. We don't drive at rush hour. But my daughter rides in the car and she is the meaning of my life.

[neo von retorch]

But my daughter rides in the car and she is the meaning of my life.

This. This is emotional. Another way to look at this would be to do the math on the other end. "If I spend $15000 getting a newer car, how much would that affect my ability/timing to reach FIRE? Is that time I would end up working and not spending with my daughter? Is it enough time for me to spend time doing lots of math?"

The odds are "very low" and you definitely shouldn't worry all day about it. If the financial impact is very low (i.e. 1 extra week to FIRE) then it's likely a gut decision.

[ShoulderThingThatGoesUp]

But my daughter rides in the car and she is the meaning of my life.

This. This is emotional. Another way to look at this would be to do the math on the other end. "If I spend $15000 getting a newer car, how much would that affect my ability/timing to reach FIRE? Is that time I would end up working and not spending with my daughter? Is it enough time for me to spend time doing lots of math?"

The odds are "very low" and you definitely shouldn't worry all day about it. If the financial impact is very low (i.e. 1 extra week to FIRE) then it's likely a gut decision.

It adjusts my FIRE year from 2028 to...2028 (that assumes a pretty high level of lifestyle inflation anyways and a relatively low growth rate).

[zolotiyeruki]

What is the interaction between the reduction in injury stats due to seat belts and the reduction in accidents (or their severity, which is a whole different question) due to ESC?  This may just be morbid curiosity, but what are the stats with ESC but without seat belts, vs with seat belts and without ESC?

[nereo]

What is the interaction between the reduction in injury stats due to seat belts and the reduction in accidents (or their severity, which is a whole different question) due to ESC?  This may just be morbid curiosity, but what are the stats with ESC but without seat belts, vs with seat belts and without ESC?

I had a similar thought.  If seatbelts reduce the number of fatal accidents by 50%, and ESC does so by a similar amount, you cannot say that ESC protects "as much" as seatbelts if you already wear seatbelts at all times.  If I'm thinking this through correctly, seatbelts would reduce the likelihood you will be in a fatal accident by half, and then ESC would cut that amount in half again (which is effectively 25% from the total).

Or put another way:
supposed 1,000 fatal accidents from drivers with no seatbelts or ESC
wearing seatbelts would limit to 500 (a reduction of 500, or 50% from the original total)
wearing seatbelts plus having ESC would limit it to 250 (a redution of 250, or 25% from the original total).

[ShoulderThingThatGoesUp]

It might make sense to put ESC first, though - it can prevent you from getting in an accident in the first place, which obviously a seat belt won't do.

[nereo]

It might make sense to put ESC first, though - it can prevent you from getting in an accident in the first place, which obviously a seat belt won't do.

perhaps... but every car has seat belts, and you are required to wear them just about everywhere.  Why would you not?
Conversely, not every car has ESC... in fact most on the road today don't.

In 10 years that might change.

[ShoulderThingThatGoesUp]

It might make sense to put ESC first, though - it can prevent you from getting in an accident in the first place, which obviously a seat belt won't do.

perhaps... but every car has seat belts, and you are required to wear them just about everywhere.  Why would you not?
Conversely, not every car has ESC... in fact most on the road today don't.

In 10 years that might change.

Not in priority when you get in the car, I meant, the ESC gets a chance to halve your accidents before the seatbelts get a chance to halve your misfortunes in an accident - chronologically.

[nereo]

It might make sense to put ESC first, though - it can prevent you from getting in an accident in the first place, which obviously a seat belt won't do.

perhaps... but every car has seat belts, and you are required to wear them just about everywhere.  Why would you not?
Conversely, not every car has ESC... in fact most on the road today don't.

In 10 years that might change.

Not in priority when you get in the car, I meant, the ESC gets a chance to halve your accidents before the seatbelts get a chance to halve your misfortunes in an accident - chronologically.

I see your point.  ESC is in many ways preventative.  Seatbelts can never be.

It still seems like you are seeking to minimize something that's already very small. If the opportunity comes up to get a vehicle with ESC by all means do it.  But whereas ESC is fairly rare in the used car market right now, it will be fairly common in 3-5 years.  The likelihood of being in an injury accident in the next three years? < 1%.  Much of that is still in your control (defensive driving).  YMMV.

[tobitonic]

It's your posts here that made me start looking at the math. The proportions I get. The money I'm honestly not even worried about if it's a reasonable thing to do - we have enormous savings, a household income over 100k a year, and we live in a pretty LCOL place. If replacing the car is the correct move, I'm even going to get an actually new one to allay my wife's concerns about used cars.

But we really do like our car, and the risks are very, very low. 1/3rd of a tiny risk (I'm not even sure about the 6000 miles per year - we bought it in fall 2010, it has just under 43,000 miles, then commuted with it for three years, then used it to bring stuff from a previous house to this one a bunch of times, and it was driven from Texas to Pennsylvania once - so I don't think we're putting much on it now) is just really, really tiny.

I don't know. It's a hard call. We don't drive in the rain. We don't drive in the snow. We do the vast majority of our driving in the daylight. We don't drive at rush hour. But my daughter rides in the car and she is the meaning of my life.

I hear you; no one can decide if it's worth it but you. When we did replace our two vehicles with ones that came with ESC and side airbags, it felt like--and still does--the right decision. But everyone's got different risk tolerances. And I hear you about the kids. Part of why I insisted on a pair of vehicles with nearly identical safety features was because I didn't ever want my wife and kids to be in the cheap-ass vehicle I was only supposed to drive if they were ever unfortunate enough to be involved in an accident. Seeing as car crashes are the primary killers of children and one of the leading causes of death for young (<44) adults, I wanted to make sure they were, generally speaking, going to be in the best vehicles I could justify. Other folks would have put the ~17k we spent on both vehicles into savings and bought another Geo Metro. YMMV.

[calimom]

I've participated in other threads on this topic with tobitonic and appreciate his point of view. Correct me if I'm wrong but I believe tobitonic is a paramedic/firefighter? He really cares about family safety and it's something to take note of.

Anyhow, my story: my 37 year old husband was killed in a side impact car crash in 2007. The drunk driver who ran the red light is still serving a prison sentence btw. DH was driving a relatively safe 2001 Saab with pretty decent safety features and still died. His daily commute was approximately 25 miles from our home in Silicon Valley, and alternated between two freeways and surface streets, depending on traffic and other factors, like picking up kids or other errands. The crash occurred  in broad daylight in good conditions in the middle of summer on El Camino Real for anyone who knows the SF Bay Area.

What do I drive now? A safe Volvo v70 wagon. I realize others might choose a Honda or Toyota or Taurus of some sort, but I'm content to make the investment in safety on this one. I have no idea of the actuarial odds of lightening striking twice to my family but not interested in finding out. I get money is important - and I know I paid more up front and  more for maintenance with my Volvo but I'm OK with this.

[ShoulderThingThatGoesUp]

What I have done so far is ordered a new car seat that will enable my daughter to face the rear until she's four, and put her in the middle seat.

Tobitonic, if that's your site, we ordered a Klek Fllo based on the review, but the link goes to the 2015 instead of the 2016, so I'm not sure you got the affiliate points.

[ooeei]

Trying to extend this over several years, since cars last longer than that, is also less simple than I'd like it to be. You can't just multiply your risk by the number of years. If I drove 30,000 miles a year for 27 years, would my risk of crashing be 100%? Clearly not. It might be really high, but it should approach 100% asymptotically.

Just to point out here, the risk is in fact ~100% in this situation. 

You're driving 30,000*27=810,000 miles

The accident rate is .00000123 crashes/mile which equals 813000 miles/crash, let's round it to 810,000 for simplicity (or you can add a couple of months of driving in the 31st year to hit that number)

.00000123 crashes/mile * 810,000 miles = ~1 crash

Granted, this is an average across a large population, so you may escape without being in a crash, the same way someone else who only drove 200,000 miles in that time frame might be in a crash, or even 2-3 crashes.  It also includes crashes with no injuries, and includes a huge amount of driving over a very long time frame. 

Your risk of non minor injury/death is ~1/3 of the above risk based on the numbers you posted, so 33% over such a long time frame with that amount of driving, assuming you are an average driver with average safety features.  Since you drive 6,000 miles per year, your risk of non minor injury/death is ~6.6% over that 30 year time frame.  It's less if you wear seatbelts, less still if you have other safety features that are "above average", less if you're a particularly careful driver, and less if you drive less.  This also makes sense anecdotally, as most of us know a few people who have been in a serious car crash over a 30 year timeframe.  It's not everyone you know, but I bet you know a few, maybe around 6.6% of people you know? 

Figuring out the numbers based on multiple people in the car seems pretty hard to do, as having 4 people in the car doesn't quadruple your risk, which you pointed out.  I wouldn't bother trying to figure that part out, you've got some good ballpark numbers that shows you a good estimate and the relative impact of different options.

[ender]

Trying to extend this over several years, since cars last longer than that, is also less simple than I'd like it to be. You can't just multiply your risk by the number of years. If I drove 30,000 miles a year for 27 years, would my risk of crashing be 100%? Clearly not. It might be really high, but it should approach 100% asymptotically.

Just to point out here, the risk is in fact ~100% in this situation. 

You're driving 30,000*27=810,000 miles

The accident rate is .00000123 crashes/mile which equals 813000 miles/crash, let's round it to 810,000 for simplicity (or you can add a couple of months of driving in the 31st year to hit that number)

.00000123 crashes/mile * 810,000 miles = ~1 crash

This is not how statistics work.

[ooeei]

Trying to extend this over several years, since cars last longer than that, is also less simple than I'd like it to be. You can't just multiply your risk by the number of years. If I drove 30,000 miles a year for 27 years, would my risk of crashing be 100%? Clearly not. It might be really high, but it should approach 100% asymptotically.

Just to point out here, the risk is in fact ~100% in this situation. 

You're driving 30,000*27=810,000 miles

The accident rate is .00000123 crashes/mile which equals 813000 miles/crash, let's round it to 810,000 for simplicity (or you can add a couple of months of driving in the 31st year to hit that number)

.00000123 crashes/mile * 810,000 miles = ~1 crash

This is not how statistics work.

Please enlighten me.

[ender]

Please enlighten me.

One way to do this is simply find the odds of a crash occurring sometime in the next N years (say 30) as being equal to 100% minus the odds of it NOT happening. The odds of it not happening is 99.26% (I guess we can assume per year indefinitely?).

So in this case, 1 - (1-0.0074)^30 = 1 - 0.8 = 20% likilhood of at least 1 crash occurring during those 30 years.

or a lengthier version of the same approach:

I see two ways of approaching this.

To begin, I believe that the non-minor injuries/deaths already INCLUDES >1 person in a car.  After all, the average number of people in per vehicle is slightly higher than 1 (i.e. there are no cars driving around with 0 drivers).  Also, if I'm understanding correctly those are crashes which resulted in injuries and deaths... meaning many of them involved two (or more) vehicles?  So some of those crashes could have had, say, 8 people involved.  It won't solve your problem but I think you can assume that your average of ~2 people/trip is close to the number of people present per crash.

Ok.  Now that we've gotten that out of the way...
you've calculated (correctly, I believe) that your odds of being in a crash each year is ~0.25%.  That means your odds of NOT being in a crash are 99.75%.  To solve for the probability of you being in a crash over a number of years it's 0.9975^n, where n = # of years. 
So in 10 years your probability of being in a crash is = 0.97527... or about 97.5% per decade.  Ergo, the odds of BEING in a crash ~=2.5% per decade

Alternatively, you could get a very similar figure by plugging in the number of miles driven over 10 years into the equation (40,882/98,600,000,000)*60,000 = 2.97%.  You'll notice they are slightly different.  That's because you'd be driving a slightly higher % of the total miles driven in the state of PA for one year, which obviously you are not.  However this is a simple ball-park method that's easy to use in spreadsheets.

Final thoughts: These calculations inherently miss aspects that are most important to personal safety.  How safe a driver you are is probably the biggest (e.g. if you speed or drive drunk).  Also it averages everywhere in the state together, so 6,000 miles around Philly is the treated the same as Harrisburg.  Ultimately I think those factors will matter more.
helpful?

[ooeei]

Please enlighten me.

One way to do this is simply find the odds of a crash occurring sometime in the next N years (say 30) as being equal to 100% minus the odds of it NOT happening. The odds of it not happening is 99.26% (I guess we can assume per year indefinitely?).

So in this case, 1 - (1-0.0074)^30 = 1 - 0.8 = 20% likilhood of at least 1 crash occurring during those 30 years.

or a lengthier version of the same approach:

I see two ways of approaching this.

To begin, I believe that the non-minor injuries/deaths already INCLUDES >1 person in a car.  After all, the average number of people in per vehicle is slightly higher than 1 (i.e. there are no cars driving around with 0 drivers).  Also, if I'm understanding correctly those are crashes which resulted in injuries and deaths... meaning many of them involved two (or more) vehicles?  So some of those crashes could have had, say, 8 people involved.  It won't solve your problem but I think you can assume that your average of ~2 people/trip is close to the number of people present per crash.

Ok.  Now that we've gotten that out of the way...
you've calculated (correctly, I believe) that your odds of being in a crash each year is ~0.25%.  That means your odds of NOT being in a crash are 99.75%.  To solve for the probability of you being in a crash over a number of years it's 0.9975^n, where n = # of years. 
So in 10 years your probability of being in a crash is = 0.97527... or about 97.5% per decade.  Ergo, the odds of BEING in a crash ~=2.5% per decade

Alternatively, you could get a very similar figure by plugging in the number of miles driven over 10 years into the equation (40,882/98,600,000,000)*60,000 = 2.97%.  You'll notice they are slightly different.  That's because you'd be driving a slightly higher % of the total miles driven in the state of PA for one year, which obviously you are not.  However this is a simple ball-park method that's easy to use in spreadsheets.

Final thoughts: These calculations inherently miss aspects that are most important to personal safety.  How safe a driver you are is probably the biggest (e.g. if you speed or drive drunk).  Also it averages everywhere in the state together, so 6,000 miles around Philly is the treated the same as Harrisburg.  Ultimately I think those factors will matter more.
helpful?

Except OP gave an example of someone driving 30,000 miles per year in the part I responded to, rather than his 6,000.  This person has 5x the risk he does, thus your 20% turns into 100%.

I agree with pretty much everything else you/nereo said. 

[ender]

Except OP gave an example of someone driving 30,000 miles per year in the part I responded to, rather than his 6,000.  This person has 5x the risk he does, thus your 20% turns into 100%.

I agree with pretty much everything else you/nereo said.

.... ok. But that's still not how statistics works. You can't just arbitrarily multiply things and have it make any cohesive sense.

If the risk is 5x as high you would calculate it (using the 0.74% / year baseline) as  1 - (1-0.0074*5)^30 = 1 - 0.32 = 68% chance.

[ShoulderThingThatGoesUp]

Consider that if somebody drives 36,000 miles a year their risk cannot be 120%.

[ooeei]

Consider that if somebody drives 36,000 miles a year their risk cannot be 120%.

Chances are they will be in more than one crash over that time frame.  I guess it depends what you mean by risk.  The probability is never 100%, but if there is a crash on average for every 10 miles driven, and someone drives 20 miles, what would you say their risk is?  The numbers say they will be in 2 crashes.  I suppose that's not 200% chance, but I'm not sure how it's quantified.

Except OP gave an example of someone driving 30,000 miles per year in the part I responded to, rather than his 6,000.  This person has 5x the risk he does, thus your 20% turns into 100%.

I agree with pretty much everything else you/nereo said.

.... ok. But that's still not how statistics works. You can't just arbitrarily multiply things and have it make any cohesive sense.

If the risk is 5x as high you would calculate it (using the 0.74% / year baseline) as  1 - (1-0.0074*5)^30 = 1 - 0.32 = 68% chance.

You're correct, my bad.

[nereo]

Consider that if somebody drives 36,000 miles a year their risk cannot be 120%.

Chances are they will be in more than one crash over that time frame.  I guess it depends what you mean by risk.  The probability is never 100%, but if there is a crash on average for every 10 miles driven, and someone drives 20 miles, what would you say their risk is?  The numbers say they will be in 2 crashes.  I suppose that's not 200% chance, but I'm not sure how it's quantified.

This is where I believe you are getting off-track. It certainly is possible for an individual to have multiple crashes (if we aren't talking about ones that are fatal to that person) but it's also possible NOT to have any crashes.  What we are calculating here is the probability of being involved in that first crash.  You could also calculate the probability of being in 2 crashes, 3 crashes, etc. 
This is why I (above) calculated out the probability of NOT being in a crash instead of the probability of being in one.  The inverse is simply the integration of all other combinations (i.e. being in 1, 2, 3, ... n crashes).

[seattlecyclone]

Yes, the expected value of number of crashes gets to be approximately 1 after a person drives 813,000 miles (or whatever the number is). That doesn't mean the probability of crashing is necessarily anywhere near 1. The expected value is defined as the sum of (n * probability of crashing n times) for all n.

Some people are going to crash two or three or ten times. Others are going to crash not at all. If the expected value is 1, that means that every time someone crashes for a second (or subsequent) time, there's someone who doesn't crash at all. The probability of crashing at least once is then not 100%, but is instead (100% - percent of population who doesn't crash).