Stats Class #1 - Crash Rates

This is the first of a series in which I combine statistics from various sources in an effort to find out something mildly interesting.

It's pretty common, when cycling comes up, that someone will mention that cyclists are a menace and that they frequently endanger pedestrians. It is certainly true that cyclists do hit pedestrians, sometimes through careless cycling and sometimes not. On rare occasion these collisions are fatal for the pedestrian and/or sometimes for the cyclist.  But are cyclists really the menace they're made out to be? Some people claim they're more scared of cyclists. Does that make sense?

Pedestrian crashes provide a pretty good means of determining the relative safety with which cyclists and drivers operate their vehicles. Assuming that pedestrians behave the same around cyclists as they do drivers, they can behave as a control group. That assumption may be flawed, as, for example, it may be that pedestrians rely too heavily on their sense of hearing and so step out in front of cyclists more often. Nonetheless, a comparison between crash ratios and exposure ratios can give an idea if cyclists really are more reckless than drivers.

Crash Ratio

Determining the reported crash ratio is pretty easy. DDOT did a study of bike and pedestrian crashes from 1997-99 and according to that report there were 29 reported bicycle-pedestrian crashes (BPC) and 1785 reported car-ped crashes (CPC) during that period. This gives a ratio of 1:62.

Of course, this only considers reported crashes. It is well documented that crashes, even ones with injuries, are under-reported. A study in Sweden determined that as few as 37 percent of all injury causing accidents are actually recorded. It has also been shown that the rate of under reporting is inversely related to the severity of the crash. Since a crash with a cyclist will be, on average, less severe than a crash with a car, it is reasonable to believe that there is more under reporting in BPC.  Since there is no way to know this ratio, I'll use a variable U, where U/62 gives us the actual ratio of BPC to CPC [U=(% of actual CPC the reported CPC represents/% of actual BPC the reported BPC represents)]. Later we can guess as to what value of U makes sense.

Exposure Ratio

This is a little tougher. What we have is a study that calculates the exposure of cyclists, pedestrians and drivers to drivers as expressed in miles for 2007 in DC. These are 37.2 million miles, 82 million miles and 362 million miles respectively.

One problem is that "miles" is the wrong measurement. Exposure by time makes more sense. I saw the tree across from my old place get hit by cars on two separate occasions. It traveled 0 miles in all that time,  but it was certainly exposed to traffic. So these have to be translated into time. That can be done by using the average speed of each mode (3 mph for pedestrians, 12 mph for cyclists and a conservative 20mph for drivers*)  Dividing by those speeds gives us the exposure as a measure of time. Note that the assumption here is that drivers on average go slower than the speed limit. This is not the case on area highways, and if too low it will understate the exposure of pedestrians to drivers.

Exposure as time (million hours)

Pedestrians - 27.3

Cyclists -  3.08

Drivers - 18.1

Using these numbers the ratio becomes 1:6.

Another problem is that we're using 2007 exposure data and 1997-99 crash data. There were more bikes on the road in 2007 than in 1997-99, so we need to reduce the exposure. Though it is not a perfect proxy, we can use the commuting rates to give an estimate of how much to reduce exposure. In 2007 the percentage commutes by bike in DC was 1.7%. We can extrapolate the percentage of bike commuters in 1997 by using the values from 1990 and 2000 which were 0.75% and 1.16% respectively and this gives us 1.04%. Which means we have to decrease the exposure of cyclists by about 40%. I'm going to assume that driver exposure is unchanged.

That changes the bicycle exposure to 1.88 million hours and the ratio to 1:9.6

However, that's still not accurate. Another problem is that these numbers are based on "exposure to cars" instead of "exposure to pedestrians" which is what we're considering here. Many of the hours for drivers are on highways where there are no pedestrians - and thus no exposure. Since not every minute of driving exposes a driver to a pedestrian, the driver number should be less than 18.1 million hours. Furthermore, pedestrians and cyclists can interact at more places than just crosswalks and parking lots. There are also sidewalks and trails, but these aren't considered in the exposure numbers. So the cyclist number should be more than 1.88 million hours.

While it is difficult to say how much the two are off by, it is almost surely true that the crash ratio is far less than 1:9.6

Conclusions

The ratio of reported BPC to reported CPC is 1:61 and the ratio of bike/ped exposure to car/ped exposure is no more than 1:9.6. Which means that each car on the roads of DC is at least 6 times more likely to be in a reported crash with a pedestrian than each bicycle. 

U, mentioned above, would need to be slightly larger than 6.35 for BPC and CPC to be equal per capita. Or, for example, if 75% of car-pedestrian crashes are reported - as estimated in one study dealing only with injury-causing crashes, no more than 11.8% of bicycle-pedestrian crashes can be reported. This seems too low to me.

I think we can conclude the following from this:

Bicycles are significantly less likely to be in crashes than cars.

It makes sense, because the lack of crash-protection equipment for cyclists, means they have more to lose in a crash than drivers do. Put another way, making cars safer has made driving less safe due to the Peltzman effect. It's reasonable to conclude that the sense of danger people have on bikes causes them to behave safer to compensate.

This analysis is not perfect. Some potential flaws:

1. The study that determined exposure had identified errors in their methods.

2. The ratio of unreported bike-ped crashes to unreported car-ped crashes is unknown

3. I used 1997-99 crash numbers with 2007 exposure numbers and my method for correcting this may be inaccurate.

4. My estimates for average bike and car speed are based on limited facts.

5. The exposure numbers were for exposure to cars, not to pedestrians.

*During congestion cars move at 14mph, but we're not always congested.

Comments

[Jim Titus]

This is worth doing, but as written it is a bit confusing. If I follow you, the problem is that you don't have an estimate of the number of miles of cycling or driving. If you did, this is much simpler. If the ratio of miles driven to miles cycled is greater than 62, then cyclists collide with pedestrians more per mile than do drivers. Given the large number of cyclists on sidewalks compared to drivers on sidewalks, it should not be that surprising.

Of course, perhaps cyclists travel less, and so it might be interesting to compare accidents per hour.

It's hard to tell what we are actually getting with these exposure estimates. Maybe we need to better define what we are trying to measure

[nookie]

Yeah, you are jumping all over the place with unassociated stats, spanning completely different periods.

Here is the core of the issue, per your link to DDOT above:

"Over the 1997-1999 time period, bicycle collisions account for approximately 2 percent of all traffic collisions". Bicycles are (as cycle blogs keep trumpeting) now responsible for a full 2% of all trips taken in the District.

There, an apples to apples comparison that isn't rocket science, that also shows that yes, bikes are just as statistically responsible for their "share" of accidents.

Actually, the argument could be made that since these numbers are ~11 years old, and the number of total trips by bikes was less then than it is now <2%, that bikes were statistically more responsible for accidents than vehicles were.

[washcycle]

Nookie, since your assertion - to me - is so obviously flawed, and I'm pretty sure I've already shown you how on another thread, and since I feel you're intellectually dishonest, I'm not going to bother showing you the flaws unless someone else replies that they find your argument convincing.

Jim, this is confusing - I'm sorry - and I tried really hard to not make it so. I have the number of miles, but not hours. But either way cyclists are in fewer crashes with pedestrians. Another way to think of this is that, on average a cyclist would have to ride 1.28 Million miles to be in a reported crash with a pedestrian. A driver would only need to go 202 hundred thousand miles to be in a reported crash with a pedestrians. If you go with hours on the road - a better metric in my opinion - the gap becomes even larger. That's the point.

[Jim Titus]

Thanks David. So if I am following you, there is one crash per 1.28 million cycling miles, because cyclists rode a total of 37.2 million miles not on bike paths during the 3 year period. I gather then that drivers in DC drove 362 million miles on roads where one might find a pedestrian (i.e., excluding interstate highways, Whitehurst freeway, and New York Avenue east of Bladensburg Rd, and Rock Creek Parkway, etc.)

While not the point of this article, that is pretty impressive that cycling is 10% of what we might call "local driving".

So if cycling was about 10% of the driving but 2% of the accidents, that is an impressive difference. Too bad it is for different years, so you guess that maybe the cycling was half as great in 1997-1999, i.e., there are now twice as many ped-bike accidents. So cycling was maybe only 5% of the miles but 2% of the accidents.

Frankly, that works for me as a nice factoid (though I have rounded and would want the actual numbers). I think it is needless torture to go past that point with something like cyclists account for 20% of the time spent on roadways and 2% of the accidents.

It would be interesting to know whether pedestrians under-report accidents based on what hit them for an accident of a given severity. That would take a study. We are stuck with the data. I'm sure that very minor collisions with cyclists are overlooked, while a collision with a car is rarely trivial. But that's better left as a caveat.

[nookie]

So, translating for washcycle "Ugh, yeah, he is right and I have no idea what I am talking about, nor how to answer a very simple arithmatic problem, so I will avoid and obfuscate by making something up which then somehow voids me having to answer even though the question is tied to the very link I provided".

On the other hand, everyone "else" who has posted on this thread has also called you on your questionable asserts and use of unrelated data. So congrats for being your own troll.

[TurbineBlade]

I think I get what you're saying, but it really doesn't make any sense to me why bicycle accidents in any way compare to car accidents - particularly when pedestrians are involved.

When you walk through a intersection would you rather be struck by an idiot on a trek 1200, or an idiot in a Ford Thunderbird?

Big words can't obscure the fact that a person driving a car has a much easier time killing someone than a person riding a bicycle.

[guez]

I think that Jim Titus has his finger on the problem, here: reporting. 3-year-olds, for instance, may be (and probably are) much more reckless with their tricycles than motorists are with their cars. But when a three-year-old crashes into your shin, it doesn't get reported to the police. Similarly, I would guess that many of the encounters between cyclists and pedestrians do not rise to the level where they are reported. This says very little about about cyclists and a lot about bicycles. (This is TurbineBlade's point, I think.)

[washcycle]

guez, I tried to cover the "underreporting" problem. Maybe that wasn't clear. The underreporting would have to be huge. If 50% of car-ped crashes are reported, no more than 5% of bike-ped crashes can be reported for the conclusion to be false (so if 6% are reported the conclusion is true). In other words, I'm aware and I've addressed it. What do you think a reasonable range for the reporting rate (reported crashes/total crashes) is for these types of crashes?

I also read TurbineBlade's comment differently, but maybe he can clarify.

[TurbineBlade]

I guess I'm not entirely sure what I really meant, other than that I just can't compare bicycle accidents to car accidents. To say that hitting a pedestrian with a bicycle pales in comparison to hitting a pedestrian with a car doesn't even approach how absurd this comparison really is.

I guess, even if cyclists were MORE likely to crash into pedestrians (which I doubt is true) - so what? I'll just go ahead and say it.

I mainly mean this as a criticism of people who are twisting stats to make cycling seem "dangerous" to pedestrians.

If I'm crossing an intersection, once again, I'll take a PACK of idiot cyclists running the light rather than one idiot in a car doing the same thing. The same extension can be made for why tractor trailers have different speed limits, weight restrictions, and lane-use rules than passenger vehicles. It's just common sense.

[washcycle]

TurbineBlade, I agree with everything you said. The answer to so what? is that I think it is a powerful advocacy tool if bike-ped crashes are less harmful AND less frequent. It's like choosing whether to live near someone who drives drunk once a day or bikes drunk once a week. You've got too variables pushing you to the same choice.

[guez]

Washcycle,

I have no idea what the reporting ratio is, but it would undoubtedly make the difference someone less dramatic, as would a fuller consideration of what happens on sidewalks and trails, which is where many of the complaints about cyclists (from pedestrians) come from.

I have to admit that I'm with TurbineBlade on the "so what" front. I suspect that most people are aware of the fact that cars are more of threat to life and limb than bikes. Those who are really angry at cyclists won't change their minds.

I am convinced that the whole approach to bike advocacy that seeks to refute, minimize, etc. the misbehavior of cyclists is counterproductive. The focus should not be on comparing bikes to cars, but on showing that cyclists are willing and eager to do their part to improve the culture of the road.

[washcycle]

Guez, I'm shocked, shocked that you think that anything other than saying "we're bad cyclists and we promise to do better" is bad advocacy. Over the years, I have yet to see one concrete thing you thing we can do as bike advocacy. Really, I mean you should look back at your comments some time. There is absolutely nothing positive you have to say about anything at all. Why don't you lay out a real advocacy vision. And I mean real measurable obtainable goals. It's real easy to be the guy who says "your idea sucks", "what your doing is a waste of time", and "you're doing it wrong". It is really fucking boring and counterproductive in my opinion.

So, why don't you finally step up and show us how to do it. Anyone can be a critic guez, can you do more?

And, I think showing that CURRENT cyclist behavior makes them less likely to crash into pedestrians shows that cyclists are ALREADY doing their part to improve the culture of the road. But we don't get credit for that.

[washcycle]

And you know what else, if your thought is "So what" than why bother making that comment? It's just so incredibly superior to drop in and say "Hey look at all this work you did. So what?" It's crap like that that makes me want to just say f--- this and walk away.

[TurbineBlade]

"I am convinced that the whole approach to bike advocacy that seeks to refute, minimize, etc. the misbehavior of cyclists is counterproductive."

I have not found this to be the case.

Many of my coworkers will tell me about cyclists they saw breaking the law when they're driving to and from work as a
"jib" at me, since they know I'm a daily commuter.

When I've pointed out red light camera stats, speeding stats, parking violations, etc. some of them go: "Well, yeah I guess you're right." Somtimes they kind of zone out and say something to the effect of "Well, I just don't like them getting in the way, making me late...etc."

In cases of the former, I have found that they actually now tell me about how much more PATIENT they are around cyclists because of me. I'm sure that "refuting" the criticism that it's always cyclists who break the law has had something to do with it. I of course also freely admit that many cyclists do indeed break laws, some of which can cause problems.

Oh, and as for quantifying cyclist/pedestrian problems on MUP's and trails, good luck with that one! That's where "he said, she said" stories go to die.

[washcycle]

Guez, on the factual case (ignoring how ridiculous it is to argue the validity of the conclusion while simultaneously arguing that it doesn't matter. If it doesn't matter, then why argue that it's wrong) you'll notice that I never state the difference, only that I think it's clear that the advantage goes to the cyclists (or more accurately the bicycle. The conclusion, I suppose, is that the bicycle is a safer vehicle than a car from a crash-prevention point of view). So the magnitude of the difference is somewhat moot. I think the margin is large enough to support the conclusion. And you're unwillingness to take a stab at the report ratios further serves to undermine your position "I don't know anything about the numbers, but I'm sure you're wrong" is not a strong position. Once again, you're comfortable criticizing someone else's position, but completely unwilling to take any sort of stand FOR something.

It's interesting you bring up sidewalks and trails since some of the crashes did happen (I know this for a fact) on trails. So, the numbers consider all the reported crashes on trails, but none of the exposure. I didn't modify the numbers to account for this - so that further enlarges the margin.

As to the "so what" element I would add to the advocacy aspect the old science maxim that you can't understand what you don't measure. Knowing that bikes and the way cyclists on average ride them are safer is a valuable fact, would you not admit? If it were the other way around, would you still say "so what"? I wouldn't. I'd be here saying "look people, we need to step it up. We have ourselves to blame." But that wasn't the case. To say "so what" to any bit of science is to say "I don't think science matters" and that's something I can't agree with.

[Contrarian]

One thing your analysis is missing is any assessment of the seriousness of the collisions. Here is my rough analysis:

In February, 2007, the Washington Post reported that a pedestrian had died after colliding with a cyclist. (http://www.washingtonpost.com/wp-dyn/content/article/2007/02/03/AR2007020301735.html). The article is skimpy on any detail about the collision, but it does mention that the last reported cyclist-pedestrian fatal crash was in 1983 -- over 23 years ago. In the metro area there are roughly 400 fatalities due to
automobiles per year. So since the last time a cyclist ran into a
pedestrian and killed him, approximately 10,000 people have been killed by local motorists.

[washcycle]

Contrarian, that is planned for later. But I will point out that the DDOT study contradicts the Post story as the DDOT study has one reported pedestrian death by bicycle crash sometime in 1998.

[washcycle]

Because I keep track of such things there have been four such fatalities in DC since 1979.

[Contrarian]

OK, with four in 31 years we still get roughly 3,000 killed by car for each one killed by bike. I think my point still stands.