In May 2013 Allstate released its “America’s Best Drivers Report“, which identifies cities with residents who have the longest years between accidents. Boise is #2 on the list, so it caught my attention. The data are based on Allstate insurance claims from January 2010 to December 2011.
Although the report is interesting, I think the name of the report is misleading (which is clear when you read how Allstate discusses the report). The report may not necessarily identify where the safest drivers are. Instead it may identify cities where environmental conditions make it safer to drive. If that is the case, the drivers are not necessarily better in these cities, they are just driving in better conditions, leading to more years between accidents. Also, it is possible that the report be identifying cities where accidents are more likely go unreported, which would make it seem like drivers in those cities have more years between accidents.
An alternative way to determine where the safest drivers are is to predict the average time between accidents in these cities based on environmental conditions and likelihood of reporting an accident, and then compare those predictions with the actual averages. If a city did worse than predicted, then perhaps those drivers are less safe. If a city did better than average, those cities may be more safe.
I collected data on factors that influence accident reporting (which include whether an accident will occur, and if so, if it will be reported). Then I made a series of predictions for each city and compared those predictions with the actual data. I identified four cities that do worse than predicted and four cities that performed better than predicted. All the other cities performed as expected.
Likelihood of Reporting Variables
I have identified two potential reasons why motorists might not report an accident. First, not all states require motors to automatically report accidents to the police. In most states motorists only have to report an accident if there is a certain amount of property damage (or if someone dies as a result of the accident). For the minimum reporting variable, I collected data on the minimum amount of property damage needed in to report an accident for the state a city was located in. For states with no minimum, I set the value to $5000.
I expected the sign of the minimum reporting variable to be positive. In places with higher minimum property damages requirements, minor accidents are less likely to be reported, increasing the measured years between accidents. Hence the higher the amount of minimum property damage to report in a city, the higher the average years between accidents in those cities.
Income may also have a positive or a negative effect on whether someone reports an accident, which would decrease or increase the average time between accidents.
Individuals with higher income are more likely to have insurance, and hence more likely to report an insurance claim when in an accident. This would reduce the measured years between accidents. For the income variable, I took the log of median household income for the state each city was located in 2005. The sign of this variable could be negative: cities with higher average income have less years between accidents.
On the other hand, someone with higher income may be less likely to report an accident because they can pay for the damages. This would increase the measured years between accidents. So I expected that the sign of this variable could also be positive: cities with higher average income have more years between accidents.
Besides reporting requirements, several environmental factors that may lead to more collisions. More densely populated cities may create more opportunities for drivers to get into accidents. I collected data on population density of these cities and logged the values. I expected the sign of this variable to be negative: individuals in more densely populated cities have less years between accidents.
Weather conditions could also lead to more accidents. For this measure, I took the average rainfall in the cities in the data set. I expected the sign of this variable to be negative: as rainfall increases in a city, the time between accidents should decrease.
More bike friendly cities may have less accidents on average because there there are less drivers on the road. This would increase the time between accidents. For this variable I used data from Bicylcing magazine’s Top 50 bike friendly cities in the US. I expected the sign of this variable to be positive: individuals who live in more bike friendly cities should have more time between accidents.
Teenagers may be more likely to get into accidents than adults. So as the minimum driving age decreases, the time between accidents should decrease. I collected data on the minimum driving age in each state a city was located in. I expected the sign of this variable to be positive: in cities with higher minimum driving age, time between accidents should increase.
Higher speed limits may also lead to less measured time between accidents. Although most studies suggest that higher speed limits do not increase the number of collisions, they may increase the number of severe collisions. If higher speed limits may lead to more severe collisions, this will reduce te time between accidents because more severe collisions are more likely to be reported. For this variable I collected data speed limits in the states the cities are in. I expected the sign of this variable to be negative: higher speed limits lead to less time between accidents.
The results in the table below suggest that individuals in cities with higher median income have less time between accidents. This may provide support for the argument that wealthier people are more likely to have insurance, so they are more likely to report a claim. The table also demonstrates that as population density and rainfall increases in a city, time between accidents in that city decreases. This suggests that environmental factors play a role in frequency of accidents. Higher speed limits also decrease the time between reported accidents.
Now to the predictions. The table below presents the predictions for each state and compares them with the actual values. Four cities did better than average: Fort Collins, CO, Brownsville, TX, Madison, WI, and Visalia, CA. And four cities did worse than average: Anchorage, AK, Portland, OR, San Francisco, CA, and Glendale, CA. But for the majority of cities, they performed as expected giving the living conditions in those cities.
So the take away message: drivers in most cities perform as expected. There are several cities where drivers have long years between accidents, but they drive in better conditions. And there are several cities where drivers have very few years between accidents, but they drive in more hazardous conditions. Drivers should be judged on the probability that they would get into an accident given the conditions they live in. That way it is easier to determine whether they are being safer than expected or more reckless than expected.