Tag Archives: Transportation

car fatality rates: an international perspective

Yesterday, Peter K. requested that I put the US driving safety statistics in an international perspective. Here are four figures on this topic.

The driving fatality rates in the EU by region. These rates include fatalities caused by driving, and therefore, pedestrians killed by cars are included. “The total road death toll was cut by 48 % between 1991 and 2008 and has fallen by 31 % since the year 2000.” Eastern Europe looks kinda dangerous here, and Italy doesn’t live up to its dangerous driving reputation.

Here are the traffic fatalities per 100K inhabitants. Only about half of the people who died were in cars, although I suspect that less developed countries contributed to more pedestrian deaths.

Here are the traffic fatalities per 100M miles driven. The last figure didn’t normalize the fatalities according to how much people drive in different countries. This figure, on the other hand, better reflects how good the drivers are in different countries. However, countries with high speed limits (think of the Autobahn) may fare a little worse, since accidents at high speeds tend more be more deadly. Again, half of the victims were not in cars. Therefore, you might not want to be a pedestrian in UAE.

This is my favorite figure. Here I tested whether people who drove more got more practice, and therefore, led to safer driving conditions in their countries, a possible upside to driving a lot [link to data from the EU countries]. The x-axis shows the number of cars per 1000 inhabitants, a proxy for how much people drove (This isn’t perfect, but I couldn’t find the actual number of miles driven). The y-axis has per capita car fatality rates (per 100K). There is certainly a negative relationship here, with more cars associated with fewer fatalities. However, this only explains ~19% of the variation.

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five charts about Americans and their cars

My post yesterday on why teenagers don’t have drivers licenses continues to generate discussion (thank you readers!). I’m going to continue the discussion here.

Despite the poor economy and expensive gas, Americans still love their cars. This love goes way, way back to the invention of cars (see my other blog post on super-highways). Here are some other interesting figures about Americans and their cars.

There are more cars than licenses drivers in the US. This is not a recent trend: there have been more cars than drivers since 1971. This gap is getting smaller, but it’s still wide, historically speaking. My husband pointed out that commercial and government vehicles may be included here. Another report shows that cars outnumbered drivers c. 2000.

This figure shows the miles of road (red). More recently, the total number of lane-miles (green) are shown, which takes multi-lane roads into account. This is a bit misleading, since adding a second lane does not double the road capacity. Compare the total number of road-miles to the total number of miles driven (blue). This suggests that there may be a road shortage. However, building more roads only encourages people to drive even more. Still, Americans love to drive more than ever.

The average annual number of miles driven per driver has steadily increased over time. Only recently people have been cutting back on their mileage, probably due to a poor economy and expensive gas. However, we have only cut back to our 1998 driving level.

Look at the purple line here. This is the average mpg relative to 1987 cars (the 1.0 level), and low is good. This shows that the average mpg has been more or less constant since 1980. This is largely because of the growing popularity of SUVs and minivans. We’ll have to see if the trend of tiny cars and Cash For Clunkers improves these values in the future.

Car, light truck (read: SUVs) and motorcycle fatalities per mile driven. This should convince you not to get around by motorcycle! You cannot see the car fatalities rates well. The fatality rate on rural rates is more than twice as large as the fatality rate on urban roads. This is probably due to urban congestion (congestion = slow driving = safer accidents) and the danger surrounding 2-lane rural highways (2-lane highways = head on collisions at high speeds). Both rural and urban fatality rates have come way down since 1980, probably due to air bags and other safety features (and despite of road rage). The urban fatality rate has dropped faster than the rural fatality rate. Again I would suspect urban congestion here. This is the upside to traffic. Takeaway: Driving is safer than ever.


Why don’t teenagers drive any more?

I got my driver’s license on my 16th birthday. I liked to be able to drive places when I needed to, but I was happy to let my friends do the driving if they wanted to. I didn’t do a whole lot of driving until I bought my first car at age 21 (and I’m still driving it – here is a link to a blog post about my car).

An article in the Atlantic summarized the percentage of people in the US who have drivers licenses by age in 1983, 2008, and 2010. The real surprise was the change that occurred between 1983 and 2008. Here, we see that many fewer young people (aged 34 and younger) had drivers licenses in 1983 than in 1983, and many people aged 55+ had licenses in 2008 than in 1983.

I posted this to twitter and google+ and received quite a bit of feedback.  I was surprised that fewer teenagers would drive. Here are some reasons why more or less teenagers would be willing to drive. I apologize in advance for the stereotypes of teenagers and their parents: these generalizations are not meant to hold on the individual level (of course!)

Reasons why fewer teenagers would have licenses today than in 1983

  1. The Internet has eroded reasons why teenagers need to drive, since they can shop online and communicate with their friends online.
  2. Everyone owns a car, so there are other people to give teenagers rides.
  3. Parents like to “helicopter” and taxi their kids around.
  4. Laws in some states restrict teenagers from giving their friends rides.
  5. People have smaller families today, so teenagers do not need to taxi siblings around as much.
  6. Students are not as independent as they once were (not sure if that is true).
  7. Teenagers are “buddies” with their parents and do not feel the need to escape from home to study, for example.
  8. The teenage right of passage to be caught doing something embarrassing on FaceBook has displaced the right of passage of getting a drivers license.

Reasons why more teenagers would have licenses today than in 1983

  1. More live in surburban neighborhoods where “destinations” are not within walking distance. The suburban model of building shopping centers with giant parking lots in the middle of nowhere are commonplace.
  2. Students are more active in student activities and need to get to and fro.
  3. People own more cars today, so teenagers have more of an opportunity to drive.
  4. Public transportation hasn’t gotten better since 1983.

The reasons for more teen driving seem to be quite compelling to me, but clearly, they do not overwhelm the reasons why teenagers do not drive. What other reasons may teenagers have for not wanting to drive?


Federal van pools: a case of too many constraints

My husband works for the Federal government. He takes a van pool to and from his work on most days (he has a 120 mile commute round trip). The van pools are a great deal. If someone rides in a van pool, they commit to riding a certain number of days per quarter. They pay a membership fee and are reimbursed for saving gas.

In response to fraud, two significant changes were made to the van pool contracts:

  1. Van riders have to ride the van at least 50% of the working days each month (instead of each quarter).
  2. The van needs to be more than 50% full (not including the driver) at least 80% of the time.

First requirement

The first requirement is a problem. Vacations, has off-site training, goes to a conference, etc, interfere with ridership. Add two of these events together, and you end up with a severely inflexible policy. Employees who have to travel or who want to take a vacation may not be able to abide with the new requirements. Employees that travel a lot may not be the best candidates for the van pool, but employees who have one long trip ever should be able to ride the van.

Second requirement

The second change is even more restrictive. My husband’s van holds 14 people. They need to have at least 8 people ride (7 out of 13 + 1 driver) at least 4 out of 5 days in the week. It’s worth noting that small vans are going to have more of a problem with this because they typically have more variability in who shows up.

Looking at the long-term, a van needs to have at least 8 riders 80% of the time. That implies that the average number of days until the van is not “half” full needs to be 5. If we assume that each day is independent of the others, then we can model this as a geometric distribution. To get the desired average of 5, we need a “success” probability of 1/5. That is, the probability of a van being less than half full on any single day needs to be 20%. Is that realistic?

Let’s look at the 14 riders. Let’s say they each ride each day with probability p and that each day is independent. Then we can model the number of riders each day R~ Binomial(14,p). We need P(R<8) < 0.2 to meet requirement #2 (from the last paragraph). But if p=0.5 (as required), then P(R<8) = 0.605.  We need p > 0.642 to get P(R<8) < 0.2.

Thus far, I’ve assumed that each day is independent. Making that assumption will yield optimistic results. The “optimistic” results suggest that even under idealistic assumptions, the new van pool requirements will be extremely difficult to meet.

But this assumption is not valid. Riders ride less on Mondays and Fridays (40% of the work week). In practice, this means a van is likely to have at least 8 riders on three days of the week (Tue-Thu), but not four as required. For simplicity, let’s say that a van always has 8 riders on Tue-Thu (an idealistic assumption, but not too unreasonable). Let’s say that each rider takes the van with probability p = 1/3 on Mondays and Fridays (a modest change), and let’s assume that each rider and day are independent. Then the van has 8 riders with probability 0.0576 on these days. The probability that the van covers at least one Monday or Friday per week is 0.111. Therefore, under more realistic assumptions, it is even more unlikely that a van can meet assumption #2.

Vans could meet these requirements if they “overbook” and allow more riders than there are seats in the van. They will surely need to risk turning riders away to meet their requirements if more than 14 show up some day.  This may happen when gas prices change, since ridership increases when gas prices shoot up. However, my husband has noted problems meeting requirement #2 in the past couple of months when gas has been ~$4 per gallon.

Van pools and (un)intended consequences

Van pools are intended to improve the environment by encouraging car pooling. Van pools ultimately create an incentive for people to live very, very far from where they work, thus leading to more fuel usage. In the end, I do not think they save much (or any) fuel from being consumed. But this is open for debate.

On the other hand, van pools are great if your significant other wants a career. It has made our “two body problem” quite manageable. Accommodating one’s spouse’s career is rarely cited as a benefit to van pools. I am grateful that van pools exist so that both my husband and I can have careers. I hope it’s still possible for him to carpool with new rules.

Final thoughts

I applaud the Federal government for trying to crack down on fraud. But I encourage them to create rules that make it possible for riders to follow the letter of the law. And maybe someone who has taken a course on probability should look over the next set of rules and crunches some numbers.

Do you ride a van? Please correct anything I got wrong in the comments and add your two cents about how they can be improved.


Happy 12th birthday to my Honda Civic! Let’s compute how much money I spent on gas.

The first and only time I bought a car was in the year 2000 when gas cost about $1.40 per gallon. A year or two earlier, gas cost about $1 per gallon, so $1.40 seemed expensive at the time. Despite how trendy SUVs had become, I opted for a small, fuel efficient Honda Civic. Twelve years and three kids later, I am still driving that same Honda Civic. It has been a great investment for many reasons. This week when I filled up the tanked for $3.83/gallon, I calculated that a fuel economy of 37 mpg. this is much better than many newer, fuel efficient cars.

I wanted to compute how lucrative a fuel efficient car has been compared to the SUVs that I passed over. So I built a spreadsheet. If you want to check out my calculations, my spreadsheet is here.

Here is what I did. I have averaged 10,000 miles per year for the past 12 years at an average of 34 mpg. I assumed that model year 2000 SUVs get 19 mpg. I also assumed that the mpg was constant over 12 years, which seems reasonable from my back of the envelope mpg estimate every time I fill up the tank. This meant that I used 24.5 gallons per month for my Civic and 43.9 gallons per month for a hypothetical SUV.  Monthly averages for fuel prices were obtained from fueleconomy.gov, and I computed the net present fuel costs assuming a 2% rate of inflation.

Buying a Civic instead of an SUV proved to be quite lucrative: My model suggests that I saved $5693 in gas in the past 12 years compared to an SUV. This is quite significant, as gas has been pretty cheap most of the 12 years and haven’t driven much.  Had I driven more, I would have saved more. If I drove 12,000 miles per year (about the national average), I would have saved $6569. If gas cost the same as it does now (a national average of $3.58) for all 12 years, I would have saved $9938 over 12 years.  I would save much more if you consider the typical lifetime of a Honda being about 250,000 miles–I’m not even halfway there yet.  The Civic cost about $15K back in 2000, which means that the gas money saved over the lifetime of the car is close to the purchase price of the car. So if you’re in the market for a car now, fuel economy is very important!

I can’t say that I really saved $5693. A report from the Texas Transportation Institute indicates that when people have more fuel efficient cars, they tend to drive more, thus negating some of their savings (I think it averages out to something like 15% more miles driven). The amount I drive is well below average, especially for someone who drives to and from work, so it’s doubtful that I would have driven much less with an SUV, but it’s something that could be added to the spreadsheet. It’s hard to overstate how much Americans love SUVs. Their market share has grown steadily since the 1970s (see the image below), and this has only recently started to erode. Gas prices have been pretty bad since 2005, and yet SUVs have only declined in popularity after the downturn in the economy. Cars have also been less popular lately–people are not buying cars or SUVs.

Here is another fuel economy fact:

Men drive way more than women. Men 35-54 drive 18,858 miles per year compared to 11,464 for women. That means that men in this age group drive 62% more than women. Similar trends occur for other age groups. There are several explanations: (a) adult women are more likely to stay at home with young children, (b) men work farther from home, (c) men like to do more joy riding.

If you’re curious, my Civic is pictured below. I hope it continues to serve me well.

civic

My sweet ride!

The number of cards and light trucks (mostly SUVs) sold per year. SUVs have become very popular.

The monthly cost calculations are below.

Cost Calculations Miles driven Price per gallon Gallons (Civic) Gallons (SUV) Gas cost (Civic) Gas cost (SUV) NPV (Civic gas) NPV (SUV gas)
Mar-00 833 $1.52 24.5 43.9 $37.16 $66.49 $29.29 $52.42
Apr-00 833 $1.47 24.5 43.9 $35.91 $64.25 $28.36 $50.74
May-00 833 $1.49 24.5 43.9 $36.45 $65.22 $28.83 $51.59
Jun-00 833 $1.63 24.5 43.9 $40.02 $71.62 $31.71 $56.75
Jul-00 833 $1.55 24.5 43.9 $38.01 $68.03 $30.17 $53.99
Aug-00 833 $1.47 24.5 43.9 $35.91 $64.25 $28.54 $51.08
Sep-00 833 $1.55 24.5 43.9 $37.99 $67.98 $30.25 $54.13
Oct-00 833 $1.53 24.5 43.9 $37.55 $67.19 $29.95 $53.59
Nov-00 833 $1.52 24.5 43.9 $37.18 $66.54 $29.70 $53.16
Dec-00 833 $1.44 24.5 43.9 $35.37 $63.29 $28.30 $50.65
Jan-01 833 $1.45 24.5 43.9 $35.47 $63.46 $28.43 $50.87
Feb-01 833 $1.45 24.5 43.9 $35.54 $63.60 $28.53 $51.06
Mar-01 833 $1.41 24.5 43.9 $34.53 $61.80 $27.77 $49.69
Apr-01 833 $1.55 24.5 43.9 $38.04 $68.07 $30.64 $54.83
May-01 833 $1.70 24.5 43.9 $41.72 $74.65 $33.66 $60.23
Jun-01 833 $1.62 24.5 43.9 $39.61 $70.88 $32.01 $57.28
Jul-01 833 $1.42 24.5 43.9 $34.83 $62.32 $28.19 $50.45
Aug-01 833 $1.42 24.5 43.9 $34.83 $62.32 $28.24 $50.53
Sep-01 833 $1.52 24.5 43.9 $37.30 $66.75 $30.30 $54.22
Oct-01 833 $1.32 24.5 43.9 $32.23 $57.68 $26.22 $46.92
Nov-01 833 $1.17 24.5 43.9 $28.70 $51.36 $23.39 $41.85
Dec-01 833 $1.09 24.5 43.9 $26.62 $47.63 $21.73 $38.88
Jan-02 833 $1.11 24.5 43.9 $27.13 $48.55 $22.18 $39.70
Feb-02 833 $1.11 24.5 43.9 $27.30 $48.86 $22.36 $40.01
Mar-02 833 $1.25 24.5 43.9 $30.61 $54.78 $25.11 $44.93
Apr-02 833 $1.40 24.5 43.9 $34.24 $61.27 $28.13 $50.34
May-02 833 $1.39 24.5 43.9 $34.12 $61.05 $28.08 $50.24
Jun-02 833 $1.38 24.5 43.9 $33.87 $60.61 $27.92 $49.97
Jul-02 833 $1.40 24.5 43.9 $34.24 $61.27 $28.27 $50.59
Aug-02 833 $1.40 24.5 43.9 $34.22 $61.23 $28.30 $50.64
Sep-02 833 $1.40 24.5 43.9 $34.31 $61.40 $28.43 $50.87
Oct-02 833 $1.45 24.5 43.9 $35.42 $63.38 $29.39 $52.59
Nov-02 833 $1.42 24.5 43.9 $34.78 $62.24 $28.91 $51.73
Dec-02 833 $1.39 24.5 43.9 $33.97 $60.79 $28.28 $50.61
Jan-03 833 $1.46 24.5 43.9 $35.74 $63.95 $29.80 $53.33
Feb-03 833 $1.61 24.5 43.9 $39.53 $70.75 $33.02 $59.10
Mar-03 833 $1.69 24.5 43.9 $41.50 $74.25 $34.72 $62.12
Apr-03 833 $1.59 24.5 43.9 $38.95 $69.69 $32.64 $58.40
May-03 833 $1.50 24.5 43.9 $36.69 $65.66 $30.80 $55.11
Jun-03 833 $1.49 24.5 43.9 $36.59 $65.48 $30.77 $55.06
Jul-03 833 $1.51 24.5 43.9 $37.08 $66.36 $31.23 $55.89
Aug-03 833 $1.62 24.5 43.9 $39.71 $71.05 $33.50 $59.94
Sep-03 833 $1.68 24.5 43.9 $41.15 $73.64 $34.77 $62.23
Oct-03 833 $1.56 24.5 43.9 $38.33 $68.60 $32.44 $58.06
Nov-03 833 $1.51 24.5 43.9 $37.06 $66.32 $31.42 $56.22
Dec-03 833 $1.48 24.5 43.9 $36.25 $64.87 $30.78 $55.09
Jan-04 833 $1.57 24.5 43.9 $38.53 $68.95 $32.77 $58.65
Feb-04 833 $1.65 24.5 43.9 $40.39 $72.28 $34.42 $61.59
Mar-04 833 $1.74 24.5 43.9 $42.55 $76.14 $36.31 $64.98
Apr-04 833 $1.80 24.5 43.9 $44.07 $78.86 $37.67 $67.41
May-04 833 $1.98 24.5 43.9 $48.60 $86.97 $41.62 $74.47
Jun-04 833 $1.97 24.5 43.9 $48.26 $86.36 $41.39 $74.07
Jul-04 833 $1.91 24.5 43.9 $46.84 $83.82 $40.24 $72.00
Aug-04 833 $1.88 24.5 43.9 $46.03 $82.37 $39.61 $70.88
Sep-04 833 $1.87 24.5 43.9 $45.83 $82.02 $39.51 $70.70
Oct-04 833 $2.00 24.5 43.9 $49.02 $87.72 $42.32 $75.73
Nov-04 833 $1.98 24.5 43.9 $48.50 $86.80 $41.95 $75.06
Dec-04 833 $1.84 24.5 43.9 $45.12 $80.75 $39.09 $69.94
Jan-05 833 $1.83 24.5 43.9 $44.88 $80.31 $38.94 $69.68
Feb-05 833 $1.91 24.5 43.9 $46.81 $83.77 $40.69 $72.81
Mar-05 833 $2.08 24.5 43.9 $50.96 $91.18 $44.36 $79.37
Apr-05 833 $2.24 24.5 43.9 $54.98 $98.38 $47.93 $85.78
May-05 833 $2.16 24.5 43.9 $52.97 $94.78 $46.26 $82.78
Jun-05 833 $2.16 24.5 43.9 $52.84 $94.56 $46.23 $82.72
Jul-05 833 $2.29 24.5 43.9 $56.13 $100.44 $49.18 $88.01
Aug-05 833 $2.49 24.5 43.9 $60.93 $109.04 $53.48 $95.70
Sep-05 833 $2.90 24.5 43.9 $71.15 $127.32 $62.56 $111.94
Oct-05 833 $2.72 24.5 43.9 $66.59 $119.17 $58.64 $104.94
Nov-05 833 $2.26 24.5 43.9 $55.32 $98.99 $48.80 $87.32
Dec-05 833 $2.19 24.5 43.9 $53.55 $95.83 $47.32 $84.67
Jan-06 833 $2.32 24.5 43.9 $56.76 $101.58 $50.24 $89.90
Feb-06 833 $2.28 24.5 43.9 $55.88 $100.00 $49.54 $88.65
Mar-06 833 $2.43 24.5 43.9 $59.44 $106.36 $52.77 $94.43
Apr-06 833 $2.74 24.5 43.9 $67.21 $120.26 $59.77 $106.96
May-06 833 $2.91 24.5 43.9 $71.25 $127.50 $63.47 $113.58
Jun-06 833 $2.89 24.5 43.9 $70.71 $126.54 $63.10 $112.91
Jul-06 833 $2.98 24.5 43.9 $73.06 $130.75 $65.30 $116.86
Aug-06 833 $2.95 24.5 43.9 $72.35 $129.47 $64.78 $115.91
Sep-06 833 $2.56 24.5 43.9 $62.62 $112.06 $56.16 $100.49
Oct-06 833 $2.25 24.5 43.9 $55.02 $98.46 $49.43 $88.45
Nov-06 833 $2.23 24.5 43.9 $54.63 $97.76 $49.16 $87.96
Dec-06 833 $2.31 24.5 43.9 $56.69 $101.45 $51.09 $91.43
Jan-07 833 $2.24 24.5 43.9 $54.90 $98.25 $49.56 $88.69
Feb-07 833 $2.28 24.5 43.9 $55.83 $99.91 $50.49 $90.35
Mar-07 833 $2.56 24.5 43.9 $62.82 $112.41 $56.89 $101.80
Apr-07 833 $2.85 24.5 43.9 $69.73 $124.78 $63.26 $113.20
May-07 833 $3.15 24.5 43.9 $77.11 $137.98 $70.06 $125.38
Jun-07 833 $3.06 24.5 43.9 $74.90 $134.04 $68.17 $121.99
Jul-07 833 $2.97 24.5 43.9 $72.67 $130.04 $66.25 $118.55
Aug-07 833 $2.79 24.5 43.9 $68.28 $122.19 $62.36 $111.58
Sep-07 833 $2.80 24.5 43.9 $68.70 $122.94 $62.84 $112.45
Oct-07 833 $2.80 24.5 43.9 $68.70 $122.94 $62.94 $112.64
Nov-07 833 $3.08 24.5 43.9 $75.49 $135.09 $69.28 $123.98
Dec-07 833 $3.02 24.5 43.9 $73.97 $132.37 $68.00 $121.68
Jan-08 833 $3.04 24.5 43.9 $74.58 $133.46 $68.68 $122.89
Feb-08 833 $3.03 24.5 43.9 $74.22 $132.81 $68.45 $122.49
Mar-08 833 $3.24 24.5 43.9 $79.51 $142.28 $73.45 $131.44
Apr-08 833 $3.46 24.5 43.9 $84.75 $151.67 $78.43 $140.34
May-08 833 $3.77 24.5 43.9 $92.30 $165.18 $85.55 $153.09
Jun-08 833 $4.05 24.5 43.9 $99.36 $177.81 $92.25 $165.08
Jul-08 833 $4.06 24.5 43.9 $99.56 $178.16 $92.58 $165.67
Aug-08 833 $3.78 24.5 43.9 $92.62 $165.75 $86.28 $154.39
Sep-08 833 $3.70 24.5 43.9 $90.76 $162.41 $84.68 $151.54
Oct-08 833 $3.05 24.5 43.9 $74.78 $133.82 $69.89 $125.06
Nov-08 833 $2.15 24.5 43.9 $52.62 $94.17 $49.26 $88.15
Dec-08 833 $1.69 24.5 43.9 $41.35 $73.99 $38.77 $69.38
Jan-09 833 $1.79 24.5 43.9 $43.82 $78.42 $41.16 $73.66
Feb-09 833 $1.92 24.5 43.9 $47.13 $84.34 $44.34 $79.35
Mar-09 833 $1.96 24.5 43.9 $48.01 $85.92 $45.24 $80.96
Apr-09 833 $2.05 24.5 43.9 $50.22 $89.87 $47.40 $84.82
May-09 833 $2.27 24.5 43.9 $55.54 $99.39 $52.51 $93.96
Jun-09 833 $2.63 24.5 43.9 $64.49 $115.39 $61.07 $109.28
Jul-09 833 $2.53 24.5 43.9 $61.94 $110.83 $58.75 $105.13
Aug-09 833 $2.62 24.5 43.9 $64.12 $114.74 $60.92 $109.01
Sep-09 833 $2.55 24.5 43.9 $62.60 $112.02 $59.58 $106.61
Oct-09 833 $2.55 24.5 43.9 $62.52 $111.89 $59.60 $106.66
Nov-09 833 $2.65 24.5 43.9 $64.98 $116.27 $62.04 $111.03
Dec-09 833 $2.61 24.5 43.9 $63.90 $114.34 $61.11 $109.36
Jan-10 833 $2.72 24.5 43.9 $66.54 $119.08 $63.75 $114.08
Feb-10 833 $2.64 24.5 43.9 $64.80 $115.96 $62.19 $111.29
Mar-10 833 $2.77 24.5 43.9 $67.94 $121.58 $65.30 $116.85
Apr-10 833 $2.85 24.5 43.9 $69.80 $124.91 $67.20 $120.26
May-10 833 $2.84 24.5 43.9 $69.51 $124.39 $67.03 $119.95
Jun-10 833 $2.73 24.5 43.9 $66.96 $119.82 $64.68 $115.74
Jul-10 833 $2.73 24.5 43.9 $66.89 $119.69 $64.71 $115.80
Aug-10 833 $2.73 24.5 43.9 $66.91 $119.74 $64.85 $116.04
Sep-10 833 $2.71 24.5 43.9 $66.30 $118.64 $64.36 $115.17
Oct-10 833 $2.80 24.5 43.9 $68.65 $122.85 $66.75 $119.45
Nov-10 833 $2.86 24.5 43.9 $70.07 $125.39 $68.25 $122.13
Dec-10 833 $2.99 24.5 43.9 $73.36 $131.27 $71.57 $128.06
Jan-11 833 $3.10 24.5 43.9 $75.86 $135.75 $74.13 $132.65
Feb-11 833 $3.21 24.5 43.9 $78.70 $140.83 $77.04 $137.85
Mar-11 833 $3.56 24.5 43.9 $87.28 $156.18 $85.56 $153.11
Apr-11 833 $3.80 24.5 43.9 $93.14 $166.67 $91.46 $163.66
May-11 833 $3.91 24.5 43.9 $95.74 $171.32 $94.16 $168.50
Jun-11 833 $3.68 24.5 43.9 $90.20 $161.40 $88.87 $159.02
Jul-11 833 $3.65 24.5 43.9 $89.46 $160.09 $88.28 $157.98
Aug-11 833 $3.64 24.5 43.9 $89.19 $159.61 $88.17 $157.77
Sep-11 833 $3.61 24.5 43.9 $88.50 $158.38 $87.64 $156.82
Oct-11 833 $3.45 24.5 43.9 $84.51 $151.23 $83.82 $149.99
Nov-11 833 $3.38 24.5 43.9 $82.94 $148.42 $82.40 $147.45
Dec-11 833 $3.27 24.5 43.9 $80.05 $143.25 $79.65 $142.54
Jan-12 833 $3.38 24.5 43.9 $82.84 $148.25 $82.57 $147.76
Feb-12 833 $3.58 24.5 43.9 $87.72 $156.97 $87.58 $156.73

the license plate game: the raw numbers

My last post discussed how one might estimate how many state license plates one would expect to see on a road trip. I made a spreadsheet to compute the probability of seeing each state license plate.

Assumptions

  1. The probability of seeing a state license plate A in another state B depends on the distance between their state capitals. It is scaled by the  number of licensed drivers in state A. (This indirectly means that the probability does not depend on how long we are in a state).
  2. Seeing state license plates A, B, etc. are independent from other license plates in a given state D.
  3. Seeing given state license plate A is independent when driving across states B, C,…
  4. We do not adjust for round trips.

The distance between state capitals was found here. The number of licensed drivers per state is here. I estimated the odds of seeing a license plate from state A in state B is captured by this formula:

P = exp(-K * (Distance from A to B in miles) / # of licensed drivers)

with K = 7000 – 2000*Summer01 – 1000*ExpensiveGas01. Summer01 is 1 if it is summer break and 0 otherwise. ExpensiveGas01 is 1 if it gas is “expensive” and AAA predicts that road trips will be down and 0 otherwise. I didn’t have time to properly identify a meaningful formula or calibrate the parameters. Suggestions here are welcome!

Validation

  • We predicted 28.3 states for our summer trip from Richmond to Chicago. We saw ~35. Here, the discrepancy seemed to be the amount of time we spent in each state. We went through fewer states, but was in each state (especially Kentucky and Indiana) a relatively long time.
  • We predicted 26.8 license plates for our winter trip from Richmond to Vermont. We saw 26. Not bad!

The results make me conclude that the first assumption is probably not true: the probabilities do depend on how long we are in a state. When driving to Vermont, we went through many (8) little states. When driving to Chicago, we went through fewer (5) states but were in each state for longer.  Moreover, many of the Midwest states are not “destination” states. Take Indiana for instance. I love Hoosiers as much as the next person, but Indiana truly is the “Crossroads of America”–it’s a state that many people from other states drive through. It’s a better place to spot license plates than, say, Delaware. I didn’t take that into account.

Below is a detailed review of our winter trip numbers. It indicates the predicted probability of seeing each state license plate and whether we actually saw it. As asterisk (*) indicates whether the model is “off”–whether we (1) did not see a state with probability greater than 0.5 or (2) did not see a state with a probability of 0.5 or lower.

A copy of my spreadsheet is here if you want to see how I computed the numbers.

State Cumulative probability of seeing each state      States we saw
Alabama 0.671 *
Alaska 0 Yes *
Arizona 0.065
Arkansas 0.060
California 0.961 Yes
Colorado 0.083 Yes *
Connecticut 1 Yes
Delaware 1 Yes
District of Columbia 1 Yes
Florida 0.999 Yes
Georgia 0.971 Yes
Hawaii 0
Idaho 0
Illinois 0.973 Yes
Indiana 0.950 *
Iowa 0.056
Kansas 0.028
Kentucky 0.710 *
Louisiana 0.236
Maine 0.565 Yes
Maryland 1 Yes
Massachusetts 1 Yes
Michigan 0.990 *
Minnesota 0.269
Mississippi 0.060 Yes *
Missouri 0.563 Yes
Montana 0
Nebraska 0.001
Nevada 3.53E-06
New Hampshire 0.911 Yes
New Jersey 1 Yes
New Mexico 3.14E-05
New York 1 Yes
North Carolina 0.999 Yes
North Dakota 0
Ohio 0.998 Yes
Oklahoma 0.032 Yes *
Oregon 0.0006
Pennsylvania 0.999 Yes
Rhode Island 0.863 *
South Carolina 0.878 Yes
South Dakota 0
Tennessee 0.841 *
Texas 0.983 Yes
Utah 5.61E-05
Vermont 1 Yes
Virginia 1 Yes
Washington 0.037
West Virginia 0.416
Wisconsin 0.671 Yes
Wyoming 0

the license plate game

My family took a lot of road trips when I grew up. To combat boredom, we tried to see how many state license plates we would see on our trip. On a trip to see Mount Rushmore, we found almost all of the states.

As an adult and geek, the license plate game has (subtlety?) changed. Now, I combat boredom by talking with my husband about how to come up with a probability distribution for how many state license plates we would expect to see on a road trip from point A to point B.

We took two road trips this year: one from Richmond, VA to Chicago, IL over the summer, the second from Richmond, VA to Burlington, VT over the winter break. We saw ~35 states in our first trip and ~25 states in our second trip.  My husband and I immediately noticed that we accrued license plates at a slower rate on our winter trip, which we suspect was from fewer people making road trips over the winter as compared to summer.

We wondered if one could estimate how many license plates you would expect to see in a road trip based on

  • the states you drive through,
  • the time of year (more people take road trips in the summer)

The state that you are in determines how likely you are to see other state license plates based on their relative distances as well as the number of licensed drivers in other states.

We simplified the problem to avoid looking at how long you drove through a state as well as interstate connectivity issues. That is, there is no difference between driving through West Virginia on I-70 and driving through Pennsylvania on I-80. Additionally, if you are in I-80 in Illinois, you are connected to neighbor states Iowa and Indiana but not neighbor states Missouri and Wisconsin, and therefore, one might expect to see Iowa and Indiana plates. We ignored this and just noted that you would be in Illinois, which gives the likelihood of seeing license plates from other states regardless of “route distance.”

My next post summarizes the model, the assumptions, and the results.

Have you tallied license plates on road trips? What do you think are the salient aspects of this problem to include in a probability model?