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

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). Seeing state license plates A, B, etc. are independent from other license plates in a given state D. Seeing given state license plate A is independent when driving across states B, C,… 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