Speeding Metaphor

Dan and I were discussing the expected benefits and costs of speeding in terms of time. The benefit of speeding is your expected time of arrival is sooner and the difference increases as the distance travelled increases.

We agree that for short commutes, speeding only yields a slightly improved expected arrival time due to traffic lights. Short distance speeds only make a difference if the fast car makes the light and the slow car does not. The more lights between start and end reduce the effect of speeding on average.

For long distances with few traffic stops, say a 700 mile drive, travelling at 80 miles instead of 70 saves an hour and 15 minutes. However, if the speed limit is 70, there is some probability per mile that you will get a speeding ticket (given obedience to other traffic laws). If given a ticket, and the driver chooses to go to traffic school, he does not save any time. So the expected time saved is probablity of not getting a ticket, multiplied by the time saved, plus the probability of getting a ticket multiplied by the time lost (negative time saved of ticket process on the roadside and traffic school time).

Time saved and lost can be easily assumed, the probability of getting a ticket at a given speed is much harder.

Now for the metaphor: I have heard a metaphor (from traffic school) that was used to explain how flow of traffic is not a valid excuse for speeding. When everyone speeds, it is like the officer has a line in the water and all the fish are biting. He can catch plenty of speeders.

When applying this metaphor to the probability situation above, it is incomplete. A police officer may not be inclined to pull people over for going 5 over or 10 over. Why? He likely has bigger fish to fry. In other words, the speeders do not choose if they get tickets like a fish chooses to bite on the bait. The speeders only choose to swim in dangerous waters. The officer is the one who selects the fish. It is more like spear fishing.

So the faster you go, the higher the probability of getting a ticket is, but the more time you save. Also the flow of traffic does matter, because if you are consistently the biggest fish in dangerous water, you are more likely to get a ticket. This would make for a nice model with an optimum speed (or speed above traffic flow). There would have to be several parameters but I would guess optimal time saving speed is somewhere between 5 to 10 over the limit.

Speeding cameras would then be like nets. Any fish in the dangerous water is going to get scooped by the net.