I am onto my second Tesla car leases now, so I think I can define another form of range anxiety with my leased cars: Driving over the lease limit.

It was actually quite interesting. When I was leasing my first Tesla, I did a rough calculation of my daily driving, and figured that 10,000 miles a year is more than enough. Boy was I wrong. I drove up the total of 30,000 miles (the max allowed in my 3-year-lease) in just about 2 years. If it were not for the pandemic lockdown in 2021, I would have been in big trouble with the overage penalty – Tesla lease agreements said that you pay 25 cents for each mile over the limit.

So I set up an Excel spreadsheet to estimate the probability of going over. Therefore, unexpectedly, I encountered the Central Limit Theorem at work. Here is what happened:

  • I first assumed a distribution of my monthly driving mileage, and then estimated the probability of going over my monthly allotment. Call this P1.
  • I then add 36 of those random monthly mileages to get the simulated 3-year total mileage. And then use simulation to estimate the probability of going over the 3-year limit. Call this P36.
  • It turns out that P36 is much much much smaller than P1, i.e., P36<<<P1!

What is going on?

Well, if we apply the idea behind the Central Limit Theorem (CLT)we can get a good understanding. CLT says that if my monthly mileage is distributed N(a,b). Then my 3-year-total-mileage is distributed asymptotically: N(36a,  (36)b)=N(36a, 6b). This assumes that my monthly numbers are independent of each other.

This means that the coefficient of variation of my 3-year-total, which is 6b/36a=(1/6)(b/a) is only 1/6 of that of my 1-month-mileage, which is b/a.

So what is the key takeaway? Even if you are over in a few particular months, you should be OK in the long run. Just make sure that you are not habitually over the monthly limits! If you do, then probably you should re-estimate the mean of your monthly driving.

Download the Excel file here and see for yourself. Here is a video of talking about the spreadsheet: