The statistically savvy among you might have noticed something odd about the graph at the end of the last post.
When I let unconstrained math (via Excel) determine the best straight-line fit to these data points, it appears to tell me that these cars lost about 4% of battery capacity for every 10K miles.
But …
But what that doesn’t do is guarantee that with zero miles, I predict that you’ll have 100% of original capacity.
And that matters, because it looks like a lot of these cars must have lost a lot of range early on, that is, at low mileage. And that loss of battery range doesn’t get factored into the 4% per 10K range loss estimate.
So this is a rare instance of a straight-line fit for which you are justified in “setting the intercept” manually, rather than letting an unconstrained least-squares fit to the data do it. By definition, the line has to pass through zero miles matching 100% of original range.
Look what happens when I do that:
On average, pinning the linear trend to pass through 0 miles = 100% of original range, range loss is more like 8% per 10K miles.
The whole cluster of dots is quite “low” on that graph, so to speak. Those cars on average followed a path of losing a lot of range early on. And having the loss taper off to a mere 4% per year.
My guess is that exponential decay is the line you’d like to fit, for something wasting away. But I can’t seem to get Excel to give a trend passing through the required point, with the required shape. So I freehanded what I think the Conventional Wisdom says about the time-path of battery loss.
No matter how you cut it, the actual observed battery loss over this range amounts to much more than 4%/10K miles. The mid-point of the fitted line sits around a 40% loss over 5K miles. That’s the 8%/year calculated when the regression line was pinned at 100% capacity at zero miles.
Why the high range losses? Is this just a market for lemons, or are the dashboard estimates biased?
George Akerlof, economist, once wrote a piece whose title began “The Market for ‘Lemons’: ” The paper is pretty deep, but the takeaway is pretty simple. In this case, it boils down to: People sell their cars when those cars are lemons, not when they are peaches.
That’s one obvious explanation of why these losses appear far larger-than-expected. (Where, lurking in the background is the idea that EVs lose, oh, like two percent a year, maybe, based on looking at a few graphs in the past.) The point is, maybe most of these cars appear in the used car listings precisely because they had above-average battery capacity losses. And that’s why their prior owners sold them. And I’m seeing them.
The other possibility is that the mileage estimated from the dashboard readout is substantially biased downwards. (I know it has a high variance, as it depends on recent driving style. Leaf aficionados refer to it as the “guess gauge”. That should just add noise, not bias, I think.)
There is one element of bias in what I did in my calculation, in that the range bars are each about 8 percent thick. For example, when I saw four range bars, my calculation assumed the car was (4/12 =) 33% charged. But if four bars is really just 3.5 bars, on average, then that charge level is actually just a shade over 28%, on average. I would then triple that error in arriving at 100% of charge, and so end up understating total range by a factor of about 15%.
Adjusting for that would require multiplying my range estimate by (1/.85 =) about 18%. The upshot is that what looked like a 60-mile range based on the dashboard could plausibly be a 70-mile range in reality.
That said, I’m not sure this materially changes the situation. No matter how I slice it, the range of the car I’m interested is far lower than the Recurrent.com estimate that I had been looking at.
Finally, I can’t fully discount that the losses observed in this low-end used car sample are typical of a random sample of Leafs. But if it were, I doubt there’d be many Leaf fans out there.
On net, I think the explanation is that I’m looking at a market for lemons. By looking only at the low-cost end of the market, and only looking at what people are trying to sell, I’m probably looking at a fairly biased sample of all Leafs.
Unfortunately, that’s the sample of cars I’m buying from, if I continue down this path. Perhaps time for a re-think.
