Actual MPG vs. car's estimate, informative?

It is well established that the car's cumulative MPG display is optimistic. (Car mpg displays tend to be pretty uniformly optimistic, across all models and brands.) Last time I filled up the actual (pump gallons/miles, same pump at preceding and current fill) was ~41 but the car said ~43. Which makes me wonder, is there any useful information in these two numbers? Or is there just so much noise (from variation in tank fill and variation in car's estimate) that no comparison actually tells us anything useful?

 

Agreed on all of that.

I was mostly wondering if the two values could be used to detect a problem. I'm going to make up an example for discussion sake. Let's say that one injector isn't working great, but it isn't so bad yet as to trigger a code. The car is always driven under the same conditions (routes, speeds, temperatures) and its estimated mpg (Mc) falls from ~43 to ~42 but the physical gas added / miles traveled (Mp) falls from ~41 to ~38. Let's use the formula (Mc-Mp)/Mc for the metric we are checking. It rises from .0465 to .0954. Conversely, if there is nothing wrong with the car, but the accuracy of both Mc and Mp is +/- 1mpg the expected range of the metric is (44-40)/44 to (42-42)/42, or .0909 to 0.0. In which case the .0954 is outside the expected range, but only just.

I guess that pretty much answers the question, as the accuracy is probably worse than +/- 1mpg, for both methods, at least at the single tank level. If it is +/- 2 mpg then the high value becomes (45-39)/45=.133, which is well past the "problem" case, and no way to see the signal through the noise. Also if the Mp on my car fell from ~41 to ~38 for no obvious reason, and stayed there, that alone would be enough to make me wonder if there was a problem, regardless of whatever Mc showed.