Pete Soule has done some statistical work on the log files from the Muncie World Champs. He took the difference between the individual stopwatches and the electronic times of the primary system for the four days of flights. Thereby he got 215 numbers. He then sorted them according to size, placed them on a horizontal axis and plotted the difference on the vertical axis.
Note that this is an analysis on the manual timekeepers plus stopwatch performance, not the on the electronic timekeeping, as we can be confident that this is more accurate by at least a factor of ten, and possibly by a hundredfold!
Here is the chart he got:
This looks very much as a "normal" (gaussian) distribution. (Follow the link to the corresponding curve you would get from an ideal normal distribution!)
Pete also calculated the mean difference to -4.12 milliseconds, and the standard deviation to 50.29 milliseconds. (With reference to zero.)
The "mean difference" here corresponds to the "bias" which has been a concern if mixing manual and electronic times. Here the bias is smaller than the resolution of the stopwatches!
The "standard deviation" you could also call the "typical error" of the individual stopwatch time (relative to the electronic time). When the mean of three stopwatches is used, the deviation should become smaller, roughly 58% (not checked).
(From Landres 2000 I got 29 milliseconds standard deviation for the mean
of the stopwatch times and +6 milliseconds mean difference.
- And this standard deviation happens to be 58% of 50 ms!! )