A user was asking about this and I remembered that my TagTime Minder Tool can answer such questions:
It looks like you need about 200 hours’ worth of pings (5 weeks of full-time work) before you can be 90% sure that TagTime’s estimate has less than a 10% error. But the estimate will be probably approximately correct much sooner than that. For example, you can be essentially completely certain that TagTime’s estimate is within a factor of 2 of ground truth by the time TagTime reports 20 hours.
And if you just need it to be right to within an order of magnitude you can be pretty sure of that by your 2nd ping.
That’s assuming the standard 45-minute average gap between pings.