As I try to think about this, I'm getting confused between records for *years* (of what?) and records for *specific days* in a year, which are also mentioned. Aha — I now see that I'm *also* confused about "expected number of record-setting events"). Since records began? Okay, now it makes sense. I would need to know *exactly what* type of record-setting events, and also *exactly what knowledge* of these events is assumed when calculating the probability. E.g., is this asking what the expected number of records will be, before record-keeping began and assuming no knowledge of new records after they are made? Looks that way. —Dan ((( Many real-world records, like fastest marathon (https://en.wikipedia.org/wiki/Marathon_world_record_progression#Men), show periods of steady, almost differentiable growth over the years, but also have plenty of what look like discontinuities. ))) —Dan Stuart Anderson wrote: ---- Also, given that official weather records have only been kept for about 150 years in the US, as there are more than twice that many days in a year it's unusual if at least one day each year *doesn't* set a record for highest or lowest temperature, or most rainfall or snowfall, for that date, even if there's no climate change. If each of the years were statistically independent with no el Nino climate correlation or climate forcing wouldn't the expected number of record setting events be equal to the sum of the number of terms of the harmonic series? For 150 years that would be about 5.6 and as time goes on records would be set less often. -----