That is the key question posed in this fun essay by Walt Hickey, who now writes for FiveThirtyEight and who graduated from the College of William and Mary with a degree in applied mathematics. Here is an excerpt from Mr Hickey’s analysis:

Nobody wants to arrive too early. Being the first guest might mean you’ll catch the host before she’s done preparing … Nobody wants to be right on time, either. What if you don’t know the other punctual guests? What if you then have to meet new people and, God forbid, remember their names for the rest of the night …?

In other words, there is a “time trade-off” in deciding when to show up to a party. If you arrive too early, you run the risk of being bored or of finding yourself in a socially-awkward situation, but at the same time, if you arrive too late, you run the risk of offending your hosts and of losing out on the fun. There are no doubt other considerations that are relevant to this analysis, such as the number of invited guests, whether food is being served, etc. In any case, the larger point here is that there is an optimal arrival time. The question, however, is how do you calculate the optimal “late-arrival” time? (Hat tip to Mrs Andrea Robinson for the pointer.)

Too late or too early?