We just ran a report for the races that use RunSignup over the past two years. Here are the results:
26.9 % 1 week in advance
16.1 % 2 weeks in advance
20.7 % 1 month in advance
35.3 % 6 months in advance
0.9 % % 12 months in advance
These numbers are skewed a bit. Larger races that sell out will lead some weight to the 6 months in advance. The numbers for smaller races are more proportional to the 1 month and less numbers.