Numerical Simulation of Low-Key 2012 week 4 Passing
Last time I made an off-the-cuff prediction each rider in today's Boulder Creek to Saratoga Gap Low-Key time trial would be passed, or be passed, by around 2 riders on average. That was based on the assumption riders varied by around 0.5% each in the sequence and that riders varied week-to-week by 2%. These were low estimates, I concluded, after examining the data. For this post I actually did a numerical simulation, using numbers derived from Low-Key historical data. For each starter, I generated a normally distributed "true speed", with sigma = 14.4% about a mean (derived from historical data). For each rider, I then ran a "qualifying climb" in which speed varied normally with sigma = 4.2% from true speed (derived from my score history). Note this was based on the old scoring system, % of median, which includes an artifact that some weeks tend to yield different amounts of score spread than others. So it's probably an over-estimate. I assigned ...