An “A+” for Le Moyne’s Dolphy Day Wizard
In a previous post, I wrote that the Wizard’s problem of deciding when Dolphy Day should occur is similar to the secretary problem in operations research. The optimal strategy is to observe the first 36.8% of the candidate days for Dolphy Day and then choose the first day that is better than all of the first 36.8% of the days observed. The ideal Dolphy Day should be one that is warm and dry.
Now that the semester is over, let’s evaluate how well the Dolphy Day Wizard performed compared to the optimal strategy. I first defined the set of candidate days for Dolphy Day to be each school day from March 20, which was the first day of spring, to May 7, which was the last day of classes. During this time period, there were a total of 32 candidate days.
The charts below show the high temperature and amount of precipitation for each of these 32 days. The data (DolphyDay2012weather.xlsx) was obtained from www.wunderground.com for Syracuse’s Hancock International Airport.
If the Wizard had followed the optimal strategy, he would have observed the first 11 candidate days (36.8% of 32 days = 11.77 days) to find the day against which the remaining 21 candidate days will be evaluated. The best day among the first 11 days was day 2 (March 21), which had a high temperature of 81°F and no precipitation. This is the Wizard’s benchmark. The Wizard should then choose the first day that is forecast to have a high temperature greater than 81°F with 0% chance of precipitation.
The first of the remaining 21 days that met this criteria was day 17 (April 16), which had a high of 90°F and no precipitation. Guess what? Monday April 16 was indeed Dolphy Day at Le Moyne! A big thumbs up to the Wizard for choosing wisely and optimally!