Rules‎ > ‎

The Asterisk

The Handicapper was asked whether the new Asterisk system for the club swim was discretionary. Could the Handicapper just pick on anyone and say they had a poor swim. I assure you I have chosen an unbiased measurement to work out who gets an asterisk. The Gross Times (handicap adjusted times) of all our swimmers, are close to log-normally distributed. The log-normal curve is like the bell shaped curve, we learnt about in high school. However the log-normal distribution allows 1 tail (the right tail) to be very large, whilst clearly the left tail can’t go below zero (you can’t have a negative swim time).

Below is a histogram of all the swims in the database (on the website). You can see that it appears somewhat log –normally distributed, and to compare I have overlaid a log-normal distribution curve by first using the data. to calculate the volatility or standard deviation of all swims (47 seconds). I theorise that the reason the histogram is bi-modal (has twin peaks) is because of our handicapping system, we increase winners handicaps greater and let losers handicaps go out more slowly. The asterisk has been set at 1.25 standard deviations (58.75 sec = 1.25 * 47) above the geometric average of the distribution.

The above chart, is simply a graphical representation of all competitors aggregate swims. Each week the Handicapper works out the volatility (standard deviation) of each individual swimmer and then set the individual swimmers asterisk at 1.25 times their individual standard deviations, above the median swim time. So it means each swimmer has a different asterisk level. Volatile swimmers are given more leniency then consistent swimmers, in how close the asterisk gets set to the median time. This probably explains why Brett Huitenga received an asterisk after the first day, as he is traditionally a very consistent swimmer (low volatility).

Below is the maths that you would use to work out where your standard deviation is, firstly download your swim data into a spreadsheet (make certain all your times are over the same distance). 

1.       Take the natural logarithm of all your swim times

·         use function LN(time) in excel

2.       Take the sample standard deviation of all the LN(times)

·         Use function - STDEV.S(LN(time1), LN(time 2),…, LN(timeN)) in excel

3.       Work out your geometric average time in seconds

·         Use excel function EXP(AVERAGE(LN(time1),LN(time2),….,LN(timeN)))

4.       Convert the number for the sample standard deviation (above) into seconds

·         Geometric average time * [EXP(0.5* Sample standard deviation) - EXP(-0.5* Sample standard deviation)]