Methods and explanation of terms
The application is based on a conjecture: that performance in a related population falls on a Bell Curve. The related population is that of high school students in California and the US. See evidence
Here the distribution of performance will follow a Normal or Gaussian curve.
It then follows that the top performer in a population of P athletes should attain a mark, e.g. speed, S, that increases with the size of P as: Square root of ln(P), where ln(P) is the natural logrithm of P. In fact Sqrt[ln(p)]=mS+b. ie. a plot of Sqrt[ln(p)] vs speed, S, will give a straight line with slope m and intercept b.
I have obtained m and b values from fits to data for all the events shown. These parameters are then used by the application to convert a performance to a population. The populations given by the program are real full populations of students. Since not all students try out for track, the procedure implicitly includes the probability that a student will participate.
The "Points" awarded are directly related to Sqrt[ln(P)], rather than to P, in order to make the scale linear with speed, ie. twice as fast gives twice as many points. The linearity of award points with performance is the convention used by IAAF, for example.
The points awarded have been scaled so that world records are awarded 1000 points on average. In fact, as you will see, some world records are worth more than others. The reason for this variation is that our points are based on a particular population. US boys, for example, perform better at sprints than distance, relative to the world record. In 2000, the best 100m mark for a US boy was 10.14 s, which is just 3.5% over the 9.79 s WR. The best 2-mile time, however, was 8:44.5, or 9.6% over the 7:58.6 WR.
This behavior emphasizes a key aspect of the current application:
The application applies specifically to US and California high school students.
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