Rules for the RMOC ranking system.

We are planning RMOC rankings by course this year. The current proposal is as follows:

Every time you run a course, you get ranking points. These are based on your finish time as compared to the time for the top three finishers on the course. At the end of the season, we add up your best scores to compile the final ranking results. For ski/snowshoe courses we add up your three best scores (there are only four events), and for regular events we will use your five top results of the year. This allows you to have a few bad runs or even skip a meet or two.

At the end of the year, the top competitors will receive kudos and, of course, the usual prizes.

The score is calculated as a function of the time:

```     f(t) = a * t + b for t < 1.5 * t100
f(t) = c * exp(-d * t)) for t > 1.5 * t100```

The coefficients a-d are determined by:

```     f(t100) = 100
f(1.5 * t100) = 50```

with t100 = average of the top three times. f(t) and its derivative are continuous for all t.

Note that teams do not receive points but are included as part of the top three for the t100 calculation.

We use a specific smooth function that converts time in seconds (t) to a ranking score in points. The larger the time, the lower the number of points.

The function is linear (a straight line) from t=0 to t=t150 (defined below) with a decaying exponential for t>t150. The reason behind the exponential tail is to avoid negative scrores for large times. The exponetial tail is grafted on to the linear function by matching values and slopes at t=t150 and approaches zero as t goes to infinity.

The linear part is chosen so that a time equal to the average of the top three finishers results in 100 points. This time is denoted as t100 above. To define a straight line we need a second point. This second point is obtained by deciding that a time of t150=1.5*t100 (that is, 50% longer than the average of the first three) should result in a score equal to 50 points.

Examples:

• If you finish the course in zero time, you get 200 points (plus a special prize, TBD, and a special investigation :-).

• If you are in second place you get ~100 points.

• If you spend 50% more time than the second place finisher you get ~50 points.

• If you are more than 50% behind, you get less than 50 points but always more than zero (unless you are *really* slow, in which case you qualify for a free beginners instruction :-).

-- Sverre

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