### Current Rankings Formula

Over the winter of 2004/2005 DVOA formed a committee to examine the rankings process and to make recommendations for improving the formula. Hugh MacMullan, Wyatt Riley, Clem McGrath, Randy Hall, John De Wolf, and Kent Shaw served on the committee. Following analysis of old formula and investigation into other approaches the committee recommended using a formula that is very similar to the formula used by USOF.

The primary difference between the USOF formula and DVOA's is that for DVOA all runners will be ranked together regardless of which course they run. In this system larger numbers are better. An orienteer with a score of 50 points is roughly half as fast as an orienteer who scores 100 points.

What makes this system work is that it is iterative. All the scores are calculated and then recalculated over and over until there are no changes in the rankings. As the rankings are recalculated over and over again it compares every runner to every other runner. As the iterations proceed the faster orienteer's gradually gravitate towards the top of the rankings while slower orienteer's move towards the bottom. In this system the scores of the top three orienteers will average 100. If your score is 50 then you about half as fast as the top orienteer.

A key component of the process is having at least a few orienteers running on different courses. When this occurs, the formula is able to compare all the runners across all the courses.

While the old system had the advantage of being easier to understand, but there were a few serious inequities. The new system addresses those problems, but is more difficult to understand. The details of the system are presented below.

As before there are some general non-math related rules

- Must participate in at least four events to be included in the rankings
- The overall Male and Female winners must participate in at least seven events
- For every five events in which you participate, the worst score will be discarded. Participate in ten events and two will be discarded, etc.
- Running as part of a group does not count
- If you run more than one course at an event, only the most difficult course for that event will count
- Must be a member of DVOA, SVO, or POC in order to be listed in the rankings
- Must be a member of DVOA in order to win
- DNFs do count in the rankings. They are assigned a time equal to 2 times the slowest finisher for that course.
- Beginning in 2010, if courses are reused within a period of 24 months, any orienteers running the same course will be list as "NC" (non-competitive)

The basic rules are:

- Your overall ranking score is the average (arithmetic mean) of all your scores for individual events.
- Your score for an individual race is the course difficulty, divided by your time in minutes.
- The course difficulty is the average (harmonic mean) of the personal course difficulty experienced by every finisher of the course.
- The personal course difficulty for a finisher is the ranking result of that person, multiplied by their finish time in minutes.
- The scores are normalized (multiplied by a constant) so that the top three finishers average 100 points.
- Rules 1-4 are circular, i.e. in order to get the overall ranking score you need the scores, for which you need the course difficulties, for which you need the personal course difficulties, for which you need the overall ranking score. Where do you start? Everybody starts with 100 points for their result and then you loop through the rules again and again. The solution always converges, and is almost non-drifting. The iteration stops when the numbers converge (stop changing from one loop to the next.)
- In order to do the final determination of course difficulties, all valid finishes are used, and all scores are averaged for the Result. Valid finishes are times (not OT, DNF, MSP, etc.).
- In order to do the final determination of results, all results are used, except DNS. Results such as OT, DNF, MSP, etc. are scored at 10% slower than the slowest finisher on the course.
- You have to run in four or more events in order to be ranked.
- For every five events you run the slowest result will be discarded. If you run in ten events the two worst scores will be discarded, and so on.
- Events in which you run as part of a group will not count in the rankings.

### Additional notes

- If you are on average twice as fast as somebody, you should end up with about twice their score.
- As with most rankings systems, it is possible to end up ranked lower than someone who you beat every time in which you ran the same race.

Say Charlie beats Albert by 1 minute in the only race they run directly against each other. Then in a second race, Albert beats Bob by 10 minutes, and in a third race, Bob beats Charlie by 10 minutes. By implication from the second and third races, Albert is much faster than Bob who is much faster than Charlie, so Albert is much, much faster than Charlie. The result of the first race suggests that Charlie is slightly faster than Albert.

To reconcile the two apparently conflicting implications, the math averages things out, and between "Albert is much, much faster than Charlie," and "Charlie is slightly faster than Albert", lies the average "Albert is faster than Charlie".

Therefore Albert would be ranked above Charlie, even though Charlie beat Albert the only time they ever raced head-to-head. The math in rules 1-4 does all of this transparently.