### 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/OUSA & AttackPoint.

The primary difference between the USOF/OUSA formula and DVOA's is that for DVOA all runners will be ranked together regardless of which course they run. This is similar to the AttackPoint rankings system. 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 orienteers.

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 (up to 2004) had the advantage of being easier to understand, 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
- Discarding your worst results before calculating your final score
- For 2005-2012, for every five events in which you participate, the worst score will be discarded. Participate in ten events and two will be discarded, etc.
- For 2013+, the best 4 events count, and then after that, the lowest half of the races will be discarded for your final score. Participate in 5-6 events, and 1 will be discarded, 7-8 events, and 2 will be discarded, 9-10 events, and 3 will be discarded, and so on.
- This is the same as Attackpoint rankings, and OUSA from at least the 1990’s through 2012.
- Compared to DVOA up through 2012, if you participate in up to 6 events, the number of results discarded is the same, but as you participate 7 and more races, you earn more discards.

- Running as part of a group does not count
- If you run more than one course at an event, only the first course you race at 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 an award at year end
- DNFs & MPs do count in the rankings.
- For 2005-2012, they are assigned a time equal to 2 times the slowest finisher for that course.
- For 2013+, they are assigned, more simply, a zero.
- In general, and esp. in 2013+, these low-scores, combined with the discard rules, allow orienteers who attend several events, and finish most of them, to be able to discard all of their DNF/MPs low-scores by year end.

- 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 nitty-gritty of the math rules are:

2013+

Note these rules are very similar to the 2005-2012 rules, and are slightly more stable, especially early in the year with fewer people ranked. Attackpoint rankings switched from the 2005-2012 DVOA method, to the 2013+ DVOA method, in about 2006 – and scores jiggled less than 1 point…

- Your overall ranking score is the average (arithmetic mean) of all your scores for individual events.
- Your score for an individual race is proportional to your speed in completing the course. The course field-strength (see below) is redistributed so that every finisher on the course receives a share of the course field-strength as the score of the event in direct proportion to their speed in completing the course.
- The course field strength is the sum of the overall-ranking-score for every finisher of the course.
Example: Al, with an overall-ranking of 80, and Bob, with an overall ranking of 70, are the only two finishers on Red. Together, they contribute their points into the course-field-strength, as 80+70 = 150.

Al finishes the course in 30 minutes, and Bob finishes the course in 60 minutes. As Al was twice as fast as Bob in finishing the course, he gets twice as many points out of the course-field-strength for his score, as Bob does. This works out to a score for the race of 100 for Al, and 50 for Bob.

- Before reporting the scores are all normalized (multiplied by a constant) so that the top three people in the overall ranking average 100 points.
- Rules 1-3 are circular, i.e. in order to get the overall ranking score you need the scores, for which you need the field-strengths, for which you need the overall ranking score. So a common question is - where do you start? Everybody starts with 50 points for their result and then you loop through the rules again and again – though it doesn’t really matter what you start with - the solution always converges to the same result. The iteration stops when the numbers converge (stop changing from one loop to the next.)
- In order to do the determination of field-strengths and scores, only valid finishes are used. Valid finishes are times (not OT, DNF, MSP, etc.).

2005-2012

- 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.).

### 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 may have beaten head to head in the few times you ran the same course.

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 1-3 does all of the same thing, with numbers.