tie-break for equal scoring

[Francesco Potortì]

As anticipated on 17 September, this year we are using a tie breaker when the scores of two competitors are less than a "Realistic measurement resolution".  Should such cases arise, the following algorithm will be used.

What follows will be published on the web site in the next days; it includes a rationale and the description of the algorithm.


# Rationale

According to the EvAAL framework, ranking is done with "Realistic measurement resolution" (point 3 at https://competition.ipin-conference.org/current-competition/the-evaal-framework).

Ranking is based on Score, which is the third quartile (75th percentile) of point error.  A Score difference less than a given threshold is not considered significant for ranking purposes.  In such a case, we will use the 90th percentile of point error as a tie breaker.

The threshold is set to 50 cm for Tracks 1, 3, 4, 6, which involve estimating the position of a person.  In 2026 the threshold for Track 7, which involves a robot, is set to 10 cm.


# Algorithm

Competitors are initially ranked by their Score (75th percentile).  Competitors whose Scores are no farther than a Treshold are then ranked by their 90th percentile.  Here is how it works:

- T is threshold
- competitors are initially ranked according to Score (75th percentile of point error)
- highest ranked (lowest Score) competitor has index R=1, next is R=2 and so on
- for each competitor with index R, its Score is score(R), its 90th perc is score90(R)
- initially, since we have just ranked competitors, we have score(R) < score(R+1)
- loop until no exchanges are done in the for loop
  - for R from 1 to maxR-1
    - if score(R)+T > score(R+1) /* meaning that Score difference is less than Treshold */
      - then if score90(R) > score90(R+1)
	- then exchange competitor(R) and competitor(R+1)

Attached you find a figure depicting how the algorithm works in a specially convoluted example case.  The Treshold in the example case is set to 1 for readability.

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