I copied the following from one of the histories of the EIC program from the CMP website. I corrected the info on the number of Legs awarded at matches, since that number changed in 2006 when they reduced the number needed at a match to award one Leg (six rather than ten). It gives a brief rundown of the program. You'll need to check the new rule book for the rules regarding what is a legal EIC pistol.
The Distinguished Badge is awarded when a competitor accumulates 30 ‘points’ earned in EIC matches. Points are awarded on the basis of an individual’s placement among the top 10% of non-distinguished competitors in the match. Points accumulate throughout a competitor’s lifetime until Distinguished status is attained, so that points earned as a member of the Armed Forces in bull’s-eye competition will transfer toward designation as a civilian, and vice versa. It is also required that one must earn at least an eight or ten-point "hard” leg by placing in the top 50% of competitors in the top ten percent.
The pistol National Match Course (NMC) is used in the EIC match and consists
of 30 record shots shot in three stages with no sighting shots. Slow fire is first with ten shots fired in ten minutes at 50 yards. The second stage is timed fire: ten shots, in two five shot strings, with a 20 second per string time limit followed by rapid fire, both being fired at 25 yards. Rapid fire, the final stage, is two five shot strings, with a ten second per string time limit. The service pistol or its commercial equivalent, .45 M1911, M1911A1, or the 9mm M9, is required. No sighting shots are allowed.
Local EIC and military matches can be particularly difficult matches at which to earn leg points as the combination of a low number of entries and highly skilled shooters can easily push the scores to the upward limits. A minimum of six non-Distinguished shooters must compete in a match for it to be approved and legs are distributed on the basis of six and the next largest fraction of ten. For example, a match with 16 entries awards two legs while one with 26 awards three. Perhaps the best place to earn leg points is at the National Matches.
When a competitor “legs” for the first time, whether it is for four, six, eight, or ten points, they are awarded a bronze EIC badge, in addition to any other award they might have earned. When 20 points are accumulated a silver leg badge is presented. Leg badges are separate and distinct from the medals presented at a regional or the National Matches for placing in the top three or above cut-off. When thirty points have been earned, the shooter is awarded the Distinguished Badge. The Badge is engraved with the competitor’s name, year earned, and, in the case of civilians and members of the Air Force, the badge’s serial number. In the services it is traditional in some commands to have the Badge presented by a general officer or other high ranking official. The CMP follows the practice of having an eminent member of the shooting community present the Badge to new recipients at the National Match Awards Ceremony, thereby adding additional dignity and prestige to a milestone that few shooters will ever forget.