The Modified Median calculation disregards either the highest-scoring and lowest-scoring scores from an opponent or the least significant opponent’s score. It also says that any unplayed games count as opponents with adjusted scores of 0.

Are these fake opponents with adjusted scores of 0 eligible to be dropped as the lowest-scoring scores (it seems like they would naturally be the most likely opponents to be dropped, then)?

34E1. Modified Median
The Median system, also known as the Harkness system for inventor Kenneth Harkness, evaluates the strength of a player’s opposition by summing the final scores of his or her opponents and then discarding the highest and lowest of these scores.
In the Modified Median system, players who tie with even scores (an even score is equal to exactly one half of the maximum possible score), have the highest- and lowest-scoring opponents’ scores excluded. The system is modified for players with non-even scores to disregard only the least significant opponents’ scores: the lowest-scoring opponent’s score is discarded for tied players with plus scores and the highest-scoring for tied players with minus scores.
For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties.
These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed. If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.

Separately, what’s a “plus-score” here? Just anything over an even score?

Yes. The zero would be the first one dropped for a player that needs a low score dropped. (Solkoff as opposed to Modified Median is rather harsh on a player with an unplayed game). And yes, plus-score is anything above an even score.

Thank you. Does the Median method (and, by implication, Solkoff) also make the same unplayed game adjustments as the Modified Median?

These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed.
If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.

I believe that Bucholz has a slightly different way of adjusting for unplayed games; I suspect Median / Solkoff do not, though.

Buchholz and Solkoff are basically synonyms. There are differences in some of the fine points depending upon whose rule sets you are using.

The US Chess adjustments for all the “Solkoff”-based TB’s (Solkoff, Median, Modified Median) are to treat an unplayed game for TB calcs for the player as a dummy opponent with a zero score. The adjustments to adjust the opponent’s score for their unplayed games is to treat those all as 1/2 point.

The FIDE adjustments are to treat an unplayed game as a game vs a dummy opponent with the same score as the player. The adjustments for the opponent’s score for their unplayed games are really complicated depending upon why and when they had an unplayed game.

Thank you. I had seen the FIDE ruleset listed as applicable to Median (Buchholz) and wanted to confirm that the USCF Median / Solkoff were the same as Modified Median for the unplayed games; appreciate it.