apologies for the belated reply. work, as you say, and life, which i read elsewhere has much of moment for you as well.

i like your analysis, and i agree that the magic number is designed for pairwise consideration.

however, i should say (should've said in the entry perhaps), that i was looking at it poetically: riffing on the term of art and referring to a number that's magical for another reason: 162 represents the blank slate, the start of the new season, the opportunity to go out and make history, and the number of opportunities to watch one's team in action (playoffs or not, everyone's guaranteed 162).

back to the term of art: although i understand that the operation of reduction includes losses by the trailing team, i like to take the (pessimist's?) point of view that the trailing team is going to win the remainder of its games (it can happen at the tail end of the season -- has happened to the tigers' detriment) and treat the number solely as the number of games the team must win in order to seize the division. (that the number falls more rapidly than such a perception would allow is always a pleasant surprise.)

i should probably therefore also track a 'jones index number' that doesn't care about the other teams. call it 94. any team in our division that can win 94 games is probably going to win the division. so i would reduce the number with each win, ignoring others' losses. if at any point in the season the adjusted jones index is higher than the remaining number of games (say, a record of 50-69 with a resulting jones number of 44 and only 43 games remaining) the team would effectively be eliminated, to an almost near-certainty (call it a crash). only if a team makes it to september without crashing are they then assigned a magic number.

and you're right about the impact of teams playing against divisional opponents -- the wiki article demonstrates that it is quite possible for a trailing team's magic number to be inaccurate when multiple teams ahead of it will be playing against each other.