Most websites that carry the Major League standings these days have a column with an elimination number. Looking at this number from the point of view of the first place team, it can also be called the "magic number." This is the number of games the first place team wins plus the losses of the team in question that will total the elimination number.
But there's a factor missing in "mathematical elimination" that I wish would appear in the elimination number. I will explain.
Scenario #1: Suppose Team A is in first place, two games ahead of Team B with three games left to play. Team A's magic number (which is the same as Team B's "elimination number") would be two. Team B can win the division if they win their three games and Team A loses its three. Or the could tie and Team B could win a playoff game. That's simple.
Scenario #2: Now suppose Teams A and B are tied for first place, and Team C is two back with three to play. Team C has an elimination number of two, but both Team A and Team B have magic numbers of four against each other. Well, in this case it is less likely, but if Team C wins all its games and both Team A and Team B lose their games, Team C still will win the division. In this scenario, Team C still has a chance.
Scenario #3: Well, there's a potential catch to scenario #2. What if Team A plays Team B the last three games of the year? Even though Team C is only two back with three to play, because one of the teams, A or B, necessarily will win at least two of three against the other, Team C has already been mathematically eliminated! Their "elimination number" is still two, but it's impossible for them to win. They were already eliminated at least from the previous game played. Elimination numbers don't take into consideration the number of games played between multiple teams in front of that given team. And if there are more than two teams ahead of the given team, it becomes even more complex. In short, the problem is that guaranteed future wins are not counted in the elimination number.
A real life example came from 1989. With a month left in the season, the Giants were 5 games up on the Padres. A short news clip noted that the woeful Braves were mathematically eliminated the previous day. The assumption was that the Braves could have won all their remaining games, the Giants would lose all their games, and the Padres would lose all games but at most five. A three-way tie would result and the Braves could win a tie-breaker. But upon looking at the schedule, I saw that the Giants and Padres still had six games against each other to play. How could the Giants lose all six and the Padres win five at most? Only if both teams lost the same game, which couldn't happen. So I figured out that the Braves were actually eliminated the day before that.
How can the real elimination number be calculated?