There is a very very narrow range of circumstances under which the Toronto Blue Jays do not make the playoffs. So narrow, in fact, that if we assume every game remaining in the MLB this year has a 50% chance of being won by either team, the odds of the Blue Jays failing to make the playoffs are 1 about 793,072. That equates to a 99.999874% chance that they make the playoffs.

So how do we work out such numbers? Buckle up for a logic roller coaster ride.

To fail to get into the playoffs, every one of the Yankees, Red Sox, Mariners, Astros, Tigers, and Gaurdians would have to beat the Blue Jays, and these are the only 6 teams capable of surpassing the Blue Jays at this point.

At this point, the Blue Jays can end up with at most 73 losses, if they lose all 7 of their remaining games. So surpassing them would especially require a lot of winning by the Gaurdians and Astros (with 71 losses each currently) and the Red Sox and Tigers (with 70 losses each).

But these teams are limited in how much winning they can do the rest of the way, because there will be 6 games played between them. The Tigers and the Gaurdians will play 3 games against each other, and the Tigers and the Red Sox will play 3 against each other. That means there will be at least 6 losses spread around among those 3 teams.

So let’s consider the possible outcomes of the Tigers/Gaurdians series. For each outcome, let’s assume the Blue Jays lose all 7 of their remaining games, ending with a record of 89-73. Let’s also assume both the Tigers and the Gaurdians win all 4 of their other remaining games.

Except that we can’t assume that. Because if the Tigers win all their other 4 games, that means they deliver 3 losses to the Red Sox, who end up at best 89-73, the same as the Blue Jays. Because the Blue Jays end up with 7 wins and 6 losses against the Red Sox, they win the tiebreaker with the Red Sox and are in the playoffs. So the Tigers must lose a game to the Red Sox, and the Red Sox must win their other 4 games not against the Tigers, for the Blue Jays to have a chance at elimination here.

So we’ll assume the Tigers lose 1 more game (versus the Red Sox) outside of the Tigers/Gaurdians series, and the Guardians don’ t lose any others.

If the Gaurdians sweep the Tigers, the Tigers end up 88-74, a game behind the Blue Jays, and the Blue Jays are in the playoffs.

If the Tigers sweep the Guardians, the Gaurdians end up 88-74, a game behind the Blue Jays, and the Blue Jays are in the playoffs.

If the Gaurdians win 2 of 3, the Tigers end up 89-73, tied with the Blue Jays. Because the Blue Jays had 4 wins and 3 losses in their games against the Tigers this year, they win the tiebreaker between the teams, and are in the playoffs.

That leaves the scenario where the Tigers win 2 of 3. Then the Tigers end up 90-72, ahead of the Blue Jays, while the Guardians tie the Blue Jays at 89-73. So as a tiebreaker we look and see that the Blue Jays and Gaurdians each won 3 games against each other this year. We have to use the second tiebreaker, which is records within their own divisions. The Gaurdians end up 36 and 16 against their weaker division; the Blue Jays 25 and 27 against their stronger division. The Gaurdians therefore win this tiebreaker, and the Blue Jays are out of the playoffs – if the other 3 teams surpass them too, that is.

That’s the only scenario in which the Blue Jays are eliminated.

What if The Tigers lose one more game against another opponent? Then they end up with the same record as the Blue Jays, and the Blue Jays are in because they win the tiebreaker with the Tigers. So the Tigers must only lose the one game against the Red Sox.

That covers what must happen with the Tigers, Gaurdians, and Red Sox. What of the Yankees, Mariners, and Astros?

The Blue Jays hold the tiebreaker over the Yankees, so the Yankees must get to at least 90 wins, and therefore must win at least 3 of their last 7 games.

The Blue Jays hold the tiebreaker over the Mariners, so the Mariners must win at least 4 of their last 7 games.

The Astros hold the tiebreaker over the Blue Jays, so they must win at least 5 of their last 7 games.

So now we must get the odds of all these things happening and multiply them together to get the odds that the Blue Jays miss the playoffs. We assume in every game that the teams have an equal chance of winning. The following table contains all the odds:

The reason the Mariners and Astros are lumped together in the last line is that they play one more game against each other, so their odds of reaching their respective win totals are linked because of that game.

When you multiply all these odds together you get 693,198 divided by 2 to the 39th power, which is about 1 in 793,072, or 0.000126%. That’s the odds that they don’t make the playoffs; so the odds that they make the playoffs are about 99.999874%.