As the baseball pennant race winds down, optimistic fans of teams trying to catch the leader keep hope alive as long as a mathematical chance of the playoffs exist. However, at some point the odds of the 1st place team clinching become a virtual certainty.
As a sample, in my Statis-Pro league, the Houston Astros now have the best record at 32-16, meaning their worst case is a 32-28 finish in my "60-game" season. That leaves the disappointing Los Angeles Angels mathematically alive at 20-28, because their best case scenario is a 32-28 finish, so if both happen and neither the A's or Mariners finish better than 32 wins, the Angels would play the Astros in a one-game playoff for the division.
The odds of that happening are one in 2,670,000,000,000,000,000,000,000,000,000.
How can the odds be that bad? I will run through the math as a guide for when it really is time to give up on your team.
First assume that to make the playoffs the Angels needed to win all 12 remaining games and the Astros needed to lose all 12 remaining games - then they needed to win a one game playoff with the Astros - so 25 straight games needed to go their way. Every year a team gets 4,140 chances to win 25 straight games (you can win games 1 through 25, 2 through 26, 138 through 162 etc. Back when it was 12 teams and a shorter season you had about 1500 chances each season. With those thousands and thousands of chances over the 150 years baseball has been played a 25-game win streak happened once - the 1916 New York Giants who somehow actually played below .500 the rest of the season. So virtually impossible.
However, the Angels in my Statis-Pro season have a better chance because they actually just need to have eight straight games go their way - because it is really just eight games for me but you need to win by five runs or more for a "3-game sweep," so that is what will happen in my league. The Astros will play Minnesota and then Baltimore, two games each, and the Angels will play Seattle and Boston two games each.
As noted in my study here, 13% of the time a team sweeps a three-game series (and 13% of the time they are swept). In a single game, a team likewise has a 13% chance of winning by 5 runs or more and a 13% chance of losing by 5 runs or more. Therefore, I simply could each Statis-Pro game as three games, with the winning team getting credit for 2 wins and 1 loss unless they win by 5 runs or more (without needing extra innings) in which case the get credit for a 3 games to 0 sweep. This also roughly tracks the Pythagorean expectation calculator that a team's win record will track the runs scored and against (if you win a bulk of 1-run games you are getting lucky and in most cases, your record will fall off over time).
So in the case of my Statis-Pro season, the Astros would need to lose their four remaining games by at least 5 runs each time, and the Angels would need to win by at least 5 runs all four times - a total of 8 games going perfectly for the Angels. At first glance, anyone would know that would be a long-shot, but it might not seem impossible.
|LAA Needs all to Happen to win AL West||Percent Chance|
|Min beats Houston by 5+||13.00000000000000000000000000000%|
|and LAA beats Sea by 5+||1.69000000000000000000000000000%|
|and Min beats Houston AGAIN by 5+||0.21970000000000000000000000000%|
|and LAA beats Sea AGAIN by 5+||0.00371293000000000000000000000%|
|and Baltimore beats Hou by 5+||0.00000815730721000000000000000%|
|and LAA beats Bos by 5+||0.00000000030287510659225300000%|
|and Baltimore beats Hou AGAIN by 5+||0.00000000000000002470645290735%|
|and LAA beats Bos AGAIN by 5+||0.00000000000000000000000000007%|
|and LAA beats Hou in 1 game playoff||0.00000000000000000000000000004%|
|and Seattle 25-23 doesn't top 32 wins||Not calculated|
|and Oakland 24-24 doesn't top 32 wins||Not calculated|
|and lower due to Hou being favored||Not calculated|
|and lower due to LAA being underdog||Not calculated|
In other words, if you played off these eight games 2,670,000,000,000,000,000,000,000,000,000 times, then the Astros would lose all four by 5+ runs and the Angels would win all four of their games by at least 5+ runs about once. As Jim Carrey said, "So you are telling me there is a chance!"
You may ask, what if you really were playing off 12 games for each team and the Angels just needed to win all 12 and the Astros needed to lose all 12? While the chances of eight straight games all going by 5+ runs in the Angels favor is low, believe it or not, the chances of actually having 24 games all go in the Angels favor as simply an Astros loss or Angels win is MUCH, MUCH lower than one in 2,670,000,000,000,000,000,000,000,000,000, so my "5+ = sweep" system actually gives them their best chance!