My 1% figure came fom some quick mental pencil figuring. To go 15-5 it made no difference when the losses came. So off the top of my head I figured the M's (as a 53% team) would be at 6 wins/5 losses in the first 11 games (or better) 50% of the time. So if 50% of the time they had hit 5 losses (their proposed maximum), in 11 games....then they had to run the tables in games 12-20 to get in. In my head I quickly figured that with a 50% chance of winning each subsequent game (actually it's 53% but 50% made it easy to figure in my head) their chance of WC-land success dropped to less than 1% over the next nine games. And I'm aware that I did some rounding and simplification. But the number gets to 1% pretty quickly. Think about flipping coins, for example. And none of that factored in the possiblity that 89 wouldn't be enough.
Then I did a bit of research this morning: There are more than 1,000,000 possible win/loss outcomes over 20 games in you figure on a 50% win/loss chance. WWWLWLWLWWLL and so forth. More than a million of them. 2 to the 20th. Again, think of flipping coins.
There are 21,700 combinations that result in 15 or more wins.
21,700/1,000,000 = 0.0217 2.1%
Because we were a 53% team, our odds were slightly better than this. My 1% guesstimate was a bit off.
Check it out here: https://www.quora.com/If-you-toss-a-coin-20-times-what-is-the-probabilit...
Now we're left with 500,000+ possbile combinations of outcomes over 19 games. 2 to the 19th.
We need to win 14 or more of those 19.
Our odds have indeed improved (from winning 15 of 20)...But not to 15%, as far as I can see. in fact, in 19 flips of the coin (50% probability) you would hit 14+ head 11,628 times in 500,00+ "chances" = 2.3%. It is 19 factorial over 14 factorial X 5 factorial. I think.
The M's have had 125 19-game streaks this year. (Game 19 would be the 1st, #20 the 2nd, #21 the 3rd, etc......)
We have twice gone 14-5. That's it. We've had 2 14-5 streaks in 125 tries.
I can't see where we have a 15% chance of doing it from here on out. Of course, the magic number might be 88 or 87...or 90. We don't yet know what the Tigers et al are going to do But regardless of the total we have to pass three of the four teams ahead of us....AND the team we're tied with in order for us to get in. We've spotted the 4 teams ahead of us between 1.5 and 3 games. Will a team in our situation do that once in every six or seven tries? That's a 15% chance. This is a handicapped horse race and the faster horses (so far) get the head start.
I suppose I'm lost in the weeds. Math was a long time ago for me....but I even checked in with our Calc class at school this morning for some backup. Our excellent teacher has helped me out some...at least to get a grip on some of this.
I love conundrums like this. Show me where I'm wrong.
Keith