I'd probably say it's more like 5-25% after the WC play-in game is played.
I'm think more of the head-to-head series. I know it's hard to choose the "favorite" based on winning % or WAR or who is hotter. Teams get better as the season goes on- soemtimes through trades or players getting healthy or just gelling at the right time (like the Rockies). It's hard to say, "The better team won," if we can't all agree on who the better team was/is. I get that this makes it hard to prove anything, but in my opinion, the better team wins closer to 75% of the time than 50%. Would you agree with that? (basically 62.5% or more)
Now, if a team is just marginally better, the chances are likely less than 62.5%.
I just happened to choose Winning % and showed that if the Astros win this year, a top 2 team from each league will have won the WS 75% of the time in the last 16 years.
If these were all a one game playoff structure all the way through, we'd see closer to a 50% number, but a 5 and 7 game series helps the better teams win more often.
Even if, like you propose, one team had a 10% chance and they play a team with a 15% chance, it's hardly a coin toss. It sounds like we both have a different isea of what a crap shoot means.