Pro sports playoffs aren't really comparable. Many of them do it very differently from a standard elimination tournament. Hockey repairs the 8 teams based on seedings so the highest seed remaining always gets the lowest seed remaining. (Was pretty amusing a couple years ago when the 7 and 8 seeds got to the east conference finals since 8 had to go through #1, #3, and #5, while 7 had to go through #2, #4 and #6, or something like that.)
In football, the top two seeds get a bye in the first week. The seeding is also determined strangely since the top four seeds are automatically the four division winners, while the 5 and 6 seeds are the two wild cards. Last year, this meant the Seahawks were a higher seed than the Saints or the Packers, who had substantially better records, because they were in a pathetically weak division.
In baseball, I'm not sure of the exact policy, but I believe the wild card gets the team with the best record, while the other two division winners face. The winners advance to face each other. I honestly couldn't care less about basketball, so I have no idea how they do it in the NBA.
It's also worth noting that in each case except for the NFL, the match-up is determined by more than one contest. They're best of 5 or best of 7 matches. In our vote-off tournaments, official GameFAQs or user-run B8, there's little point in rerunning a match 5 times since they'd come out the same each time.