Odds of bad team beating good team in a series?

[soccer10k]

I was talking with my dad about this last night but I'm not sure how to do the math on it so hopefully somebody can help me out.

 

If you matched up a really bad team (like the 2011 Astros) against a really good team (like the 2011 Phillies), what are the chances the bad team wins a five-game series or a seven-game series?

[bukie]

I'd say about a 10% chance. I took a quick grid of the worst four teams in each league against the four playoff teams in each league (so HOU/CHC/SD/FLA vs PHI/MIL/ARI/STL and MIN/SEA/BAL/KC vs NYY/TEX/DET/TB). The bad teams won about 1/3 of the games overall, won 3 of the 32 series, and tied four others. None of the bad teams won any season series that went beyond 10 games (so intradivisional), and only one tied such a series (BAL vs TB was 9-9).

 

The longer the series, though, the less the chance the bad team wins it.

[Northside Blues]

Well, in theory, the Phillies (102 wins) would be expected to beat the Astros (56 wins) about 76% of the time via the log5 method at a neutral site. If we make the generous assumption that the games would all be played at one, then in a five game series the Astros would be expected to win about 9% of the time, not a lot but about 1 in 11. Of course we're comparing the extremes here. To go even further, the 2003 Tigers would beat the 2001 Mariners about 2% of the time in a five game series.

[davearm2]

Well, in theory, the Phillies (102 wins) would be expected to beat the Astros (56 wins) about 76% of the time via the log5 method at a neutral site. If we make the generous assumption that the games would all be played at one, then in a five game series the Astros would be expected to win about 9% of the time, not a lot but about 1 in 11. Of course we're comparing the extremes here. To go even further, the 2003 Tigers would beat the 2001 Mariners about 2% of the time in a five game series.

This is spot on. First determine the odds to win a single game using log5 or some other method, then extrapolate to a series.

 

A team with a 55% probability of winning one game has a 59.3% probability of winning a 5-game series.

60%: 68.3%

65%: 76.5%

70%: 83.7%

75%: 89.6%

80%: 94.2%

 

Apply the same analysis to a 7-game series and you get...

55%: 60.8%

60%: 71.0%

65%: 80.0%

70%: 87.4%

75%: 92.9%

80%: 96.7%