# Sports standings probabilities

**URL:** <https://boards.straightdope.com/t/sports-standings-probabilities/8439>\
**Category:** Factual Questions\
**Created:** [March 11, 2000, 7:55pm UTC](https://boards.straightdope.com/t/sports-standings-probabilities/8439 "2000-03-11T19:55:00Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![PatrickM](https://avatars.discourse-cdn.com/v4/letter/p/7feea3/32.png) [@PatrickM](https://boards.straightdope.com/u/PatrickM)\
**Post date:** [March 12, 2000, 6:08am UTC](https://boards.straightdope.com/t/sports-standings-probabilities/8439/1 "2000-03-12T06:08:00Z")

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I need help with a statistical probabilities question. (My college stats class was a long time ago.) Here goes:

Assuming a professional sports league like major league baseball’s American league (ie 14 teams in the league, 3 divisions of 5-5-4 teams, with each of the 3 division winners and one ‘wild card’ team qualifying for post-season play) and assuming each of the teams in the league was equal to each other, then what are the chances that one particular team will make the playoffs.

I figure that each team in the 5 team division has a 1 in 5 chance of winning the division championship, and the teams in the 4 team division have a 1 in 4 chance of winning the division, but I can’t figure out how to account for probability of winning the ‘wild card.’ The Teeming Millions help will be greatly appreciated.

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**Author:** ![Jimpy](https://avatars.discourse-cdn.com/v4/letter/j/c68b51/32.png) [@Jimpy](https://boards.straightdope.com/u/Jimpy)\
**Post date:** [March 11, 2000, 7:55pm UTC](https://boards.straightdope.com/t/sports-standings-probabilities/8439/2 "2000-03-11T19:55:00Z")

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OK, assuming my college stats aren’t failing me to–

In a five team division, 1 in 5 for winning equals 0.2 and a 1 in 14 chance of winning the wild card equals 0.0714285714285714285714285714285714 (apx.). Add the two and invert it you get a 1 in 3.68421052631578947368421052631579 (apx.) chance. Doing the same for a four team division your get odds of 1 in 3.11111…

OK, you say, why use a one in 14 chance for the wild card and not a 1 in 11 because three teams will make the playoffs anyways. You can only use the 1 in 11 figure if you want to know the odds of a team making the wildcard and you already know who’s winning the division. If you used it above you’d get statistically invalid results. Trust me, because I did it first and then did a quick test against the blanket odds of making the playoffs (1 in 3.5)and figured out I goofed because every team would have better odds than that. It’s a good thing I doublechecked and that I still have my college statistic books.

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**Jim Petty  
 _An oak tree is just a nut that stood it’s ground_**

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**Author:** ![jcgmoi](https://avatars.discourse-cdn.com/v4/letter/j/a9adbd/32.png) [@jcgmoi](https://boards.straightdope.com/u/jcgmoi)\
**Post date:** [March 11, 2000, 11:33pm UTC](https://boards.straightdope.com/t/sports-standings-probabilities/8439/3 "2000-03-11T23:33:00Z")

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Gotta disagree Jimpy. In a 5-team division, each team has 1 chance in 5 of winning outright and in the other 4 chances in 5 has 1 chance in 11 of grabbing a wild-card:

1/5 + 4/5\*1/11 = 3/11.

For 4 teams,similarly 1/4 + 3/4\*1/11 = 7/22.

As a check note that the percentages should total 400, since 4 teams do win.

10_3/11 + 4_7/22 = 4, ie, 400%.