How many times have wild card teams won BBA championship?

[allenciox]

I don't think I have seen anybody cover the question stated, but as we move to the end of the season, a lot more of us are in wild card position than division champion. In current MLB baseball, there are 30 teams, 10 make the playoffs (33.3%) and 4 of those (40% of playoff teams) are wild card teams.

So what about BBA? Well, we have 32 teams, 12 make the playoffs (37.5%) and 8 of those (67% of playoff teams) are wild card teams.

So the majority of our teams that are in the postseason are wild card teams. So a natural question to ask is how many times has a wild card team run the gauntlet to win the BBA championship?

So, as in many questions, statsplus is the place to go for this info. Unfortunately, it only goes back to 2021 in terms of showing the complete playoff record (before that it just shows the overall winner). But that still gives us 25 years of data.

So, if it is entirely random (i.e. 1/12 chance for every team) who wins the ultimate crown, then you would expect 67% of the time that it would be won by a wild card team. But we know it is not, as every wild card team has to play an additional series. If we assume that team quality is evenly distributed among all playoff teams (our null hypothesis), then we would expect that every team would have an equal chance from the second round on (i.e. 1/8 for each team, 1/2 of which are wild card teams, so 50% of the time going to the wild card team).

So which years in this 25 year period did wild card teams win "it all"? These years: 2023-2024, 2026, 2032-2033, 2038-2041, 2045: ten times in total, but not at all equally distributed: in fact, four of those ten times are in a single four year period! (Another question would be to see if this streak is happenstance or there might be more to it).

So 40% of the time. Well, although that is less than 50% it is not different enough from 50% (in only 25 trials) to disprove our null hypothesis (a simple binomial can be computed for that; the exercise is left to reader). But assuming this 40% holds up over a longer period of time, this would imply:

Each of the four division winners has approximately a 15% chance to win the championship, while each of the eight wild card teams has to content itself with about a 5% chance. Still, it is better by far than a team that doesn't make the playoffs!

[shoeless.db]

40% of the time, they win every time.

[allenciox]

So an example of a binomial would be: If I flip a fair coin X number of times, what is the probability that it will come up heads Y or less times?

Here is a site that has a binomial calculator: https://stattrek.com/online-calculator/binomial.aspx

In this case, you can plug in .5 as the event probability, 25 as the number of trials, and 10 as number of successes. You will then see, in the line: "Cumulative probability: P(X <= x)" is .212, or a 21.2% chance that you would get 10 or less times if they were truly equal teams. That is a pretty common occurrence, so we cannot reject the null hypothesis.

[Dington]

What is the probability of YS9 winning?

[allenciox]

empirically, p(YS9 winning championship) is approximately 0.

[Dington]

empirically, p(YS9 winning championship) is approximately 0.

We all the know the absolute chance of Ron winning will always be zero, but what do statistics say are the chances of Ron not coming out of playoffs without a championship throughout all these years given every team in playoffs has same chance of winning?

[RonCo]

Heh ...

Here's a table with data from 1995-2044...in other words, 278 teams had won their division and all went to the playoffs. 278 teams came in second, but only 146 qualified for the post season (gained a Wild Card).

Position	Teams	Playoffs	Champions	Champ/PO
1st	278	278	37	13.3%
2nd	278	146	8	5.5%
3rd	277	45	2	4.4%
4th	279	9	1	11.1%
5th	74	1		0.0%
6th	44
7th	44
8th	20
Total	1294	479	48

[RonCo]

Hmmmm.... I need to fix that a bit. Just a sec.

[aaronweiner]

The 5th place one was last year of course. Exceedingly rare.

[RonCo]

Fixed.

Position	Teams	Playoffs	Champions	Champ/PO
1st	278	278	38	13.7%
2nd	278	146	8	5.5%
3rd	277	45	3	6.7%
4th	279	9	1	11.1%
5th	74	1		0.0%
6th	44
7th	44
8th	20
Total	1294	479	50	10.4%

[RonCo]

The 5th place one was last year of course. Exceedingly rare.

I don't have last year's data in it. The one 5th place appearance was Chicago in 2042. So it's happened twice in four years. Sign of Heartland dominance ... I should note that in 2042, the last team out was Nashville, another Heartland team.

[RonCo]

Part of the "issue" with the BBA data above is that we have not always had the same number of teams and byes.

Each of the four division winners has approximately a 15% chance to win the championship, while each of the eight wild card teams has to content itself with about a 5% chance. Still, it is better by far than a team that doesn't make the playoffs!

I always love those kinds of questions. Another way of confirming it is that it's pretty much given that Las Vegas is going to tab the "best" teams with about 3:1 odds, swayed a little here or there. The big advantage to being a division winner is that you don't have to go through one of the 50/50 gates. The other advantage, of course, is that you are theoretically a better team, hence have a few % better chance of winning, and you gain the home field advantage--which is worth a few more percentage points.

[allenciox]

empirically, p(YS9 winning championship) is approximately 0.

We all the know the absolute chance of Ron winning will always be zero, but what do statistics say are the chances of Ron not coming out of playoffs without a championship throughout all these years given every team in playoffs has same chance of winning?

That's a great question! So, I just took a look at YS9 history. They have been in the playoffs 21 out of the last 30 seasons: fourteen of those as division champions. For the fourteen as division champions, their probability of winning any particular one would be .125 (1/8). So the probability of no wins in those fourteen years is .875^14 = .1542. The probability of no wins in the seven of those as wild cards would be .9375^7=.6365. Since those are disjoint events you can just multiply those probabilities to get the total probability, .1542*.6365=.098 (9.8%) --- so really not as odd as one might think.

[allenciox]

So my last response had to do with Dington's specific assumption about every team having the same chance of winning. However, if you do assume that long-term will show the same pattern as the last twenty-five years (and I think that is a pretty reasonable hypothesis), then the odds of any division champion winning goes up to .15 and wild card team down to .05. In that case, the probability of no wins in those 14 years as division champion is .85^14=.1028, the probability of no wins in those 7 wild card teams changes to .95^7=.6983, and the joint probability is then .1028*.6983=.0718 (7.18%). So it does change it some but it is still not extreme.

[RonCo]

I wrote a piece in the 2045 media guide that muses with numbers on that subject.

[JimBob2232]

I feel like i remember doing it once.

[CTBrewCrew]

40% of the time, they win every time.

that's the smell of desire baby....