Author Topic: Chances Of...  (Read 2318 times)

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Offline Mandoli

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Chances Of...
« on: August 25, 2008, 02:32:05 AM »
Really bored, so I'll start a little discussion before the season begins.

Knowing that a girl/girl team can land in the final three teams, what are the chances of them actually winning their season? All of the teams that have won are either guy/guy or guy/girl. And I believe that the All-Star season had two girl/girl teams in the final three. So it's possible, but it's never happened.

But is a girl/girl team ever going to win the race? And if so, will it be done before CBS stops making seasons?


Offline Slowhatch

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Re: Chances Of...
« Reply #1 on: August 25, 2008, 09:39:03 AM »
 :party: Congrats on the big 1K!  :congrats:

It's an interesting topic because it's hard to apply probability to the race; as Marc/Rovilson pointed out, no matter how good you are, one bad taxi driver and your team is history. All of us can think of at least one good team that was eliminated early, and conversely one mediocre team that went to the final 3 (or even won the race). As for your particular point, I think the BQs were the strongest F/F team ever fielded; I don't hold much hope this season for the Belles and I think the Divorcees will make the top half--but maybe not the final 3.

Offline TARAsia Fan

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Re: Chances Of...
« Reply #2 on: August 25, 2008, 12:30:57 PM »
It's already happened with Zabrina and Joe Jer in the Amazing Race Asia. They were the first all-female team to win any edition of the race so it is possible.

For the US version, the Beauty Queens had the best shot and almost won All-Stars. I do think it's possible. It will have to take some effort, but I do think if the race casts a strong all-female team (and I don't mean physically) like the BQ's, I think it will happen.

The Southern Belles don't look like that team, but you never know.
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Offline apskip

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Re: Chances Of...
« Reply #3 on: August 25, 2008, 01:56:02 PM »
I think that taking a look at probabilities is instructive. I believe that teams with two females are at a disadvantage compared to both straight male/male teams and to male/female teams. I will assign an arbitrary factor to incorporate what the history of the Amazing Race tells us(but the not 0% that actual statistics would use).  Let's assign a probability of them as 50% less than either of the other 2 types. So in AR13 by applying that information mathematically to a 11 team race, we have this for probabilities of winning:

each of two M/M team has a 10% chance of winning
each of seven M/F team has a 10% chance of winning
each of two F/F team has a 5% chance of winning

That feels about right to meas it says that an Amazing Race with two F/F in is has a 10% chance of F/F victory. None has occurred in 12 prior races.

In Amazing Race Asia 3, the statistics will be somewhat different because F/F teams have done much better there for whatever reason. I would say the F/F teams have a probability of only 20% less than either of the other 2 types of winning ARA3 (possibly beacuse their M/M teams are traditionally weaker than those who ran the early U.S. Amazing Races as the casting decisions were made to give the ARA F/F teams a higher chance of succeeding). So by applying that information to a 10 team race, we have this for probabilties of winning:

each of three M/M has a  10.6% chance of winning
each of four M/F teams has a 10.6 % chance of winning
each of three F/F teams has a  8.5% chance of winning

This indicates that an Amazing Race Asia with three F/F teams in it (traditionally there are more than for a regular Amazing Race) has a 25% chance of a F/F victory. One out of two have happened that way.

The mathematics indicated here are not complex. If you have a different set of assumptions on probabilities for each class of team, then you can run an alternative analysis and come to different conclusions.

Offline sunnyca

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Re: Chances Of...
« Reply #4 on: August 25, 2008, 04:10:26 PM »
ok, this may fall under the category of "statistics abuse"  :whips : (not quite the jumpy  i was looking for, but i like this one!!)
but if a F/F team has only a 50% chance of winning as any other combo, then each F only brings to the table a 0.25 chance - so by extension, the male in a M/F team brings the other 0.75?  That seems too high, unless somehow the F/F team is LESS than the sum of its parts, which seems unlikely?  So we must assign them a higher chance. Maybe rather than assigning this in a arbitrary way, we can assign each of the 28 F/F teams (yes, i counted! in case you want to know, here's the breakdown (TAR1 : 3, 2:3, 3:2, 4:2, 5:3, 6;2,7:2, 9:3,10:3, 11:2, 12:3) an "ability" value based on their finishing position, do the same for the other types, normalize to the winning probability of the M/F teams (6/11), and then..oooh oooh my head hurts already!! someone else needs to do this calculation.. help!   :'(


Offline apskip

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Re: Chances Of...
« Reply #5 on: August 25, 2008, 07:25:23 PM »
sunnyca, I am not following your mathematical logic. In order for a F/F to have half the probability of either a M/F or M/M team of winning the race, for 11 teams with 2 F/F teams the proabilities are 10% for each of 9 teams and 5% for each of 2 teams, giving a total probability of 100%. Your numbers do not add up to 100%, which is essential in such an analysis.

Offline sunnyca

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Re: Chances Of...
« Reply #6 on: August 25, 2008, 08:52:23 PM »
sorry! i'm not making myself clear, probably because i'm a bit confused about it myself. but here's another try:
In order for a F/F to have half the probability of either a M/F or M/M team of winning the race
This is the part I was talking about. Instead of assuming that a F/F team has 50% of the probability of a M/F team, is it possible to calculate some sort of ability scale based on the finishing positions of the F/F vs M/F teams? For example, if we assign teams scores in reverse order of finishing position, in TAR12, Ari & Stella (M/F) get 1 while TK & Rach (M/F) get 11 & so on:
Then the 3 F/F teams get 2, 3, 5 for an average of 3.33 and the 7 M/F teams get 1, 4, 6, 7, 8, 10, 11 for an average of 6.7 - so the F/F teams were 6.7/3.3 = 0.5 times as good as the M/F - so in this case your 50% assumption is dead on!
But in TAR11, it was F/F = 9.5, M/F=5.16 and M/M=8, so the all-female teams were way better.
In TAR10, it was F/F 7.3, M/F 7.0, M/M 6.5 -pretty close but the F/F teams did better.
I think if we average over all 12 seasons, this might reflect the "ability" of the F/F teams better. I'm still afraid that the F/F teams might do better overall than the M/F teams, which means they're way underperforming relative to the M/F and M/Ms in terms of actually winning!

 


Offline sunnyca

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Re: Chances Of...
« Reply #7 on: August 26, 2008, 01:14:16 AM »
It's already happened with Zabrina and Joe Jer in the Amazing Race Asia. They were the first all-female team to win any edition of the race so it is possible.

For the US version, the Beauty Queens had the best shot and almost won All-Stars. I do think it's possible. It will have to take some effort, but I do think if the race casts a strong all-female team (and I don't mean physically) like the BQ's, I think it will happen.

The Southern Belles don't look like that team, but you never know.
they have been casting pretty strong f/f teams in the last 3 US races TAR 10, 11, 12 - at least in terms of finishes. the three before that - TAR 6, 7, 9 were pretty dismal (though people seem to think that lena/kristy was robbed).
and the f/f teams in TAR 4 & 5 did pretty well too - i think if Tian had had a better partner, she might have had a very good shot that year - at least made the final 3 for sure - she had to do some of the toughest tasks in india.  and of course the bowling moms were incredible, but did anyone seriously think they would win it all? and there you have the crux of the matter - when you looked at the teams at the beginning of the season (like we are now), did you ever think of any f/f team, ok, this team look like they're pretty strong- they could win this one? other than the BQs (well actually, even them - but BEFORE the race started airing?). for me, the one time i thought that was debbie/bianca in TAR7, especially since they started in Latin America. but i was cruelly let down..

Offline apskip

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Re: Chances Of...
« Reply #8 on: August 26, 2008, 07:35:02 AM »
Last night before RFF ate my post as a result of timing out while I was posting, I completed an anlysis of each Amazing Race according to the sunnyca point system. I normalized the results by dividing to get the average score for F/F teams and for other (M/F and M/M) teams. They showed pretty much what you already know per  the snippets cited by sunnyca above. The only seasons where F/F teams ahead on that score were AR11, AR10, and AR5. AR4 was close but no cigar. Here is the points summary:

AR1 - Emily/Nancy 7, Pat and Brenda 3, Kim and Leslie 2 out of 11
AR2 - Peach/Mary 6, Peggy/claire 3, Deidre/Hilary 1 of 11
AR3 - Heather/Eve 4, Gina/Sylvia 1 of 12
AR4 - Tian/Jaree 7, Monica/Sheree 6 of 12
AR5 - Linda/Karen 8, Kami/Karli 7, Charla/Mirna 6 of 11
AR6 - Lena/Kristy 3, Meredith/Maria 2 of 11
AR7 - Debbie/bianca 3, Megan/Heidi 2 of 11
AR8 - Not Applicable
AR9 - Dani/Danielle 4, Wanda/Desiree 3, Joni/Lisa 2 of 11
AR10 - Dustin/Kandace 10, Lyn/Karlyn 9, Kelli/Jamie 2 of 11
AR11 - Dustin/Kandace 10, Charla/Mirna 9 of 11
AR12 - Shana/Jennifer 5, Marianna/Julia 3, Kate/Pat 2 of 11

Offline Mandoli

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Re: Chances Of...
« Reply #9 on: August 27, 2008, 12:24:40 AM »
As much as the stats are confusing me, those are amazing. Thanks, gang. :)



Offline Rabbit

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Re: Chances Of...
« Reply #10 on: September 03, 2008, 07:26:34 PM »
One thing to keep in mind is not just how many F/F teams there are in the group, but what the OTHER teams consist of. I had a discussion last month on another board concerning the fact that if there is a young M/M team in the competition, it greatly reduces the chance of any other combination of team of winning.

Here is my post from back then:

Season/winners

1. Rob & Brennan
2. Chris & Alex
3. Flo & Zach (young M/M team 4th)
4. Reichen & Chip
5. Chip & Kim (no young M/M team)
6. Freddy & Kendra (only youngish (32yo) M/M team knocked out first eppy)
7. Uchenna & Joyce (young M/M team 5th)
8. Linz family (3 young M 1 young F)
9. BJ & Tyler (2nd place was a M/M team too)
10. James & Tyler
11. Eric & Danielle (no young M/M team)
12. TK & Rachel (no young M/M team)

Out of 12 seasons, 4 seasons did not have any young M/M teams. (i included season 6 as Avi & Joe were knocked out first eppy). So out of 8 seasons with a young M/M team racing, 6 of the 8 had a young M/M team WIN!! That's 75% of the time! The only 2 seasons that had a young M/M racing that didn't go on to win were #3 and #7 with the young M/M teams finishing 4th and 5th respectively. So by that history, if there's a young M/M team on the race, there's a 75% chance a M/M will win and 100% chance they'll end up in at least the Top 5.

AND of all 12 seasons, only TWO of them had winners that were not young. (chip & Kim and Uchenna & joyce).

So here are the odds/stats:

Scenario: young M/M team is competing (8 seasons)

-If you're young M/M, there's a 75% chance you'll win (6/8 seasons)
-If you're a young F/M, there's a 13% chance you'll win (1/8 seasons)
-If you're an older team, there's a 13% chance you'll win (1/8 seasons)


Scenario: NO young M/M team is competing (4 seasons)

-If you're a young F/M, there's a 75% chance you'll win (3/4 seasons)
-If you're an older team, there's a 25% chance you'll win (1/4 seasons)

Overall in 12 seasons:
-young M/M won 50% of the time (6/12)
-young M/F won 33% of the time (4/12)
-older team won 17% of the time (2/12)

making it a whopping 83% chance the winners will be YOUNG!

Offline michael

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Re: Chances Of...
« Reply #11 on: September 03, 2008, 10:35:01 PM »
Chances of an all F/F team winning are 1000000% because I say so!


 

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