# I have a real-life Probability problem

• I
• Wi_N
In summary: So for example, if there are 32 wrestlers in a weight class, and you have to exclude one wrestler because they didn't wrestle in a certain weight class, then the odds of that wrestler being drawn in the opposite bracket is 1 in 32. So if you have 8 brackets and you want to exclude a wrestler from a particular bracket, then the odds of that wrestler being drawn in the opposite bracket is 1 in 8. So if there are more wrestlers in one bracket than the other, then the odds of that wrestler being drawn in the opposite bracket is lower. Well sometimes you... you have to be careful about excluding data. So for example, if there are 32 wrestlers in
Wi_N
TL;DR Summary
Regarding match fixing in a wrestling tournament.
I'll try to keep this short. Kazakhstan just hosted the world championship wrestling tournament and I noticed that they did exceptionally well this time around, hometown psychological advantage aside they finished in 2nd place. Last year they finished 13th in Budapest. So immediately I knew something was wrong. And i figured it out. In the brackets draw for the 10 weight classes, they drew 8 straight brackets with no Russian wrestler in them (Russian wrestlers are the best). The last 2 weight classes 97kg and 130kg wouldn't have made a difference for them if a Russian was there or not, I won't go into why that is.

So some simple math, heads or tails i drew the conclusion that the odds of Kazakhstan drawing a bracket TOP or BOTTOM with no Russian in them has to be 1 in 128. Now this is heavily simplified I'm sure as some brackets had more competitors in them. But usually a weight class has about 32-24 wrestlers in them, in an elimination tournament setup. What are the odds of 2 countries not drawing the same bracket 8 times in a row? Please remember there are only 2 Brackets TOP and Bottom.

Wi_N said:
Summary: Regarding match fixing in a wrestling tournament.

I'll try to keep this short. Kazakhstan just hosted the world championship wrestling tournament and I noticed that they did exceptionally well this time around, hometown psychological advantage aside they finished in 2nd place. Last year they finished 13th in Budapest. So immediately I knew something was wrong. And i figured it out. In the brackets draw for the 10 weight classes, they drew 8 straight brackets with no Russian wrestler in them (Russian wrestlers are the best). The last 2 weight classes 97kg and 130kg wouldn't have made a difference for them if a Russian was there or not, I won't go into why that is.

So some simple math, heads or tails i drew the conclusion that the odds of Kazakhstan drawing a bracket TOP or BOTTOM with no Russian in them has to be 1 in 128. Now this is heavily simplified I'm sure as some brackets had more competitors in them. But usually a weight class has about 32-24 wrestlers in them, in an elimination tournament setup. What are the odds of 2 countries not drawing the same bracket 8 times in a row? Please remember there are only 2 Brackets TOP and Bottom.

If you have 10 weight categories, then the odds of Kazakhstan being in the opposite bracket to Russia in 8/10 categories (or more) is 7/128. That's quite low.

This assumes a straight draw without seeding, and one Russian and one Kazakhstani in each category. You need to be careful that there aren't legitimate reasons why the wrestlers got drawn apart: like they were the top two seeds.

You also need to be careful about excluding data for various reasons. It's better to treat this as 8/10 and not treat this as 8/8 with two categories excluded for whatever reason. You can potentially always find reasons to exclude data that contradicts a hypothesis.

WWGD
PeroK said:
If you have 10 weight categories, then the odds of Kazakhstan being in the opposite bracket to Russia in 8/10 categories (or more) is 7/128. That's quite low.

This assumes a straight draw without seeding, and one Russian and one Kazakhstani in each category. You need to be careful that there aren't legitimate reasons why the wrestlers got drawn apart: like they were the top two seeds.

You also need to be careful about excluding data for various reasons. It's better to treat this as 8/10 and not treat this as 8/8 with two categories excluded for whatever reason. You can potentially always find reasons to exclude data that contradicts a hypothesis.

do the number of wrestlers in each weight class and unevenly spread between the two brackets play a role at all? also kazakhstan had no top seeds at all. is it safe to safe some manipulation of the draws occurred?

Wi_N said:
do the number of wrestlers in each weight class and unevenly spread between the two brackets play a role at all?

Not really. There's a 50-50 chance of any two wrestlers being in the same bracket and a 50-50 chance of being in the opposite bracket. That's the fundamental assumption. If there are more wrestlers in one bracket than the other, then you'd have to explain in more detail how the draw is made.

PeroK said:
Not really. There's a 50-50 chance of any two wrestlers being in the same bracket and a 50-50 chance of being in the opposite bracket. That's the fundamental assumption. If there are more wrestlers in one bracket than the other, then you'd have to explain in more detail how the draw is made.

Well sometimes you have a bracket with all 1/32 finale matches (only 16 wrestlers in that bracket) and the other bracket has mix of 1/32 and 1/64 matches. So some wrestlers go an extra match.

Each weightclass has 4 top seeds which garantees them they don't go that extra match but their position in which bracket they will be in is (suppose to be) random. So even if Kazakhstan has top seed together with a Russian or without them their placement in which bracket is suppose to be random.

The real issue in many of these cases is to have some prior hypothesis of what might happen. The logic is this:

Although it's unlikely that Kazakhstan will avoid the Russians, it's not so unlikely that one particular country will be lucky and avoid the Russians. That country may then do better than expected, partly though their lucky draw. But, unless you have a separate reason to believe the draw was fixed in their favour, then this is just a regular part of a random draw.

You might say that Kazakhstan being the home team and getting a lucky draw is a coincidence; and it is. But that itself is not really enough.

Wi_N said:
Each weightclass has 4 top seeds which garantees them they don't go that extra match but their position in which bracket they will be in is (suppose to be) random. So even if Kazakhstan has top seed together with a Russian or without them their placement in which bracket is suppose to be random.

That changes things a lot. If a wrestler is a top-4 seed, then there is only a 1/3 chance of being drawn against the Russian: as a top 4 seed you have only 1/3 of the other seeds in your bracket. If we assume that the Kazakhstani and Russian wrestlers were all top-4 seeds, then there is about a 30% chance of avoiding the Russians in 8/10 brackets.

If some of the Kazakhstanis were seeded and some not, then it will be less than 30%. You'd have to do a specific calculation based on how many were seeded and how many not seeded.

The seeding makes all the difference. It makes it much more likely that two seeded wrestlers will avoid each other.

PeroK said:
The real issue in many of these cases is to have some prior hypothesis of what might happen. The logic is this:

Although it's unlikely that Kazakhstan will avoid the Russians, it's not so unlikely that one particular country will be lucky and avoid the Russians. That country may then do better than expected, partly though their lucky draw. But, unless you have a separate reason to believe the draw was fixed in their favour, then this is just a regular part of a random draw.

You might say that Kazakhstan being the home team and getting a lucky draw is a coincidence; and it is. But that itself is not really enough.
That changes things a lot. If a wrestler is a top-4 seed, then there is only a 1/3 chance of being drawn against the Russian: as a top 4 seed you have only 1/3 of the other seeds in your bracket. If we assume that the Kazakhstani and Russian wrestlers were all top-4 seeds, then there is about a 30% chance of avoiding the Russians in 8/10 brackets.

If some of the Kazakhstanis were seeded and some not, then it will be less than 30%. You'd have to do a specific calculation based on how many were seeded and how many not seeded.

The seeding makes all the difference. It makes it much more likely that two seeded wrestlers will avoid each other.

it is fully possible that all 4 top seeds are in the same bracket. as i said their position in which bracket is random. this should not change anything.

Wi_N said:
it is fully possible that all 4 top seeds are in the same bracket. as i said their position in which bracket is random. this should not change anything.

What's the point of being seeded? Apart from avoiding an extra 1/64 match? I've never heard of a seeding method where the seeds can all meet in the first round - in this case the 1/32 round.

Can you provide data to show a draw where all four seeds are in the same bracket?

There is simply no point in being seeded if the draw is subsequently random and being seeded makes no difference!

PeroK said:
What's the point of being seeded? Apart from avoiding an extra 1/64 match? I've never heard of a seeding method where the seeds can all meet in the first round - in this case the 1/32 round.

Can you provide data to show a draw where all four seeds are in the same bracket?

There is simply no point in being seeded if the draw is subsequently random and being seeded makes no difference!

It's hard to prove cause in most weight classes one of the top seeds didn't show up and were replaced. But Kazakhstan only had 1 top seed so the placements of top seeds should not matter in this case. But let's say top seeds are evenly distributed across the brackets. still that leaves us 7/9 (according to you) or 7/7. But bare in mind when we are dealing with manipulation we can't be completely unbiased either. The match fixing happened in weight classes were it mattered. 57kg didn't cause Kazakhs had a top seed. 97kg and 125kg didn't matter either for them. The rest of the weight classes IT MATTERED and voila they faced no Russians.

edit: in 57kg Kazakhstan top seed was still not in the same bracket as the russian.

(just as a side note: wrestling is 50% strength and conditioning. That extra match matters A LOT.)

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## What is probability?

Probability is a measure of the likelihood that a certain event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

## How do you calculate probability?

To calculate probability, you divide the number of desired outcomes by the total number of possible outcomes. This is known as the probability formula: P(A) = number of desired outcomes / total number of possible outcomes.

## What is the difference between theoretical and experimental probability?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability is based on actual data collected from experiments or observations, and may be different from theoretical probability due to chance or other factors.

## What is the difference between independent and dependent events?

Independent events are events that do not affect each other's probability of occurring. For example, flipping a coin twice is an independent event because the outcome of the first flip does not affect the outcome of the second flip. Dependent events, on the other hand, are events that do affect each other's probability. For example, drawing two cards from a deck without replacement is a dependent event because the probability of drawing the second card is affected by the first card drawn.

## How can probability be applied in real life?

Probability can be applied in various fields such as finance, sports, and medicine. For example, insurance companies use probability to calculate risk and determine insurance premiums. In sports, probability can be used to predict the outcome of a game or the performance of a player. In medicine, probability can be used to assess the effectiveness of a treatment or to predict the likelihood of a disease occurring in a certain population.

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