# Need help settling argument

## Recommended Posts

A friend of mine correctly predicted who would win a football game (college I think so no tie) the other day. He was congratulated by my other friend but another dismissed his prediction as 50/50. An argument ensued as obviously football games themselves are not (necessarily) 50/50 like heads vs tails on a balanced coin is 50/50. My question is: Does my friend who dismissed my other friend's prediction have a point in any way? He did acknowledge that there were odds in play but insisted that "it's still 50/50." Not sure what "it" is then.

Also, I know that if you guess on a multiple choice test (4 choices to a question), you have a 25/75 of getting it right. Is that like what's going on here? Since there are only 2 answers to who will win the game, it's 50/50 of being correct, right?

Edited by Curious523
##### Share on other sites

The total outcomes of the game are: Team A wins or Team B wins.

The total outcomes of a coin toss are: Heads or Tails.

Both outcomes are 50/50.

However, predicting the probability based on events within in the game is nearly limitless, such as: What is the probability the ball will be intercepted? What is the probability the QB will get injured, etc. Each scenario would have a different number of outcomes. You would then take the sum of the probabilities to "predict" your chances.

Really it comes down to "what" you are predicting. In this case it seems you were predicting who would win. Not who would win, BECAUSE of XYZ probabilities.

~EE

Edited by Elite Engineer
##### Share on other sites

So my friend was correct to say it was still 50/50?

##### Share on other sites

So my friend was correct to say it was still 50/50?

Yes. If he was talking only about one team winning, and winning only.

##### Share on other sites

But isn't it that the odds of whatever team you pick has of winning are your odds of you being correct? You may pick a team randomly/guess, but the odds are still not 50/50. And, what if it's "who will win the match between say, the Eagles and the Raiders?"

Edited by Curious523
##### Share on other sites

It is not a 50:50 chance anymore than [win lottery]:[don't win lottery] is a 50:50. It is a process with two outcomes - it they were equally likely then the chances would be 50:50; but the chances are not equal and the odds are not 50:50.

Any final position of two outcome process can be simply described - but that doesn't mean that each position is equally likely. 50:50 is a description of the likelihood of each event and states that out of a 100 trials 50 times one thing happens and 50 times the other happens; thus if the likelihoods are not even then using the term is incorrect.

In essence probability is an estimation of how many times something would happen if the trial was to be repeated a huge number of times - now that is impossible with football matches because each game is different (which is why we love them). You never get half a head and half a tail when you toss a coin - you get a head or a tail; but if you repeat it enough times you get around the same number of heads as tails - 50:50. You could equally say that rolling a d6 gives a chance of getting a 6 or not - two outcomes therefore 50:50; this is clearly nonsense. If we repeat the trial enough times we get a 6 one sixth of the time

##### Share on other sites

Yes. If he was talking only about one team winning, and winning only.

No, Imagine it was a premiership side playing a schools' under 16 side.

The odds would be nothing like 50:50.

In any realistic football game the odds might be pretty close to 50%, but one side is almost certain to be "favourite"

##### Share on other sites

But if you guess randomly, since one team WILL win (and the other lose) and your pick is 50% of the total number of possible outcomes, isn't it 50/50 in that way?

##### Share on other sites

But if you guess randomly, since one team WILL win (and the other lose) and your pick is 50% of the total number of possible outcomes, isn't it 50/50 in that way?

No. Think about it - Brazil vs Steeple Sinderby Wanderers of (NW league 2); do you seriously think that out of a hundred games Brazil would win 50 and Steeple Sinderby win 50? Cos that is what a 50:50 choice is

##### Share on other sites

No. Think about it - Brazil vs Steeple Sinderby Wanderers of (NW league 2); do you seriously think that out of a hundred games Brazil would win 50 and Steeple Sinderby win 50? Cos that is what a 50:50 choice is

But from his POV (a random guess) that knowledge isn't available to him, so if all his picks were random and different, a big enough run should be close to 50/50.

##### Share on other sites

So I see the logic now of why it isn't 50/50. However, what if it were an unbiased bet on one of the teams for one game? In Brazil vs Steeple, you're comparing the statistics of two teams, and then making a decision with fairly reliable insight. If I had no idea about the stats of either team and just placed a bet for one game, would it still be 50/50?

##### Share on other sites

But from his POV (a random guess) that knowledge isn't available to him, so if all his picks were random and different, a big enough run should be close to 50/50.

Ah - I see what you are getting at. Yes; but that is due to your choices being random rather than it being a 50:50. You have a choice with an English coin for it to land edge or face; if you choose at random you have a 50:50 but that is due to your choice being random and you will be right when you choose face and wrong when you choose edge. It is not however a 50:50 when someone has read the question and realised that it is only likely to land face.

If you think it is a 50:50 choice can we play for money?

##### Share on other sites

If you think it is a 50:50 choice can we play for money?

If you think I think that, I'd be happy to sit down to a few hands of poker...

##### Share on other sites

A friend of mine correctly predicted who would win a football game (college I think so no tie) the other day. He was congratulated by my other friend but another dismissed his prediction as 50/50. An argument ensued as obviously football games themselves are not (necessarily) 50/50 like heads vs tails on a balanced coin is 50/50. My question is: Does my friend who dismissed my other friend's prediction have a point in any way? He did acknowledge that there were odds in play but insisted that "it's still 50/50." Not sure what "it" is then.

Also, I know that if you guess on a multiple choice test (4 choices to a question), you have a 25/75 of getting it right. Is that like what's going on here? Since there are only 2 answers to who will win the game, it's 50/50 of being correct, right?

What do you make of the fact that Las Vegas bookmakers set specific odds on each and every sporting contest, and that the odds are very rarely 50-50?

##### Share on other sites

What do you make of the fact that Las Vegas bookmakers set specific odds on each and every sporting contest, and that the odds are very rarely 50-50?

This exactly. There is a whole business built around this.

Though when looking at Vegas odds, you do have to remember that they set the lines so that betting is more or less equal on both sides, not necessarily to make the end result as close to equal. Some fan bases are more likely to bet on their team than be rational about the odds.

##### Share on other sites

Ah - I see what you are getting at. Yes; but that is due to your choices being random rather than it being a 50:50. You have a choice with an English coin for it to land edge or face; if you choose at random you have a 50:50 but that is due to your choice being random and you will be right when you choose face and wrong when you choose edge. It is not however a 50:50 when someone has read the question and realised that it is only likely to land face.

If you think it is a 50:50 choice can we play for money?

So I did a little experiment. I looked up the schedule for the day's baseball games and randomly chose someone to win for 14 games (and I know baseball like I know the mating habits of unicorns so no bias). If you randomly guess on a coin toss each toss, you should be right 50% of the time and wrong the other 50% (or close to that) because it is 50/50. I flipped a coin 98 times with 7 trials of 14 flips as a control; six of the trials ended in 6 heads/tails to 8 and the other was exactly 7 to 7. Now, when I got the results of the baseball games, this distribution did not occur. For this, it was 10 to 4.

So, statistically it seems even guessing isn't 50/50. Also, I'm doing another trial today with the day's football games.

##### Share on other sites

You are conflating two different situations.

Odds given by Vegas of who the winner of a football game is likely to be is based on having information about the contestants. The odds of one team beating another are rarely 50/50.

The other situation is when no one has any information about the two contestants. In this case, the odds of picking the winner will be 50/50.

If there is a football game and you have to pick the winner by pulling their name out of a hat, then the odds of you choosing the winner are 50/50.

If in that same game you have information about the contestants and are allowed to choose who you think will win based on that information, your odds will not be 50/50.

Whether or not the probability of your friend choosing correctly was 50/50, is dependent on whether or not your friend used any information to help make his selection.

Edited by zapatos
##### Share on other sites

Buy the odds of one team winning over another? Doesn't that play into his choice being right or wrong whether anyone knows it or not

##### Share on other sites

I'm not sure I understand your question. Can you please rephrase it?

##### Share on other sites

I mean, even if you don't know what the odds are the odds don't go away, they still affect the likelihood of one team winning (I.e., your prediction being right or wrong). So even if I were to make my prediction based off a coin toss, my ultimately being right or wrong is in the hands of odds which are not 50/50, correct?

##### Share on other sites

I mean, even if you don't know what the odds are the odds don't go away, they still affect the likelihood of one team winning (I.e., your prediction being right or wrong). So even if I were to make my prediction based off a coin toss, my ultimately being right or wrong is in the hands of odds which are not 50/50, correct?

Imagine the case where one team always wins and the other always loses. If you know that, then you can predict the result (and the odds are 1:0).

However, if you don't know that (or, equivalently, pick the winner from a hat) then the chance of getting the right answer is 50%.

##### Share on other sites

No. If you make your choice based on tossing a coin, then you are not using any information about the teams on which to base your decision. Therefore you are just as likely to choose the team that is likely to win as the team that is likely to lose.

Even if the game is over and thus the odds for the winning team are now 100%, if you didn't know which team won and had to choose one based on a coin toss, you would still have a 50% chance of picking the winning (or losing) team. If you DO know which team won, then you would have a 100% chance of choosing the winning team.

What matters is what YOU know, not what someone else knows.

(Cross-posted essentially the same answer as Strange)

Edited by zapatos
##### Share on other sites

This comes down to the fact that (classical) probabilities are about quantifying our knowledge of the world, not something about the world itself.

That appears not to be the case for probability in quantum theory, though.

Although some interpretations disagree with that, e.g.: https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Quantum_information_theories

## Create an account

Register a new account