Maths question of the day

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The "balls" will not be uniformly spherical, or the same weight. The fact that different numbers are carved into them will impact on weight & sphericalicity (made up word). It's negligible, but not exactly random. Go to extremes - one is a pea, one a golf ball, one a tennis ball, one a football, one a medicine ball & one is the moon. No way is that draw random....

But surely that only matters if the person doing the draw knows which ball is which? If I have a tennis ball and a bowling ball to pick from, and one is home and one is away, it's still a 50/50 chance unless I know which is which.
 
But surely that only matters if the person doing the draw knows which ball is which? If I have a tennis ball and a bowling ball to pick from, and one is home and one is away, it's still a 50/50 chance unless I know which is which.
Your hand will "more naturally" select the tennis ball than the pea. You'd have to rattle around in the bag to "find" the pea
 
Your hand will "more naturally" select the tennis ball than the pea. You'd have to rattle around in the bag to "find" the pea

Which still makes no difference, because until the ball is revealed, there's a 50/50 chance we're the pea or the tennis ball. Schrödinger's football club, or something.
 
If we're ball 16, marked on the smallest ball in the bag, the pea, we are more likely to be "hidden in a corner, or in the bottom", more likely to come out last of the 16, more likely to be away, it's not random
 
If we're ball 16, marked on the smallest ball in the bag, the pea, we are more likely to be "hidden in a corner, or in the bottom", more likely to come out last of the 16, more likely to be away, it's not random

That would only matter if you put the same team on the same number and put the same number on the same ball in every draw and used the same balls for every draw (and given the minuscule differences, it would have to be thousands or even millions of draws to make a difference).

Back in reality.. different balls are used and different teams are assigned to different numbers in different draws. That in itself is not random, but it does negate any size/weight/etc difference across draws, because the person making the draw cannot know which team is which from year to year (one year we'll be the pea, and the next a tennis ball).

Unless you're suggesting a conspiracy? Which I'd be fully on board with if we'd got away so many consecutive away draws 😂)
 
That would only matter if you put the same team on the same number and put the same number on the same ball in every draw and used the same balls for every draw (and given the minuscule differences, it would have to be thousands or even millions of draws to make a difference).

Back in reality.. different balls are used and different teams are assigned to different numbers in different draws. That in itself is not random, but it does negate any size/weight/etc difference across draws, because the person making the draw cannot know which team is which from year to year (one year we'll be the pea, and the next a tennis ball).

Unless you're suggesting a conspiracy? Which I'd be fully on board with if we'd got away so many consecutive away draws 😂)
I'm making a much simpler point. Put an even number of balls in a bag, bowl or box. Take them out of the bag, bowl, box one at a time. Call the first one out Home, the second Away, etc. The chance of any single ball being Home or Away is likely to be very very close to being evens, 50%, a half. But it is virtually impossible to design a PERFECTLY random process, coin toss, dice, balls whatever. Because the dice, coin, balls will not be exactly uniform. There will be a bias.
 
The "balls" will not be uniformly spherical, or the same weight. The fact that different numbers are carved into them will impact on weight & sphericalicity (made up word). It's negligible, but not exactly random. Go to extremes - one is a pea, one a golf ball, one a tennis ball, one a football, one a medicine ball & one is the moon. No way is that draw random....

Taking it back to the balls in the bag. Isn't this experimental (as opposed to theoretical) probability? If it is then it's what practically happens which matters.

As I understand it you'd have to carry out the experiment with an H0, H1, and a significance level, but I'd've thought for all practical purposes the balls are equally likely.
 
I'm making a much simpler point. Put an even number of balls in a bag, bowl or box. Take them out of the bag, bowl, box one at a time. Call the first one out Home, the second Away, etc. The chance of any single ball being Home or Away is likely to be very very close to being evens, 50%, a half. But it is virtually impossible to design a PERFECTLY random process, coin toss, dice, balls whatever. Because the dice, coin, balls will not be exactly uniform. There will be a bias.
I did notice for yesterday's draw the first few ties were numbers close to each other, maybe they didn't shake things up enough!
 
Taking it back to the balls in the bag. Isn't this experimental (as opposed to theoretical) probability? If it is then it's what practically happens which matters.

As I understand it you'd have to carry out the experiment with an H0, H1, and a significance level, but I'd've thought for all practical purposes the balls are equally likely.
Yes. You're right (in my view). But, (repeating) I've got two Degrees in Statistics, why would I be remotely interested in so called "practical purposes" (winking smiley face thing). I've not come on this forum, where I run a parody football firm, for anything in the same County as "practical".
Jog on.....
 
Yes. You're right (in my view). But, (repeating) I've got two Degrees in Statistics, why would I be remotely interested in so called "practical purposes" (winking smiley face thing). I've not come on this forum, where I run a parody football firm, for anything in the same County as "practical".
Jog on.....

Ok. I asked because I thought there was more to it than that.

There are quite a few really interesting probability and statistical "paradoxes", I thought I might be about to learn a new one.

Back to getting my head round Newcomb ;-)
 
Ok. I asked because I thought there was more to it than that.

There are quite a few really interesting probability and statistical "paradoxes", I thought I might be about to learn a new one.
I've forgotten more than I ever knew. I was very much an Applied Statistician. And increasingly in my "job" became a Social Statistician (as in not an Economic Statistician). But, I do think you're right. Given the difficulties of designing something truly random, you have to have something which for all practical purposes is as close to random as you can get. Computerised Random Number generation algorithms are often used in "modern life"
 
Did I mention I've got two Degrees in Statistics?
Drawing balls from a bag is not truly random, only quasi random. The chances of a home draw in any round are not exactly evens.....
Sorry to disappoint
There’s a 50/50 chance one of your degrees were wrong ;)
Yes. You're right (in my view).
Erm, statistically int one degree in statistics good enough? ;)
 

There’s a 50/50 chance one of your degrees were wrong ;)

Erm, statistically int one degree in statistics good enough? ;)
I have a reputation for telling tall tales. I studied in a building opposite the Old Queen's Head "in Pond St". I had a disagreement with a lecturer about a Standard Deviation interpretation. He threatened to throw me out of the third floor window. He was a wrestler in his spare time. It was a Polytechnic. That is all true. Great times......
 
I have a reputation for telling tall tales. I studied in a building opposite the Old Queen's Head "in Pond St". I had a disagreement with a lecturer about a Standard Deviation interpretation. He threatened to throw me out of the third floor window. He was a wrestler in his spare time. It was a Polytechnic. That is all true. Great times......
I went ‘t same college, Adsets building. I was on next to the top floor doing HND in mechanical engineering. Around 1975.
 
I went ‘t same college, Adsets building. I was on next to the top floor doing hand in mechanical engineering. Around 1975.
Sheffield City Polytechnic. But, I was in Heriot House. The Old Queen's Head was literally 20 yards across the street. (I think it's now called Aspect House)
 
I've forgotten more than I ever knew. I was very much an Applied Statistician. And increasingly in my "job" became a Social Statistician (as in not an Economic Statistician). But, I do think you're right. Given the difficulties of designing something truly random, you have to have something which for all practical purposes is as close to random as you can get. Computerised Random Number generation algorithms are often used in "modern life"
I get that size, weight, texture, temperature, etc of the balls and the influencing factors of the people picking the home and away teams will effect, to a degree, which ball is picked. But if the ball numbers are allocated to the clubs truly randomly before each and every draw then the odds will be back to evens for a club to be allocated away or at home on every draw?
 
I get that size, weight, texture, temperature, etc of the balls and the influencing factors of the people picking the home and away teams will effect, to a degree, which ball is picked. But if the ball numbers are allocated to the clubs truly randomly before each and every draw then the odds will be back to evens for a club to away or at home on every draw?
OK. Run me through the perfectly random process of allocating ball numbers to clubs mate. You know, given the essentially impossible task of designing perfectly random processes.
 
OK. Run me through the perfectly random process of allocating ball numbers to clubs mate. You know, given the essentially impossible task of designing perfectly random processes.
That does create a new challenge. But it does eliminate all the issues you raised. Using the exact time the previous tie finished to chronologically number the teams could be an option?
 
That does create a new challenge. But it does eliminate all the issues you raised. Using the exact time the previous tie finished to chronologically number the teams could be an option?
Good idea. How are you measuring exact time, exactly? First peep of the whistle? Last peep? Perfection & exactness are the issues here. The difficulty is in order to get around the "fact" that drawing balls out of a bag is not perfectly random, you layer on more & more slightly inexact & slightly imperfect processes.
 
Good idea. How are you measuring exact time, exactly? First peep of the whistle? Last peep? Perfection & exactness are the issues here. The difficulty is in order to get around the "fact" that drawing balls out of a bag is not perfectly random, you layer on more & more slightly inexact & slightly imperfect processes.

I don't get how accurately/inaccurately allocating the balls to the clubs in this way would influence the "randomness" of the draw. The accuracy is not relevant, only the fact it generates differing numbers?
 
I had the choice of statistics or mechanics and I foolishly chose mechanics, consequently I am unable to answer this question. But if anyone wants to know about firing cannons into the air and knowing where the ball will land I am your man.
 

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