27 Oct 2017 19:05:55
The Carabao draw was suspicious, with the big teams kept apart, providing the opportunity of the two big Manchester clubs and London's biggest clubs progressing to the semis. The 5th round also kept the big boys apart. Very odd indeed and the draws were badly organised.

{Ed002's Note - No it wasn’t.

1.) 27 Oct 2017
27 Oct 2017 19:42:44
Seriously Ed? None of the big four met in the last 16 or the last 8, which statistically is no doubt highly unlikely, almost impossible. I will confirm this with my father-in-law who worked for the French Government and OECD, what the chances were.

{Ed002's Note - Sorry, perhaps if you have a child with pre-teen math they will show you that it is not “almost impossible”.}

2.) 27 Oct 2017
27 Oct 2017 22:46:06
Absolute insanity. None of the top four met in the last 16 or 8. Maybe that's why their still in the competition I guess. The odds don't change depending on what the team is. In a draw for the last 16 you have a one in 15 chance of drawing anyone, then the last 8 a one in 7.

3.) 27 Oct 2017
27 Oct 2017 23:00:22
I did the maths. Ed’s right.

4.) 28 Oct 2017
28 Oct 2017 04:59:03
I for one would love to know what RG61's OCD father-in-law has to say.

5.) 28 Oct 2017
28 Oct 2017 06:22:42
Could anyone that made derogatory comments kindly explain the mathematical formula for calculating the odds of none of the top 4 teams clearly kept apart in the quarter final draw from meeting each other in either the last 16 or the last 8 in consecutive draws. Apparently it's child's play! As I expected, it's almost a mathematical impossibility.
Whilst researching my observation, apparently many fans thought the QF draw was fixed to keep the big teams apart and there were articles in national papers making similar comments. The Carabao draws have been a farce, the QF draw being 2 hours late, with no real explanation given.

{Ed001's Note - there is no mathematical formula other than, for each draw, there being a 1 in X amount chance of each team being drawn. X being the amount of teams left to be drawn. You clearly do not understand maths and the nature of chance. It is far from a mathematical impossibility. It is the exact same odds as them being drawn against each other or any other single combination of teams you can get from the draw.

It is a shame that you think national papers are anything to believe in, as they would have to be morons to think that the draw would be fixed to keep them all apart, when it would have made more sense to have at least 2 of them face off, for TV ratings. It also would ensure that at least one got through that way, whereas now they run the risk of them all going out and the ratings being non-existent next round. I guess that went over the head of the dross that passes for journalists these days. Too busy writing clickbait and copying and pasting off the internet to use their brains.}

6.) 28 Oct 2017
28 Oct 2017 07:02:43
Hi Ed, my final comment on the matter and I mean no disrespect, of course there is a mathematical formula. The problem is that it is far from the child's play that everyone is incorrectly stating, with so many combinations and the added complication of two draws. I do not claim to be a mathematical genius and the highest level of maths that I studied was at O Level and I gained an A grade. However, both your method and Sanogo's are not expansive enough.
Keeping the big boys apart provides a better chance of the top teams meeting in the semi's and a big final, rasing the profile of the competition, raising viewing figures and ultimately revenue.
As for the papers they reported fans discontent with the draw.
Finally, even Mourinho made comments about the draw on Sky and he clearly held back on his true thoughts. Two hours late for a supposedly live draw of 8 balls, quite rightly arouses suspicion.

{Ed001's Note - well then you should stop talking and accept the answer, as it is clear the truth is going over your head. You are confusing gambling odds with statistical chance. There is a massive difference. Odds are irrelevant when calculating the chance of a result actually happening. It is the same when you flip a coin, odds will tell you that if you get heads the first time that the second time it is likely to be tails. The truth is that the chances reset each time you do it. It is a 1 in 2 chance each time. You are trying to complicate simple maths, just like teachers do in school.}

7.) 28 Oct 2017
28 Oct 2017 07:34:54
There have been claims that European games were fixed by using hot and cold balls, so it's not impossible to believe the lesser competition of the league cup wouldn't be fixed, but also anything can happen when drawing out of the hat!

8.) 28 Oct 2017
28 Oct 2017 07:46:09
I don't accept the answer as it isn't as simple as you say and comparing it to flipping a two sided coin and criticising maths teachers still fails to convince me otherwise,
There is a complicated mathematical formula that could work out the odds, it is beyond me and clearly beyond any of the people who made comments, as they would have explained it to me opposed to simply being rude.
I remain highly suspicious of the two draws in question, the unexplained two hour delay, was the QF draw even broadcast live? His year's draws have been farcical.

{Ed001's Note - why are you arguing when, by your own admission you do not understand? It is simple and trying to make it complicated because of ignorance is idiotic. The odds are irrelevant, they are nothing to do with the chance of it happening.

For starters it is obvious to anyone that understands mathematics that there is a greater chance of the 'big 4' not being drawn against each other in the previous round as there were 12 other teams in the draw! So the chances of them being drawn against each other are lessened. The odds are for simpletons to bet on, they are totally unrelated to the actual reality of the situation.

Maybe I should explain more simply, though for someone like me, who actually is a genius, it is difficult to understand how something so simple can be difficult, however I will endeavour to explain. In the initial draw there is a 1 in 4 chance of a big 4 club coming out and a 3 in 4 chance of one of the others. If one of the big 4 is drawn that changes the chances as there are now only 3 left and 12 others. So the chance of a big 4 club being drawn next is 1 in 5 (there are 15 in the pot, divided by the 3 big clubs left or you could stick with 3 in 15 if you like), but there is only a 4 in 5 chance of one of the others being drawn. Which is the more likely outcome do you think?

The odds you keep referring to are huge for any specific outcome, they are utterly irrelevant to the chances of it happening. It is millions to one odds against any particular lottery draw outcome but they still happen. It could be the same outcome multiple times in a row and not be against the laws of chance, though the odds would go up of it happening. However the chances of it happening stay the same each time. It is the chance of it happening that matters, not the odds.}

9.) 28 Oct 2017
28 Oct 2017 08:21:01
In short when the physical manifestation of clubs in a draw is the ball the ball has the value of 1. Just because 4 of the balls belong to a 'big club' that doesn't change the value of the ball. The chance would be exactly the same was it palace, West Brom, Newcastle and Bournemouth that made it to the quarters. And the overwhelming point that blows the conspiracy out of the water is like ed pointed out there's a very good chance of the big teams going out considering they play more squad players. Arsenal were only a few mins away from going out at home to Norwich.

10.) 28 Oct 2017
28 Oct 2017 08:46:41
The responses are getting increasingly bizzaire, without actually giving the mathematical formula I require. It's my own fault for requesting this from people that clearly don't have the necessary tools to actually work the odds out.
I will of course obtain the odds from a statistician and I have no doubt whatsoever that they will confirm my own thoughts on the improbability of both draws mentioned.
I would love to know the educational and vocational qualifications of the people that commented and their actual occupations. The true ones that is.

{Ed001's Note - this is truly embarrassing now. I have explained it simply, but it still isn't sinking in. Some people just are beyond help. In case you are struggling to work it out, I am referring to you RG61. I really do not get what bit you are having difficulty with, this is basic, simple, easy maths of the kind we are taught in primary schools.}

11.) 28 Oct 2017
28 Oct 2017 10:34:25
I remember watching the fa cup qf draw once when before the draw took place they actually flashed up the draw results by mistake which they said was from a rehearsal.
Just so happened to match the actual draw exactly?
Who knows and at the end of the day does it really matter as long as the actual games are straight surely that's the main thing.

12.) 28 Oct 2017
28 Oct 2017 11:31:08
I also don't have the ability to gice you the forumla you want, but i bet if you did work it out, the odds for drawing big teams the whole way through and small teams the whole way through would actually cone in very close.

13.) 28 Oct 2017
28 Oct 2017 12:44:33
Good point mate. It would be more unlikely and less probable that in theory the smaller teams all reach the quarters . But in practice smaller teams do better because the big clubs field weaker sides in this comp.

14.) 28 Oct 2017
28 Oct 2017 15:53:12
RG, on a serious note, look up rook polynomial.

I did a similar computational analysis several years ago for a CL draw. Keep in mind that CL draws have some restrictions in terms of winners of a group and runners-up in a group drawing from different pools. You were looking at roughly 6000 possible matches giving you a 1 in 6000 probability (keep in mind that this figure is dynamic after each drawing) .

Without the constraints placed in a carabao cup, the probability exponentially increases, meaning an outcome like the one you've seen becomes more probable.

15.) 28 Oct 2017
28 Oct 2017 16:44:32
RG,
8 balls, 1 in 8 chance of being chosen 4 big teams 4 small
Arsenal got drawn first, leaving 3 'big teams' and 4 'small'
West Ham next, leaving 3 big teams and 3 small
Chelsea next leaving 2 big and 3 small
Bournemouth next leaving 2 big 2 small
Bristol city next leaving 2 big 1 small
United next leaving one of each

The draw may seem fixed but it is basic averages, the stats you are alluding to are events occurring back to back so you would need to work out the probability of the big teams missing out each other in both draws then times them together which would get you the likelihood of that happening. I haven't got the patience to do that for you. So whilst it may seem unlikely it was possible hence the two draws not having big teams drawn against each other.

16.) 28 Oct 2017
28 Oct 2017 17:16:17
Not just possible but very possible . It's certainly not a 1000-1 shot. I thought this would be child's play for an financial consultant or what ever you are. I believe you have a few billionaires on your books. I hope they don't see that your struggling to comprehend very basic maths. It made me chuckle when you asked for people's real jobs. You have to have a good memory to be a good liar RG and you consistently trip your self up.

17.) 28 Oct 2017
28 Oct 2017 18:05:09
. is it odd, yes. Do the circumstances of the delayed draw look strange - yes. Is it a million to one shot - no.

You have less chance getting 4 numbers in the lottery off a single ticket purchase than the cup draw scenario.

Have fun and keep smiling.

18.) 28 Oct 2017
28 Oct 2017 20:42:52
I don’t think he understands statical odds and bookies odds aren’t the same thing
The odds aren’t affected by what the team is
But bookies are ( more money on one side changes their odds )
He’s looking at that as someone who gambles and is used to being presented with the odds can’t seem to grasp the maths required to actually work out the actual mathamatical odds that really matter

The odds of that exact draw where about 5000-1
But that was the odds for any draw.

19.) 28 Oct 2017
28 Oct 2017 21:29:41
That's the thing to ad form into equation is a diffent entity all together. As it stands in a draw every team has a value of 1 to do what he is suggesting is diffent but even for bookies to work out they have to find the value of each team!