Take a coin out of your pocket and throw it in the air. Where does it land? Heads or tails?
Write it down, throw it again and write down the second result.
Then, just for the hell of it, throw it a third time and write that down too.
There are eight possible combinations for what you could be holding in your hand. Heads-heads-heads. Heads-heads-tails. Heads-tails-heads. And so on. Whatever exact sequence you have written down had a one-in-eight chance of occurring.
That’s 12.5%.
Throw the coin another two times, making five in total, and record the full sequence. There are now 32 possible combinations. The particular five-result sequence sitting in front of you had a one-in-32 chance of appearing, or 3.125%.
Now throw it ten times.
Whatever exact sequence you end up with has some pretty big odds attached to it.
The chance of producing that particular sequence was one in 1,024, or roughly 0.098%.
I am not predicting which sequence you will get. That is the whole point.
I am saying that whatever you eventually write on the piece of paper is one of 1,024 possible outcomes.
And why am I talking about this?
Because last night, the Ibrox club was drawn at home to Celtic in the League Cup quarter-final, meaning that, counting the Hampden tie in which they were designated the home side while Ibrox was unavailable, they have now had eleven consecutive home cup draws.
Eleven. The mathematical probability of eleven home outcomes in succession, with the 50-50 home-or-away proposition each time, is:
1 in 2,048.
Or, in percentage terms, approximately 0.0488%.
Now let me say something immediately, because people lose their minds when you discuss probability.
That does not prove anything improper has happened.
It does not prove the draw is fixed. It does not prove somebody has magnets hidden in the balls, Alan Hutton has developed supernatural powers or the SFA has constructed an underground laboratory for producing favourable Ibrox cup draws.
Rare events happen. Statistical outliers exist. A run can be both completely legitimate and extraordinarily unlikely. Those propositions are not contradictory.
But one in 2,048 is extraordinarily unlikely.
If you were in a public place and you and someone else were betting on the flip of a coin the chances that you would win eleven in a row with the same pick would be considered so ludicrous there would be a crowd watching long before someone said you were obviously cheating.
Think about the scale of it.
The Glasgow Royal Concert Hall has roughly 2,000 seats. Imagine being allowed to choose any seat you wanted. Now imagine that somebody else had already written down, before you entered the building, exactly which one you were going to pick.
Possible? Of course. Would you expect it? Damn right you wouldn’t.
And that’s the odds we’re talking about.
That is why I wish people would stop exaggerating this stuff.
Last night I saw one of the Twitter attention-seeking brigade claiming that Ibrox had somehow been drawn at home 42 times in succession. Obviously nonsense. And completely unnecessary nonsense.
Why invent an absurd statistic when the real one is already remarkable enough?
Eleven consecutive home cup draws, including that designated Hampden home fixture, gives you a sequence with the most amazing odds.
You don’t need to embellish that.
Let the number breathe. Let it sit. Let people ponder the fact of it.
The truth of it. The likelihood of it.
Let them think about those odds.
1 in 2,048. A probability score of 0.0488%
The important thing is to understand what probability doesn’t tell us. The next cup draw is not somehow required to send them away. They will again have a 50-50 chance of being at home.
Eleven previous home draws do not make an away tie “due.”
That is the gambler’s fallacy.
Each individual toss of the coin remains independent.
But that, you see, is also what makes it remarkable.
If you have tossed ten heads in succession, the eleventh toss is still 50-50. But if that eleventh toss is another head, you can then look backwards at the completed sequence and say that eleven-head run had odds through the roof.
It is precisely because the coin has no memory that that score is absurdly high.
And if the Ibrox club gets another home cup draw next time? The individual draw will still have been 50-50. But the completed sequence will then be twelve consecutive home draws, with odds of one in 4,096.
Approximately 0.0244%.
The improbability lies in the accumulated sequence.
One home draw: one chance in two. Two consecutive home draws: one chance in four. Three: one chance in eight. Four: one in sixteen.
It is primary-school arithmetic carried far enough to produce a fairly astonishing result.
And what makes this particularly funny is how predictable the outcome had become in the minds of supporters before the draw was even made. People were joking about another Ibrox home tie. People were predicting it. People watching the draw were scrutinising how enthusiastically Alan Hutton stirred the balls.
Then out comes the Ibrox club. Sighs of “of course.” Then Celtic.
Now, I am not going to pretend that somebody failing to swirl plastic balls around a bowl with sufficient vigour amounts to evidence of anything. It doesn’t.
But once a sequence becomes this unusual, people inevitably start watching the mechanics of the draw more closely.
That is human nature.
And it has now reached the point where the Ibrox home draw has almost become its own Scottish football meme.
It is reminiscent of the jokes about the inevitable Ibrox penalty.
There comes a stage where people aren’t even shocked by the outcome anymore. They are waiting for it. When it was “penalty to Ibrox” people were betting on it. Every weekend. And I bet a few of them bought nice things with their winnings over the course of a couple of campaigns.
It’s worth remember that cup ties at Ibrox produce gate money. And right now, with the club having dropped from Europa League contention into the Conference League route, every additional piece of revenue is useful.
Again, that proves absolutely nothing about the draw itself. I’m making no allegations here.
But that ground was half empty yesterday. Their next home gate in the cup needed to be a beauty, one which guaranteed a full house and sky high ticket prices and TV execs fighting for the rights to screen it.
Supporters of other clubs notice these things. Eleven successive home cup draws would be statistically interesting at any football club. When they happen to a club for whom another major home fixture is particularly welcome, people are inevitably going to raise an eyebrow.
That is why the right way to discuss this is not to invent conspiracies.
It is not to invent 42-game sequences.
It is not to shout that mathematics has somehow proven corruption.
The right thing to do is simply put the actual number on the table. The hard facts. The stats.
Eleven consecutive home cup draws.
One chance in 2,048. 0.0488%.
Then let people make of that whatever they wish.
For me, the sheer improbability is interesting enough.
Sometimes statistical runs happen which are so peculiar that you don’t need to attach a sinister explanation to them.
You can simply stand back and admire how spectacularly the coin has continued to land on the same side, and when the Scottish Cup draw eventually comes around, their chance of being drawn at home will once again be exactly what it should be.
Fifty-fifty. But if the ball comes out that way for a twelfth consecutive time, the sequence, the odds, the probability, becomes one in 4,096.
Even at that point I am still not going to accuse anybody of fixing anything.
But come on.
If this was a toss of the coin, people would have been scanning the coin already to find out what the Hell was going on.
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Although it seems a bit out of range for the draw of consecutive home games, I think they’ve just gotten the “luck of the draw”. I actually said to my partner that I hoped we would be drawn with them at Ibrox. We can make a serious dent in their season ambition by knocking them out of the League Cup, and possibly stretching our lead in the league the following weekend. Bring it on. On a side note, it will be interesting to see how the police and the Ibrox club manage this game even with a reduced allocation for Celtic fans. What do you think will happen, James?
I said it was 12 yesterday, it’s 11. Not a deliberate exaggeration, I just thought it was 11 before the draw. Hopefully the law of averages starts levelling it out and they’ve got years of away ties to look forward to.
Between 2015 and 2017 the tribute act had a run of 12 consecutive home draws in cups, another statistical anomaly, coupled with the current bun, I mean run, what’s the chances of that happening to the same club again?
I can’t help but imagine the fallout if these were all away fixtures, they’d be spitting so many feathers Ibrox would look like a drag queens wardrobe.
I don’t think the reason for manipulating this draw will be purely financial in the “establishment” club’s favour. It offers the best possibility of them winning the league cup, the last chance to play Celtic at home before the semi finals and/or final. This has also formed a sequence recently as I think it’s happened three times.
The other oddity about it is that when it’s not deemed necessary to draw Celtic at home, they usually draw the weakest team left in the competition. If you can factor this into the odds of this happening it would only lead to one conclusion.
What makes it even stranger though is that, what ever “establishment” forces made this draw happen, are surely part of the same “establishment” that have come under pressure for their part in the previous cup-tie at Ibrox. You would’ve thought they’d want to avoid a repeat.
As a guy who likes a bet, 11 home ties in a row is pretty suspicious, I wonder if it has happened before for any Scottish club, and if Brattbak is correct that it happened to the tribute act 12 times between 2015-17 it becomes more than suspicious. If there was anything going on I would think it would primarily be for financial reasons, but a bit of help competitively comes in handy.
All I would say is that having watched The Rangers a few times this season on TV, in my opinion they are a very ordinary team, even yesterday St Mirren’s Kamikaze defending helped them big time. Get our act together and we should overcome any advantage the home draw gives them.
I remember back to the decades of the old firm, Celtic and Rangers avoided each other in the draw for the Scottish Cup all the way to the final for many years.
A Scottish Maths Professor was recruited by the media to work out the odds of this happening based on the laws of probability, and it was over 2,000,000 to 1.
Just a thought, maybe the Football authorities in Scotland have decided to try and make things look more competitive, and these continuous home draws are one way of trying to do it.
It may be that it is only a case of an outside bet coming up, but I would bet that if by chance the Ibrox mob get to the semis, their number will come out of the hat 2nd or 4th at Hampden. The odds on that is only even money and anybody who has bet The Rangers getting drawn away in the last 11 draws at even money, is on some losing streak, if he doubed his bet each time he has lost a hell of a lot of money and gamblers anonymous beckons.
Why not take the human factor away altogether?
Do it like the national lottery.
However there is something seriously odd about this sequence of home draws.
The odds of 1024 to 1 are not quite as high as Leicester winning the EPL or any of us winning the lottery. but they’re heading in that direction if it continues.
Just as strange is the usual Ibrox conspiracy theorists (fans and media) who rant at refereeing decisions since VAR was introduced, yet appear to be silent on the issue of continuous home cup draws.
Derren Brown did a show about gambling and probability, where he tossed a coin for 10 heads in a row. To achieve the result it took hours of filming over an entire weekend.
I had to laugh about their fans wanting to lock us out, regardless of how many tickets we get, we are due 45% of gate money.
That doesn’t apply to the League Cup Rouse73, it’s the Scottish Cup only.
We must be entitled to a significant share of gate revenue.
Interesting stuff James but are we really saying the draw has been fixed 12 times in a row. Is this the tie they really want just now? Im not sure.
I also remember the great suspicion over the cup draws when the “old firm” were always kept apart which was to the detriment of all the other clubs. Apparantly this was to give the best possible chance of an “old firm” final or at least one of them in the final. I wonder if anyone ever worked out the odds back then. I remember the great shock when that ended as nobody expected a draw before the final but after that it became fairly common.
Ive looked into this because it is a strange coincidence but hard to get details of the actual draws. The famous Rod Stewart Alan Stubbs one when Rod was drunk comes up in searches and that was a home draw at Ibrox. A fix? not sure about that one.
If it is a fix I would think they would draw them away for games against teams like Annan surely? Of course the home draw against Annan could be a legit draw but the big ones against us are the ones that are fixed. I honestly think at this stage this is the 2nd worst draw they could get. 2nd only to us at home.
Another interesting stat out of all this for me, is that throughout this entire run of “coincidences” they have won zero trophies, so long may it continue.
As per my earlier post, re the every season old firm cup finals, ea Scottish Maths Professor was recruited by the media to work out the odds of this happening based on the laws of probability, and it was over 2,000,000 to 1.
Had a look at this regarding the scottish cup only, there was a period of 20 years between 1970 and 1990 when the 2 glasgow clubs avoided each other apart from the final. They played each other 5 times in the final but never beforehand despite both teams being in the semi final draw together many times. There used to be an inevitability about it with the other 2 teams in the semi draw fully expecting to draw either us or them. The thinking was the SFA wanted us or them, preferably both, in the final to maximise revenue from the punters. It was a massive surprise to everyone even the folk making the draw when we were drawn at home to them in the 4th round in 1990. We got them again the next year at home again in the quarter finals the St Patrick’s day massacre if anyone remembers it?
I think the draw has been fair since then…it seems improbable that both competitions, are currently fixed, it just looks logistically difficult especially if you have a drunk Rod Stewart involved…but who knows?