Charles Bannerman

Back for the moment.

Power failure in main stand has taken commentary off air for now.

Well at least it used to be - before we had imposed on us Sunday afternoons, Sunday lunchtimes, Friday nights, Monday nights, more Tuesday nights, Wednesday nights.....

Today's programme found me sympathising with the Americans as enlightened citizens of the world. Following the Scottish Cup draw, OTB were looking for suggestions of other great blunders and came up with the mixing up of the North and South Korean flags at Hampden. However they couldn't remember at which event this took place - and their short list included the Commonwealth Games! Well, last time I looked, neither Korea was a member of the Commonwealth - unless I've missed Her Majesty receiving a humble bow from the Little Fat Leader with the Silly Haircut. How would I improve it? Take it off the air. Much as it pains me to admit this, I thought that even Traynor's Your Call was a lot better, and actually better still when Chic stood in. With the current format, you'd be better putting a microphone in a pub in front of two random guys shouting at each other. Quite frankly, seven solid hours on a Saturday of nothing but increasingly moribund Scottish football, often on all frequencies, is really too much and the best way to sort that is as suggested.

On the other hand the outcome Celtic have actually had is no more or less likely than all the other possible outcomes. Think of the lottery. With the 49 numbers there were something like 13,982,000 possible permutations of six numbers and 123456 was no more or less probable than any of the others. (With the 59 it's even bigger than that.) Here's hoping not too many Celtic fans read this - it might put them off doing the Lottery!

The trouble there is that if you've got over a million options, as we do here, then by that reckoning they would all be certain to occur over half a million times each! See Sneckboy's explanation.

I'm actually a Chemist (you know what I mean.... if it moves, it's Biology, if it smells it's Chemistry and if it doesn't work - it's Physics!) which is probably worse but also a confirmed technophobe who had thought that the second click would just cancel out the first one

We'll put that one down to my inability to manage the "quote" function on here and I couldn't work out how to quote both Mantis and myself! Similarly I can't work out how to quote the above and also Mantis' suggestion that Pascal's triangle would take hours to work out that far, but based on Sneckboy's table, the largest (11th) Pascal coefficient (for 10 homes and 10 aways) would be in the region of 184,750!

Agreed. The quoted expression comes to the number Mantis has produced. If you have 20 cup draws resulting in home or away, then each and every possible sequence of 20 H/A permutations will have an equal probability of materialising - ie 1/(2 to the power 20). In the case of two homes and 18 aways, there are 190 - ie (20 x 19)/2 - different places in the sequence where you could have your "homes" and hence 190 different versions of it. This will be equivalent to the binomial solution Mantis refers to and I could also take an intuitive guess that the third term in the relevant line of Pascal's Triangle will have the number 190 as its coefficient - ie 190 x (0.5 to the power 18) x (0.5 squared). Sneckboy's table appears to reflect (to 1 dp) the relative values of the Pascal coefficients when expressed as percentages of their total value.

Unfortunately, despite the Scottish Cup sitting on a shelf nearby, that state of affairs is hardly surprising in a school, given the nature of Scottish football. I mean that from two points of view. Firstly, the overall product is poor and pretty insignificant relative to the bigger picture, although not much worse than you should expect in a small population base of 5 million where a hugely disproportionate slice of resources are being hogged by just two clubs. And that brings me on to my second point. In any educational establishment, I could understand if there were reservations about getting too embroiled in a set up which is dominated by two bodies which in turn are front organisations for intolerance and much else that is completely undesirable in Scottish society. One other concern is the extent to which Scottish football tends to be right up its own backside in terms of its delusions of importance. This is possibly epitomised by Stuart and Tam on Off The Ball, which is so parochial that the uninitiated could be pardoned for concluding that the entire world revolves round "Scoa'ish Fitba".

My feelings exactly. The Scottish football establishment allows Celtic and Rangers to do what they like. And I don't just mean Rangers owing millions, going totally bust and a new club of that name, playing in a ground which any decent society would have insisted was sold to honour these debts, being parachuted straight into the Third Division without as much as a selection process. I also agree strongly with what DD said. We are already in a situation where TV requirements are calling the shots to a greater and greater extent and there is no reason why this shouldn't happen more and more. Even in the case of ICT does anyone happen to know how many of the 16/17 pre split home games are 3pm Saturday kick offs? I read a claim the other day that almost a tenth of the world's population claim to be ManU "supporters". The game is going to focus more and more on the very biggest teams and there is going to be an increasing disconnect between the haves, who will be watched in full stadia and also by huge TV audiences as well as followed on social media.... and the have nots who will be watched by smaller and smaller crowds with even those who claim to be their true fans relying more and more on tablets and smart phones to follow progress and watch highlights rather than pay to watch at the ground. Renegade has also just commented on the increasing number of local people becoming fans of ManU, Chelsea etc. Yes, there has possibly been a bit of a recent retreat from Celtic and especially Rangers but rather than redirect towards ICT I fear that many are going the way Renegade suggests.

They actually seem to start them younger than that. One Saturday, pre-match, I parked in a street close to Parkhead, politely declining a shrill offer from a 7 year old to "Mindyurmo'urmisturr?" It still struck me as something of a calculated risk to turn the kind offer down.

It's quite ironic. A couple of weeks ago I attended the draw for five shinty cups with between 13 and 28 entries which were all drawn from the first round stage right through to the semi finals. Using mini shinty balls with numbers painted on them, it all went flawlessly and there was certainly no hint of Newtonmore, having originally come out away to Glenurquhart, then getting Beauly at home in a re-draw. Meanwhile the SFA can't even draw four pairs of balls out of a goldfish bowl properly.

As I think I said on another thread.... is this not in danger of creating an Invernessian version of July 12th or the Dons fans' Gothenburg Syndrome? It's 16 years now - 16 years during which ICT has ousted Celtic from two further cups, won a cup, reached a further final and three further semi-finals, won the First Division (twice), been promoted to the SPL, defeated Celtic in the SPL, finished Top Six, finished Top Three and played in Europe. Sure, that was a great night at Celtic Park, but should it not now be allowed to settle gracefully into a still honourable place in the annals of history?

Definitely a strong contender for Post of the Year!

So where does this leave the conspiracy theory of an Old Firm final which wouldn't be possible in the above scenario? But without crossing the several intervening bridges, I think a Highland Derby semi-final would attract a bit more than 6000 - unless of course these two teams reaching semi-finals has now also ceased to be a novelty. Hampden would clearly be nonsensical, Pittodrie would be a good shout as a venue but not as an accessible one so I would opt for McDiarmid on the grounds that the A9 isn't quite as bad as the A96. On the other hand that 40mph stretch in Badenoch would be a bit of a pain. And yes.... Caley Thistle 5 Ross County 2 in front of 2500 at Grant Street in December 1995. Hat trick for Iain Stewart, star performance from Daisy Ross, debuts for Brian Thomson and Mike Teasdale. That was some afternoon!

I believe that DU v Celtic came out and it went bellyup on the second pairing so they went back to the start. If you're driving from Inverness to Dingwall, break down at Tore and have to get the AA out to do a roadside repair, do you then go back to Inverness and start your journey again?

So who supplied the cheapo balls? I believe Lidl is one of the cup's sponsors

I've now caught up with what happened! Couldn't really have been a much more ironic hitch. I don't think anyone's statistical speculation on the other thread took account of a "burst ball".

So what went wrong? All I have to go on is the OP.

I know what you mean but if ICT fans are going to insist on acquiring their own version of the Dons' Gothenburg Syndrome, might it not be better to adopt May 30th as the "sacred" date?

On the other hand this - and I am prepared to be contradicted if I speculate that the probability of it may be (190/2 to the power 20) - is no less likely than any of the other possible permutations for Celtic or indeed anybody else. If it's anything other than genuine, it must involve a very elaborate and long running conspiracy indeed which has it in for Celtic so much that it is prepared to deny so many lesser supported clubs profitable pay days at Celtic Park in order to achieve its ends!

I make the probability of the draw coming out exactly as quoted (or indeed in any other possible permutation) to be 1/40320, the probability of these four pairings in any order but with the stated home clubs to be 1/1680 and the probability of simply these four pairings to be 1/105. The first one, rendered somewhat academic by the requirement for the ties to emerge in that order, is as CMIB says, 1/8! (factorial 8) or 1/40320, since the probability of the first club is 1/8, of the second 1/7 etc through the entire 8. Of more practical relevance is the second one since all its determining factors relate to who meets whom and where. The probability of any particular team meeting any specified other is 1/7, but home/away arrangements then make that 1/14. Six teams are now left so the probability of another specific pairing becomes 1/5 which goes to 1/10 with ground arrangements. The probabilities of the remaining two ties similarly come out at 1/6 and 1/2. Multiply these together to get the combined probability and it comes out at 1/1680. To get the third one you remove the 1/2 home/away factor from each of the four ties - ie you multiply 1/1680 by "2 to the power 4" (i.e. 16) to get 1/105. In terms of factorials, 40320 is 8! as stated by CMIB. 1680 is 8!/4! (the 4! removes the "order" part of it) while 105 is 8!/(4! x 2 to the power 4). To optimise chances of progress, I would guess that most of the "bigger" clubs would be looking for a home tie, preferably against Morton or, in the possibly unlikely event of them beating Dundee, Dumbarton.)

There are indeed not two but three certainties in life - death, taxes ..... and an grumpy response from Joe Indeed I've sometimes wondered if Joe could possibly be some long lost relation of the late Sir Geoffrey Howe since his rebukes do have a certain flavour of being savaged by a dead sheep!

That seems to be a very reasonable explanation.