Friday, March 20, 2020

Coronavirus - the basic maths

This is a distribution known as the Normal Curve.
It has other names and is also known as a Bell Curve (because it looks like a bell) or Maxwell Distribution. Both ends tail off into infinity but never actually reach the zero baseline I have deliberately chosen a diagram with no numbers on it because the numbers do not matter very much at this stage. It is used to model all sorts of things. The peak of the curve often represents the mean of whatever data is collected (adult height or weight, perhaps). This curve also models the number of people infected during an epidemic at any given point if left unchecked. To start with the numbers infected are very low and do not increase much or very quickly, then it grows rapidly and then it peters out. The reasons for this are fairly obvious when it comes down to it. Just imagine 6 people. To start with 1 of them will have the virus and there are 5 possible targets for infection. Once one person is infected 2 have the virus with new 4 targets, then 3 and 3, then 4 and 2, then 5 and 1, then 6 and 0. Nobody left to infect that hasn’t had it and those who have had it will now have natural anti-bodies to protect them against re-infection. However in the UK we have around 65m people not 6. The same logic applies but the numbers are far bigger. Once 1 person infects another there are 2 people spreading the disease. Those 2 might infect another 2. Now we have 4 people. Those 4 people infect another 4 making 8. Those 8 infect another 8 and it is now 16 and so on. So the number of new infections with each passing day is 1, 2, 4, 8, 16… Before long the number of new cases is huge. This is known as exponential growth and an exponential curve looks like this:
This next bit is quite technical. I’ll mention it because it fundamentally underpins all that follows. After which I will abbreviate massively so skip to that bit if you don’t understand what follows. The curve above is based on 2. 2 is a real number. It’s just 2. Like 2 legs or eyes or feet. 2. There is another number a little greater than 2 but less than 3. It is an irrational number meaning it can never be written down with exact accuracy (just like π or √2) and so has a symbol: e. If I replace 2 with e in the graph above the curve looks much the same but, crucially, the gradient of the curve is now also exactly the same as the value of the function (equation) that produces it.
This can be used to model all sorts of naturally occurring phenemona such as radioactive decay and much else besides. Don’t worry too much about e. Suffice it to say e is approximately 2.72. What matters here is the shape of the curve. It represents something that grows ever more quickly. It can also be used to model the spread of infection during an epidemic. There is family of curves which are all vaguely similar and are all known collectively as exponential functions. The exponential function, essentially the Daddy of them all, as already mentioned is y = e^x. The general form for all of the exponential functions is y = ae^bx + c where a, b and c are the particular constants (i.e. just numbers like 2, e, 9, 131, π…) which define the particular curve and x represents the time variable. In terms of viral spread a, b and c are unique to each virus. If you like they are the control factors. One of them is rate of contagion (just how contagious is it?), another is the number of interactions between people (which is why we are being urged to self-isolate) and another is the number of people who already have it. Nothing to be done about the passage of time, nothing to be done about those who already have it and nothing to be done to stop the exponential growth but it can be slowed down if we reduce the number of interactions (hence self-isolation) r the likelihood of it spreading (hence the hand washing). We are currently witnessing an absolutely classical example of exponential growth:
There you go. That’s where we are. I could model the curves and deduce the exact equation that defines them but that’s a level of detail unnecessary. The plan recently announced by our government was to suppress the rate of spread, move the peak forward as far as possible and so allow our medical capacity some chance of coping and not being completely overwhelmed. They used this graph to illustrate it.
Finally there is talk of “acting at the right time” and “maximising the effect” etc. This is mathematically incoherent. The mathematics of maximisation is known as calculus and you need to do something called differerentiation. This works well with some curves with quadratics being the easiest example to understand (you can see where the maximum is immediately).
…but if you differentiate an exponential function you just get another exponential function. There is no maximum anywhere on the curve. There is no exponential part of the curve because it is all exponential. The best way make a difference - to slow it down - is to act early. That’s it. I hope that this helps you to understand the underlying mathematics at least a little better than you did before.     And where we are headed is not good.

Saturday, November 16, 2019

A Nation Rejoices!!

vRogcast2 is back!

Monday, May 07, 2018

Billy Holmes RIP

I’ve just had the almost perfect Janner Bank Holiday Monday. Took Mrs W out to Lopwell Dam, had a pint in Milton Combe’s Who’d’ve’thought It and then back home for a mini-pubcrawl heading towards fish and chips on The Barbican and a pint in The Dolphin to cap it all off.

Only to arrive and see this:

At which point the memories came flooding back. My first paid job was working behind the bar at the George Hotel at Roborough which was, back then, on the very northern-most edge, perhaps a little beyond, of the city of Plymouth. I have a story or two to tell about that but they are for another day. 1983 was a long time ago now but I started at The George on my 18th birthday. I think I got paid about £20 for 3 nights. Getting there was a nuisance, Dad used to drive me, and it wasn’t long before he found me another job, £30 for 3 nights, at The Dolphin on Plymouth’s Barbican which was, crucially, within walking distance.

The difference between the two pubs could not have been starker. The George was the sort of pub where The Hunt used to meet and I was only allowed to work in the Lounge; The Dolphin was at the heart of Plymouth’s fishing community and only had the one bar. One had a grand piano in the corner the other had a stand-up piano…

At The George I had to wear a uniform of black trousers and a white shirt behind the bar so for my first night at The Dolphin I wore the same. My first customer was my Dad. “A bottle of Guinness, off the shelf, please” quoth he. At which point I made a legendary start.

At The George there was cap remover with a trap below. You inserted the cap of the bottle cracked it forwards, the cap would fall into a catcher, you poured the beer. Job done. Crucially you cracked the bottle towards you. At The Dolphin there was a similar arrangement but different. You cracked the bottle away from you. I did not know this. So there I am trying to get the bottle into the opener. It doesn’t go as I expect it to. All the time I am shaking it up a bit more. Bottled Guinness (can you even still buy proper bottled Guinness?) isn’t like other drinks…. Eventually I got the bottle into the cap remover kind of like the only way it would go (so far as I knew) and cracked the cap off at which point I got a faceful of bottled Guinness as it exploded out of the bottle and drenched me. My white shirt was white no more.

Seconds into my first ever shift I had made a complete half-arse of myself. A fella, coincidentally, named Roger, who was in the pub at the time ran a Barbican T-Shirt Shop and he kitted me out for the rest of evening in a black T-shirt… That behind me I worked there for about 4 years, off and on. I was a student, mostly, at the time and so worked there when I came back and their usual staff, also students went away. But what times…

The Barbican then wasn’t what it now. All the things that are there now were still there then but it was the centre of the fishing community. This has all changed and Southside Street got much less smellier since the Fish Market moved across the harbour to Coxside. But the things that went on in The Dolphin: the fish trading; proper big bastard crabs running around the bar… spoofing, Criminal underlife that seemed to live there: Mike Ede, Hong Kong John, Gambo, Jack Laing (I think they are all dead now – bloody hope so (no offence intended)). Unbelievable. And over it all reigned first Betty, long since gone, and then Billy Holmes.

Billy was a true gent. As Cork Irish as they come and all but incomprehensible for much of the time. I remember him swearing at me as a callow youth who didn’t share his weight of a 22 gallon barrel as we lifted it onto the stillage at the back of the bar. I remember him being as chuffed as anybody ever was at meeting Noel Redding, the bass player in the Jimi Hendrix Experience, on one of his trips back to Ireland. I remember a bloke not of my city who gave far more to it than most people ever will. Billy Holmes was a legend amongst legends and an absolute gent with it. I’ll miss him dearly.

The Barbican will never be the same again.

Wednesday, October 25, 2017



Monday, April 17, 2017

Promotion 2017

As I write this I have to admit to having partaken in alcohol. Not that excessively, ‘tis true. I have to be up at stupid o’clock tomorrow so had to cut the evening short.

“Why might that be?” you may well ask.

Today Argyle sealed a promotion by way of a 6-1 thumping of Newport County and to honest we might have scored 10. I suppose a last minute winner might be better but this is pretty good.
Glory days don’t often come along to Argyle but today was definitely one of them. I’ve been going week in week out ever since I was a kid which is over 40 years now and I was there when we went up v Colchester in ’75, at Wembley in ’96, versus QPR in 2004 and today. In all that time only 4 promotions (there was a couple of others in 1986 and 2002 but I couldn’t make it to those games).
That is only the start of it though. As a club we’ve gone as close to disappearing as any and hung on. We’ve endured 6 years in the basement division  and only hung in there by the skin of our teeth on two occasions. Two years ago we failed in the play-offs. Last year we failed at Wembley. There’s been nothing to celebrate in any of those years other than our mere continuance and the disappointment has been crushing with last year’s Wembley capitulation a particularly gutless low despite the various calamities that had befallen us previously.

And now this…

The tsunami of joy, of celebration, of relief was like a force of nature at Home Park today: tangible; irrepressible. There was a vibrancy, an energy that simply must not be allowed to dissipate. We must build on this. It cannot be seen as an end to itself because, magnificent though it was, it is only a step on the journey.

But I don’t want to speculate about the future; I want to look back. Today’s team, management and owners will bask in the glory but that glory was only possible due to a level of dedication and sacrifice from a whole host of people: those who set up the Argyle Fans’ Trust with the very real intention of starting again from scratch somehow; the staff who went for months upaid; players (even if they were crap – and most of them were) who signed for us despite not knowing if they’d be paid or not – players who signed for us when nobody else would; Peter Reid for paying a heating bill; Carl Fletcher for keeping us up when all seemed lost; John Sheridan likewise; Vivien Pengelly (leader of Plymouth City Council at the time) for financing James Brent’s rescue package that allowed us to escape administration; everybody who put money into the club by chucking coins in buckets, buying season tickets when the next season wasn’t even likely to happen or buying merchandise they just didn’t need… Without them there would have been no Derek Adams; no glorious 6-1 promotion game; arguably no anything.

Argyle should never have been in this division and it should never have taken us 6 years to get out of it. Let us never forget how we ended up in “Division 4”; let us never take our eye off the ball and let us never allow it to happen again.

Today has been all kinds of wonderful and we’ve quite rightly celebrated the living daylights out of it but we must never, ever stoop so low again. The club, the fans, the city all deserve better than this and we should loudly, incessantly demand better.

No ifs, no buts, no excuses… this is not as good as it gets. All this is is a necessary stage that has to be gone through. We are nowhere near our glass ceiling, if such a thing exists at all; we must press on.

Greater glory awaits.

Sunday, April 09, 2017

How Far Do We Want To Go?

On the face of it it’s a silly question. Only one answer. “All the way to the very top.” And that has to be the way. If a football club isn’t striving to be the very best that it can be, and that means better than anybody else, then it isn’t doing its job. Equally it is fair to say that Argyle are absolutely light years away from that: currently we’re not even the best team in League 2. So that destination, if we can park the obvious fact that it is more or less completely unattainable for a moment or two, seems so distant that it may as well not exist.

That’s no excuse though. A journey of a thousand miles begins with a single step. Rome wasn’t built in a day. Continuous improvement. Marginal gains. That’s the very least we can expect and in wilder flights of fancy we could see a whole paradigm shift such as that currently enjoyed by Bournemouth and, to a lesser extent Swansea and Burnley, as they ply their trade in what we are now supposed to call the English Premier League (EPL). After all if a club isn’t trying to win every game, every week and every trophy it enters then it should be. Whoever it is. That’s what it is for. What point is there being in a competition if you do not compete to win?

So let us assume, oh joy of all joys!, that that happens and a resurgent Argyle resurgams its way to hitherto unanticipated glory and that elusive EPL goal is scored and that the pipe dream of Argyle competing and winning at the very top becomes as common place as the old primula vulgaris is in our gardens, hedgerows and verges right now.

Consider the steps already taken, consider Rome rapidly built, consider further improvement unnecessary and consider gains no longer marginal but seismic; consider the paradigm to have permanently shifted.

Week after week Manchesters United and City, Arsenal, Chelsea, Liverpool and Spurs arrive in town fearing for their once great reputations. Week after week we spank ‘em all and their worst fears are proven to be well-founded. Imagine that! (If you can.)

It’d be great, wouldn’t it! It’s exactly what I have hoped for for most of my life. The whole world would marvel and there’d be articles in Le Monde, the NYT, La Republicca and El Pais asking how we had done it and could it happen there. There’d be endless segues on Sky Sports News. We’d be first up on Match Of The Day every week. Hell! We’d be on MotD every week!! Think on that for a moment.

The question I am asking is: do we really want that? To which you might respond “why wouldn’t we?”

Well there’s a few reasons…

Difficult though it is to travel all over the country from Plymouth to wherever at least we can be fairly sure the game will take place at 3pm on a Saturday or 1945 on a Tuesday. That’d be gone if we were in the EPL with their massively variable kick-off times. Travelling to away games is difficult enough now but it would be worse once the paradigm has shifted.

Programmes. There’s another thing. £3 each they are now. Well not in the EPL they aren’t. More like £5 is common. That said we don’t have to buy them. Beer? £5/pint. Again we don’t have to buy it. Likewise the more expensive food on offer.

Entry costs. This is where it starts to get really worrying. £20 to get in could become £50. Can I afford that? No. My season ticket currently around £300 might be nearly £1000. Can I afford that? No. Putting it quite simply following Argyle would be too expensive for me. I wouldn’t be able to go. I wouldn’t be able to share in the moments I have spent almost 50 years yearning hopefully for and my seat would be sold to somebody else. Somebody who could afford it. Probably somebody with rather less time and emotion invested into the club’s fortunes than me. I’d be an Armchair Supporter no more likely to see my team play in the flesh than the Plymouth Reds/Blues/Gooners/Spurs/’Gers/Celts etc are. It’d be the Saturday lunchtime/Sunday afternoon trip to a pub with Sky/BT Sports for me. That’d be as good as it got.

And let’s be vaguely realistic here. Argyle wouldn’t be sweeping away all opposition before them in the EPL (Argyle in the EPL realistic? Just play along, please, if you can.) They’d be scrapping like dogs to avoid relegation. The title would still be impossibly distant. All we’d have to celebrate is getting the 40 or so points needed to stay up and having half an eye on the European qualification places. That’d be it and where’s the glory, where’s the excitement and where’s the fun in that? We’d be a  West Ham United, Stoke City or WBA – and, let’s face it, who aspires to being one of them?
So maybe, just maybe, striving for success for its own sake, striving for goal-driven success is a foolish aspiration. Maybe, just maybe, the true joy comes not from the destination but from the journey itself. We should be offering 100% balls-out commitment to get there in every aspect of everything that we do.

We should never be accepting of stasis and mediocrity because that way we will inevitably fall back, in comparison to others, and eventually know more dark days than sunny ones. We should celebrate the Good Days like billy-o when they come and demand rather more of them because we’ve been starved of them for far too long now.

So back to the original question “how far do we want to go?” the answer is “we’re going to try our damnedest to go all the way, baby!” and there is no need to add the caveats. Just let them rest undefined and unconsidered like the proverbial elephant in the sitting room.

Saturday, March 04, 2017

"If it wasn't for the 10 point deduction we wouldn't have got relegated."

This is always the mantra for fans of teams relegated as a result of administration. And it is true as far as it goes; it was seemingly true for argyle back along. Sadly it is a myth. It is self-delusion. The penalty is set so that it pretty much guarantees relegation for anybody “unlucky” enough to go into admin so admin leading to relegation is hardly a matter of chance more one of design.

And the finger of blame implicit in the statement is pointing in entirely the wrong direction. Clubs, from the boardroom all the way to the terraces, should man up and accept that the reasons they went into admin were avoidable and that it was a potent cocktail of bungling incompetence, Mikawberish hope, willful negligence and/or deliberate strategy that was responsible and “luck” had nothing to do with it.

The exact methodology involved will vary from case to case but essentially they all boil down to the same thing: expenditure has grossly exceded income leading to a build-up of debt which eventually can no longer be supported.

In Argyle’s case as a CCC club we recruited players on contracts that we could ill-afford. That led to a debt-level that in turn led to the sale of a host of important players who were replaced by players of lower quality also on contracts we could ill afford either in cash terms or duration. That relatively weakened squad was decimated by injury, results nose-dived, confidence collapsed, the manager was changed, he introduced more expensive players on contracts that proved to be unsustainable, relegation followed, TV income dropped, crowds dropped, admin followed, another relegation resulted.

The root cause of all of this was over-stretching financially while being successful on the pitch – and who doesn’t want their club to be successful on the pitch? Essentially it was the story of Icarus flying so high that he got too close to the sun that his wax melted and his feathers fell off recast as the fate of a football club for our modern times. I’m by no means a classicist but even I know the story. It is hardly a secret.

So the real problem was getting into debt to start with even though that debt actually built the best XI Argyle has had in decades. It was a problem that by virtue of some huge, for us, transfer income we could have avoided but the same core mistake (players earning wages that were too high on contracts that were guaranteed for too long) were repeated and eventually the wheels came off and we’re right back to admin, the points deduction and relegation again.

We might have avoided the worst excesses of our meltdown had we paid lower salaries. But we didn’t. We might have avoided the worst excesses of our meltdown had we stipulated shorter contracts. But we didn’t. We might have avoided the worst excesses of our meltdown had we exit clauses on the contracts. But we didn’t.

So through a mixture of panic, misguided ambition, reckless spending, soft negotiation all coated with either negligence or incompetence we recruited players we never should have signed and probably would not have signed had the offers been shorter, cheaper and less secure. And it was those players who won the points that “would have been enough apart from the points deduction” and those players should never have been donning our famous green shirts in the first place as those points were won.

“Cheating” is a strong word to use but what else is signing players knowing the wherewithal is not there to support them? The fact that we went into admin and were relegated was our own damned fault and not the fault of the Football League rulebook or some sort of freak vendetta. We broke the rules. We cheated. We were punished. And rightly so.

The fact that the dominoes toppled one after the other that did not need to topple and that our club was nearly extinguished forever as a result should never be forgotten and nor should the lunacy that prevailed in our boardroom at the time. A repeat must never be allowed and it is beholden to us as fans to place the blame fairly and squarely where it lies and that is most certainly not with the Football League for applying a sanction that everybody had known was coming for months before it did.

Never again should we afford our owners, whoever they are, the luxury of unquestioning, blind faith in their decision making because failure to question, scrutinise, complain and, if necessary, sound an alarm represents the same bungling incompetence, Mikawberish hope, wilful negligence and/or deliberate strategy in the fanbase as it did all those years ago in the boardroom.

Being vigilant about our club’s management is our duty as supporters not a treasonable activity perpetrated by Quislings.