Unless you were hiding in a field in Rothbury for most of last week, I am guessing you have heard all about Paul the Octopus.

Paul is in fact actually a psychic Octopus.  What a turn up!

He has been predicting the outcome of Germany’s games for a couple of years now, and just like his compatriots, Messers Schweinsteiger and Mueller, he has been in fine form.

He goes into tonight’s game on a run of seven straight successful predictions having correctly predicted Germany’s route through to the semi-finals, before showing as much loyalty as Lucas Neill by changing his spots and jumping on the Xavi/Iniesta bandwagon.

Why not, eh? Seems to work for every other journo, commentator and pundit in world football.

Anyway, all this media attention for our eight tentacled friend got me thinking.  How impressive is Paul’s little run of form?

Although not quite the Monty Hall Problem, this one did get my brain thinking for a few minutes when I first considered it.  On Friday, a colleague asked me what Paul’s chance s were of having pulled off such a feat.

“About 100/1?” was his initial stab, over a lunchtime beer.

My instinctive response to that suggestion? “Nah, mate.  It will be considerably longer than that I would have thought.”

However, at that point in time I had not yet put my thinking cap on straight.

As it turns out, Paul’s achievements are far less spectacular than they seem at first glance.

Before we get into the specifics, a quick refresher of the laws of probability and expected value can be found here for those that are really really bored of my aimless chat.

It is important to recognise that Paul makes his predictions before the games have been played.  You would have thought this was a fairly obvious statement, however in the world of Derren Brown et al, it appears we are allowed to claim brownie points for predicting things after the event these days.

To be fair, there is someone doing exactly this in every boozer up and down the country at about 5pm every Saturday too.  Anyway, I digress.

Let’s have a look at his performance so far during the World Cup.

Before we do, a few quick points of note – although they believe Paul to be a psychic, das German’s clearly don’t trust him enough to ever offer him the option of a game ending in a draw.  What do they think this is, soccer?

At this point I have to admit I smell more rat than I do octopus, that is for sure, what with those sneaky (and highly intelligent) Germans on the case.  More on this in the footnotes.

From here on in, I am going to assess this scenario assuming the following:

1. Paul knows as much about football as our very own Mark Lawrenson; and
2. The Germans are not up to any funny monkey business.

So during the Group stages, Paul is offered two identical tasty treats and is then left to his own devices.

Therefore the chances of Paul selecting a draw are zero and the chances of him selecting either of the individual teams to win is a fair coin toss.  Even Stevens, a 50/50.

Paul the Octopus’ World Cup Predictions – Germany v Australia

Game	Prediction	Home	Draw	Away	Paul’s chances
Germany v Australia	Germany	60%	26%	14%	37%

Let’s quickly run through his first selection against Australia as an example, using the probabilities I have assigned above.

The chances of Paul predicting the winner of this game successfully were:

= P(Selecting Germany) * P(Germany winning) + P(Selecting Draw) * P(Draw) + P(Selecting Australia) * P(Australia winning)

= 0.50*0.60 + 0.00*0.26 + 0.50*0.14

= 0.30 + 0.00 + 0.07

= 0.37 / 37%

Following this same process through, Paul’s chances of pulling off the Group stage trifecta were circa 21/1.  Not bad going, but then again nothing spectacular:

Paul the Octopus’ World Cup Predictions – Group stages

Game	Prediction	Home	Draw	Away	Paul’s chances
Germany v Australia	Germany	60%	26%	14%	37%
Serbia v Germany	Serbia	16%	29%	55%	36%
Germany v Ghana	Germany	55%	31%	14%	35%
Product					4.53%

*These prices are neither bookies prices or 100% accurate.  They are much more complicated than that.  I have a secret privately developed detailed pricing system which produced these numbers, which is known only to the masses as “the fag packet”.

As we entered the knockout stages, Paul’s task actually became easier.  With the draw no longer a possible ultimate outcome, I would assume he would be credited with any successful extra time or penalty win predictions.

Unlike the UK bookmakers, for the purposes of this exercise I have priced both the England v Germany and Germany v Argentina ties up as straight 50/50’s.  I really don’t think that would have been too far off.

Logically, this gives Paul a simple 50/50 chance of success, improved upon from the Group stages as he no longer has the “draw risk” working against him which his sneaky owners didn’t offer him during the Group stages.

Paul the Octopus’ World Cup Predictions – after the quarter-final stage

Game	Prediction	Home	Draw	Away	Paul’s chances
Germany v Australia	Germany	60%	26%	14%	37%
Serbia v Germany	Serbia	16%	29%	55%	36%
Germany v Ghana	Germany	55%	31%	14%	35%
Germany v England	Germany	50%	n/a	50%	50%
Germany v Argentina	Germany	50%	n/a	50%	50%
Product					1.13%

Now we are getting to more impressive numbers.  Not everyday an Octopus pulls off an 88/1 shot.

At the semi-final stage, this is where it gets interesting.  Spain v Germany.  Intuitively, what do we think the chances are of Paul pulling this one out of the bag?

It turns out he is as much “Paul the Verrator” as much as he is “Paul the Psychic”, but what is interesting here is to recognise that it makes absolutely no odds who the two teams competing are to Paul’s chances of success.

The chances of Paul successfully predicting this considerably more imbalanced fixture correctly are no different – it is a bog standard 50/50 coin toss.

Don’t believe me?  Lets consider a situation where Germany were playing North Korea in a knockout game.

In that scenario, let’s say North Korea had only a 5% chance of qualifying, with Germany a 95% “”cert”.

Then using the same formula from above, the chances of Paul pulling this one off are:

= P(Selecting Germany) * P(Germany qualifying) + P(Selecting Korea) * P(Korea qualifying)

= 0.50*0.95 + 0.50*0.05

= 0.475 + 0.025

= 0.50 / 50%

Counter intuitive at first isn’t it?

Paul the Octopus’ World Cup Predictions – after the semi-final stage

Game	Prediction	Home	Draw	Away	Paul’s chances
Germany v Australia	Germany	60%	26%	14%	37%
Serbia v Germany	Serbia	16%	29%	55%	36%
Germany v Ghana	Germany	55%	31%	14%	35%
Germany v England	Germany	50%	n/a	50%	50%
Germany v Argentina	Germany	50%	n/a	50%	50%
Germany v Spain	Spain	68%	n/a	32%	50%
Product					0.57%

So there you have it. The chances are Paul having pulled off his run thus far are about 175/1.

Not bad at all.  But probably not worthy of all the media hysteria given that you have a 220/1 chance of being dealt AA in a game of Texas Hold’em poker or a 1032/1 chance of getting 4 numbers on the national lottery (think about that, considering you get about £90…)

Enjoy the game tonight everyone.  And when Paul the Octopus is taking column inches away from any meaningful analysis about how big a contribution Sergio Ramos’ off the ball runs had to the success of his team, bear in mind all that Paul really did was win a coin toss.

Although, who knows, maybe Paul is sharper than he looks after all.  Maybe he know the ins and outs of Serbian football like no other, and his defection to Spain is one last attempt to avoid being boiled alive and dumped in Del Bosque’s celebratory “Pulpo a la Gallega” later tonight…

N.B.

Like most things in life, there are already rumours of cheating and pillaging going on in Deutschland if this is anything to go by.  Combining the fact that this has all spawned from a German organisation and that Paul has predicted German wins in 11 of 13 games so far, I wouldn’t be surprised if the Witchetty grubs in the German sections are considerably fatter and juicer than the others on offer to our hungry octopus…  Food for thought anyway.

Also, the Monty Hall problem reference above is one of my favourite problems of all time.  Nothing really hits home so easily to your average man in the street as to both the power and complexity of probability.

It is crucial to recognise how the human mind naturally responds when presented with such scenario’s if you are ever going to truly master sports betting.

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