Is Harry Kane really the new Alan Shearer? Or is he simply this season's Michael Ricketts? The question is crying out for an application of Bayes theorem.

I say so because otherwise we risk being misled by cognitive biases.

One of these is a sampling bias; we tend to draw excessively strong inferences from small samples: lots of players look good when they are on form, but it is wrong to infer from this that the player is a genuine world-beater. Only very silly managers buy players on the strength of a highlights video.

Another is wishful thinking. Spuds want to believe Kane will be a an all-time great. Gooners do not, with some suggesting that "great Sp*rs player" raises the same sort of philosophical issues as Bertrand Russell's golden mountain*.

One way of correcting such biases is to use maths. Enter Bayes theorem. This is:

P(A¦B) =

^{[P(B¦A) x P(A)]}/_{P(B)}

Let P(A) be the probability of having a new great player. And let P(B) be the probability of us seeing a player doing what Kane has done this season. P(A¦B) is then the probability of us having a new Shearer, given Kane's performances.

Let's put some numbers on this.

Over 3500 players have appeared in the Premier League since its inception. Only a handful, though, can be called true greats of the Shearer/Henry type. So let's call P(A) 0.5%.

P(B¦A) is the probability of a player delivering Kane's performances if he were a true great. Kane has scored 24 goals in 37 appearances this season - a goals per game ratio of 0.65. This is more than Shearer or van Nistelrooy managed in their career, but less than Henry. It is therefore the sort of thing a great would do. Let's call this probability one.

P(B) is the probability of a player doing what Kane has done this season. A binomial distribution tells us the chance of someone scoring 24 in 37 games if they were really only a 0.4 goals per game player is tiny - just 0.2%. However, there are lots of players in the league, so the chance of someone having a great season if they were ordinary is much higher than this. Let's call it 1.5 per cent. This captures the fact that there are many young players who briefly shone but sank into obscurity: remember Franny Jeffers, Danny Cadamateri, Seth Johnson, Michael Bridges...?

If we put these numbers together, we get:

^{[1.0 x 0.005]}/_{0.015}= 0.333

In other words, there's a one-in-three chance of Kane being a true great. I suspect this splits the difference between what Spuds want and what Gooners want.

Now, I don't intend this to be a precise answer: think of it instead as a Fermi estimate. Instead, I say this to illustrate a general point. Maths isn't useful merely because it gives us precise answers. It can also be used as a way of cautioning us against egregious biases.

** This is not the only link between philosophy and Sp*rs. A.J. Ayer - Nigella's stepdad - was a keen Spud. Gooners devised the chant "Who's that team they call the Arsenal?" to wind him up. *

Who is that woman and what does she have to do with this blogpost?

Posted by: Thumbs up for pagethreeification! | February 23, 2015 at 04:14 PM

Definitely the new Peter Crouch.

Posted by: Dave Timoney | February 23, 2015 at 04:41 PM

The woman (Nigella Lawson) was put there so that those of us without the maths to follow this post would still get something out of it.

Posted by: Bill Posters | February 23, 2015 at 08:01 PM

What is the probability of me getting off with Nigella?

We can't use the maths because the sample is too small. I would say let us see him over 3 seasons and then plug in the figures.

Though Messi was clearly great from day one, whereas the jury is still out on Kane. Not sure that is factored into the maths.

Posted by: An Alien Visitor | February 23, 2015 at 08:54 PM

kudos for making the tenuous link in order to post a pic of Nigella Lawson!

Posted by: Greg | February 23, 2015 at 11:55 PM

Nice try at a diversion from the descent into averageness of Jack Wilshere

Posted by: Andrew | February 24, 2015 at 12:09 AM

Michael Bridges had a very bad injury and struggled to get back to the top level after that. It would be stretching things to describe Seth Johnson as 'shining'. He was always a mediocre player who happened to be a beneficiary of Peter Ridsdale's madness.

Neither count as 'flash in the pan' footballers.

Posted by: Igor Belanov | February 24, 2015 at 12:15 PM