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.