St Swithin's day weather - fact or fiction?

[A Face like Thunder]

St Swithun's day if thou dost rain
For forty days it will remain
St Swithun's day if thou be fair
For forty days 'twill rain nae mare  (Wiki)

Today is St Swithin's Day (I have used the more traditional spelling of the name) and my wife's birthday, and as I look out on the steady rain here in South Cheshire, I wonder how true the above saying might be.

Let me put forward two years when the saying certainly seemed to ring true:

2006 - sunny and hot all day and this continued until the end of July.

2007 - wet all day and this continued for a while longer in what was a very wet summer anyway.

I am sure that 1976 must have been close to the truth, with the sun and heat of July continuing until the last week of August. The dry summers of 2013 and 2018 must also feature although we had some thunderstorms towards the end of July 2018. 

Hopefully, with the steady rain outside this morning, 2020 will be an exception to the saying!

I am not a stats man but I would be interested to see any comments on the truth - or otherwise - of the saying.