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Who Scored All the Pi's ?

The day that the average goals per match was a famous ratio

Last month I wrote about the record-breaking goal glut in this year's Premier League.  At the time, there was an average of about 3.8 goals per match, an increase of nearly 50% over a typical season.

I predicted that this ratio would probably drop, and last Sunday night I checked the latest figures: 

                  245 goals / 78 matches = 3.14

Yes, the goal-per-match ratio has indeed dropped.  But hang on, 3.14, I recognise that ratio.  It's pi ! 

I've known for a long time that 22/7 is a very good approximation of pi, but it turns out that 245/78 is even more accurate.  It felt like an amazing fluke had happened.  Then I checked up other ratios involving numbers in the range 1 to 999.  It turns out that 245/78 only ranks No.52 in the list of accurate whole number approximations of pi in that range.

Before the end of the season there will be plenty more opportunities for a pi ratio to crop up.  Next up is 267/85 (accurate to within 0.013% of pi). Then there's 289/92 (accurate to an incredible 0.009%).  But about three weeks from the date of this blog we could get the absolute humdinger, the best pi approximation of all. 

If, after 113 games in the Premier League, it so happens that the goal tally is 355, then the number of goals per game will work out to be 3.1415929.  Which differs from pi by just 0.000008%. 

What are the chances?