On the previous post we identified that by simply picking teams based on last years ladder picked (at that point in the season) on average 5.4 winners. The average punter (and there were 160,000 of them) picked on average 4.4. But is this better than a coin toss (random chance).
I initially thought average number picked by flipping a coin must be 4.5.
My reasoning was 8 games per round (9 possible outcomes including picking no games) divided by 2. However a colleague of mine quite heatedly (and as it turned out quite correctly) said 4.
Without the aid of a handy formula (or the math skills to use it) to prove this I simply plugged the randbetween(0,8) function into excel and filled down 20,000 rows and took the average. A fairly rudimentary version of a "Monte Carlo Generator" http://en.wikipedia.org/wiki/Monte_Carlo_method and lo and behold an average of approx 4 picks.
Still having trouble wrapping my head around it, if anyone can explain it better please leave a comment in the comments section (or drop me an email).
Lessons learned.
1. Probability appears to be counter intuitive (and difficult to describe, explain or prove).
2. Even TR is right every now and then.
3. The average punter is slightly better than flipping a coin.
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