A Test as to Whether Jan’s Pre-game Summary is Accurate – a Case Study: Cambridge South Men’s 2nd XI versus Peterborough 4th XIJack Chalk
The text not in bold in this report is not essential and is included for those who only studied medieval poetry in Latin and similar. Those that did not limit themselves in this way can just skip to the bold text. I apologise for the use of decimals as opposed to fractions – Graham, the equation editor on this website leaves a lot to be desired.
In the M2s’ WhatsApp group there is a large amount of chat every week as to the accuracy of Jan’s pre-game summary. This needs to be tested to see whether it is accurate or not.
Using the Year 7 axiom that things are either true or not true with equal chance, we can model Jan’s pre-game statements and predictions as a binomial distribution with a probability of being correct of 0.5.
H0: p = 0.5 (null hypothesis Jan’s statements are equally likely to be true or not)
H1: p > 0.5 (over half of Jan’s statements are true)
Where p is the probability of a correct statement.
Let X be the number of correct statements. 29 statements are made, therefore X~B(0.5, 29)
We will test to 90% confidence, i.e. we can be sure that overall Jan’s preview is generally accurate 90% of the time.
10% Significance, 1 tailed.
14:30, Bretton Gate – M2 @ City of Peterborough 4ths (correct)
After the wash-out at a ropey satellite venue back in October (correct), the M2s have been upgraded to Peterborough’s main venue for the second attempt at this game (new pitch was not as good as promised, it had a weird bonce – incorrect). That should at least ensure the game happens this time around (with huge delays in traffic it was a miracle we all got there before the game started; good job the previous game was behind schedule – incorrect).
Jan, you made no mention of the debut of Thomas Sneade, Neil’s estranged son that Puds recruited to bulk up our numbers today. Unusual for you not to predict the team.
The challenge they face is still similar to what it was back then (we are in a much better league position than when the game was originally scheduled – incorrect). Peterborough are still right up at the top end of the table (correct). They no longer boast a 100% record though after being held to a 4-4 draw by Spalding a few weeks back, and that result has cost them the leadership of the section to the Uni 3rds, who have won all their games to date (correct) (quite luckily against South (hhhmmm to be fair to Uni, this would have been the greatest upset in league history had we got a point – incorrect)…but that is one for a preview later in the season). The M2s also drew against Spalding very recently, last Saturday in fact, thanks to a goal on his South debut from James B (correct) and one snaffled on the line by Shinny (but did it actually go in? Yes, according to the umpire, so – correct).
On the other side of the pitch things look rather different though as South have emerged as a significant force in Division 3NW after a very strong run since the start of November (correct). Unbeaten in five with eleven points gained from those fixtures, James and co have pushed up to fifth in the table (incorrect – we are now 4th). As noted last week, this appears to have been based on getting the balance right between attack and defence (we conceded two goals – incorrect). In the first five league games the M2s scored fifteen but also conceded eighteen (correct); it was explosive, but too open (correct). Since then the side have kept the goals flowing at the right end and indeed increased the rate slightly with twenty-four in the last five (only three goals today so this average has been reduced – incorrect), but have stemmed the flow at the back to a trickle (Peterborough lead the game two-one until the last fifteen minutes: still to many conceded so – incorrect), just five conceded over the same period.
I believe the chance is there for the M2s to spring a shock (we did – correct). They have already shown with the three-two loss to the Uni that they can operate at the same level as the best in 3NW (correct). It should be an even (South had the majority of possession throughout the game and took an early lead through a Baggers sweep from top D before squandering it within twenty seconds to a ball bundle over the line, then Peterborough went ahead from a powerful strike in the second half, so – correct) and interesting game (we won after Chalk equalised with a classic return to injector from Catley the Second and Tom Sneade deflected in Pete’s powerful shot with three minutes to go – correct), and one that our boys, as the underdogs (is this a reference to the Saint getting his dog to poo on Peterborough’s brand new pitch? If so, amazingly - correct), can approach with little pressure on their shoulders as they look to go into the festive break on a real high (correct - we are going up).
Observed sample 19 correct statements out of 29.
The probability of 19 or more correct states out of 29 is: P(X≥19) = 0.06802 (4sf)
Unfortunately choose notation cannot be displayed on this website so the formulas have not been quoted but please check this with your own calculator.
0.06082 < 0.1 This probability is less than the 10% chance we are looking for to prove the hypothesis.
Therefore, reject H0; there is evidence to suggest that Jan’s pre-game summary is an accurate prediction of the game.