Sunday, 5 February 2012

Chelsea v Manchester United.

Chelsea 3 Manchester United 3.

On a weekend where some of the biggest matchday drama came during the journey back from the game(a 20 minute return trip from Stoke took 4 hours because of the snow),title contenders and title has-beens Manchester United and Chelsea respectively served up a cracking six goal thriller.


The stalemate in an evenly balanced contest was broken when Evans made a hash of clearing  Sturridge's dangerous cross ball.United's chances looked remote when first Mata,with a stunning volley and Luis with a deflected header gave the Blue a seemingly unassailable 3-0 lead with under half the game left.The fightback started half an hour from time when Rooney converted a soft penalty and followed up with another just 10 minutes later.Hernandez's 84th minute levelling header put the game back up for grabs as Chelsea saw a large chunk of their mid game Expected Points superiority drain away.Ultimately 40 minutes of dramatic twists and turns dumped the game back to pretty much where it had started and a match between to evenly matched sides ended all square.

From a statistical viewpoint you could chose a host of angles to model.How likely were United to be 3-0 down after an hour (1 in 55) or how likely were Chelsea to give up a 3-0 lead with half an hour left (1 in 105) ,to name but two.However,we'll concentrate on the United's two successfully converted penalties.Coupled with the brace of spot kicks they scored in midweek at home to Stoke,ManU had been awarded and scored from four consecutive penalties.Hernandez and Berbatov scored at Old Trafford on Tuesday and Rooney stepped up to the plate both times at Stamford Bridge.

Berbatov,one of United's 3 penalty scorers in the last 6 days.

So how likely was the Red Devils' 100% conversion rate,if we assume that their diverse cast of spot kickers have the typical 75% success rate from 12 yards.There are 16 possible combinations of successful or unsuccessful kick spread over four attempts.Obviously only one of those combinations will see all four kicks result in goals.There are four combinations that could have given rise to one miss and three goals,likewise four sequences can result in one goal and three misses.Six combinations of four kicks can result in a 50% conversion rate.If we now incorporate the different generic probabilities for each success or failure we can calculate the probability of each of the five possible outcomes of the sequence of the four Manchester United penalties.

The Probability of United scoring or missing some of their last four spot kicks. 

of Four Penalties.
Four Goals. 0.316
Three Goals
+ One Miss.
Two Goals +
Two Misses.
One Goal +
Three Misses.
Four Misses. 0.004

Four successes was the second most likely outcome from a run of four spot kicks,it would occur about once every three sequences.Missing all four kicks,which would have been nice for both Chelsea and Stoke would happen about once every 250 four penalty runs.

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