With League Two’s Bradford City only one match away from playing at Wembley in the League Cup final I thought it would be interesting to see what the chances were of them getting this far.
It has been an unbelievable cup run for Bradford City as they have had to play against teams in higher divisions nearly every step of the way. The first round of the cup pitted them against League One team Notts County who they managed to defeat in extra time. This was then followed a couple of weeks later with a 2–1 victory away at Championship side Watford.
The third round was somewhat kinder to them as they played at home against Burton Albion, a team from their own division. However, having seen off Burton the fourth round then took them to Premier League side Wigan Athletic who they managed to defeat on penalties.
The quarter final again put Bradford against another Premier League team, with Arsenal this time Bradford’s victims. Next up was Aston Villa who lost 3–1 to Bradford at the Valley Parade although Villa did come away with an away goal, which could prove to be critical for them.
To work out the probability of Bradford’s cup run I collected the odds for each match from www.oddsportal.com and removed the overround to get the true odds. The overround is the bookies profit margin created by offering odds lower than the actual true odds of the event occurring. To remove it we just need to scale the odds by the excess so that they add up to exactly 100%.
Once we have the true odds we can them work out the cumulative probability of the cup run by multiplying the odds together (note that bookies odds generally refer to what happens over the first ninety minutes of the match so Bradford City beating Notts County in extra time is actually classed as a draw rather than an away win).
\(Prob(Cup Run) = prob draw with Notts County * prob beating Watford * prob…\)
Overall, the probability of Bradford City’s current cup run so far is 0.008%. If we take into account tonight’s match then the chances of Bradford’s cup run taking them all the way to Wembley is around 0.001% or 1 in 100,000. It’s not quite a lottery win, which is around 100 times less likely again, but it is a fantastic achievement for Bradford City and is likely to be a once in a lifetime experience for their fans.
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