## Sunday 25 September 2011

### For How Long Will Manchester United be Behind in a Game ?

When Manchester United travelled to Stoke on Saturday they lost their 100% start to the season.Nani's crisp shot from a simple one two on the edge of the Stoke area after 27 minutes was cancelled out by Crouch's first goal for his new club 25 playing minutes later.A cracking game for anyone lucky enough to witness it,but equally interesting from a statistical point of view.

The game was level for the first 27 minutes,United then led for 25 minutes and then the final 38 minutes remained deadlocked,despite the best efforts of Crouch and woeful late finishing from Giggs.But pre game is there some way we can try to estimate the most likely time a team can expect to lead,trail or draw during the game ?

 United defending  a 1-0 lead at Stoke.
Expected points calculations rely on the ability to chart the win and draw probability for each team at any point during the match,which in turn are derived from the pre game goal expectancies for each participating teams.Therefore we can use this approach to predict how long a team is likely to be leading,drawing or losing during a game.It seems sensible to initially chart the league's most successful team,as this sets the height of the bar for all other teams.It also helps to give a fan an expectation of how much pleasure,pain or anticipation they are likely to experience during a match.

Probability of course relates to events happening over the long term,so it's not possible to compare predictions generated from those kind of figures over a short time span such as a single game.Therefore to test the methodology I've used all of Manchester United's games from their 2010/11 championship winning season.

I've averaged the pre game goal expectancy for goals scored and goals allowed for all of United's 38 games during that Premiership year.United's goal expectancy on average per game was 1.95 goals and they'd be expected to concede 0.85 goals.By charting how these two goal expectancies decay throughout the game it's possible to calculate how likely it is that United will lead after the first minute,the second minute and so on until the end of the game.

For example,on average United had about a 26% chance of leading in the game's 20th minute,a 64% chance of drawing and a 10% chance of losing.Thus they would be expected to lead on average for 15.5 seconds of each 20th minute,draw for 38.5 seconds and trail for 6 seconds.

If we do this calculation for every minute of the game we can total all the seconds up and calculate for how many minutes during a game the EPL Champions in theory should have led,drew or been losing during that season.

If we do this we find that Man Utd could be expected on average to lead for 36 minutes and 2 seconds of
the 90.They would be drawing for 44 minutes and 10 seconds and trail for the remaining 9 minutes and 48 seconds.So in a soccer world dominated by large margin Manchester United victory highlights,it's probably quite surprising to find that on average they are ahead for only 40% of the time.As a consolation,fans of the Red Devils only have to endure an average of 10 minutes per game when their team is behind.

Because we have made the calculations to cover an entire season we can further test the methodology by seeing how the predicted times compare to the times in reality.

Time Spent Leading,Drawing or Losing For Manchester United 2010/11.

 Home Team. Away Team. Time Leading. Time Drawing. Time Losing. MAN UTD. Newcastle. 57 33 0 Fulham. MAN UTD. 51 39 0 MAN UTD. WestHam 57 33 0 Everton. MAN UTD. 43 43 4 MAN UTD. Liverpool. 34 56 0 Bolton. MAN UTD. 0 66 24 Sunderland. MAN UTD. 0 90 0 MAN UTD. WestBrom. 50 40 0 Stoke MAN UTD. 58 32 0 MAN UTD. Tottenham. 59 31 0 MAN UTD. Wolves. 21 69 0 ManCity MAN UTD. 0 90 0 AstonVilla. MAN UTD. 0 77 13 MAN UTD. Wigan. 45 45 0 MAN UTD. Blackburn. 88 2 0 MAN UTD. Arsenal. 49 41 0 MAN UTD. Sunderland. 85 5 0 Birmingham. MAN UTD. 31 59 0 WestBrom. MAN UTD. 26 64 0 MAN UTD. Stoke. 51 39 0 Tottenham. MAN UTD. 0 90 0 MAN UTD. Birmingham. 88 2 0 Blackpool. MAN UTD. 2 29 57 MAN UTD. AstonVilla 90 0 0 Wolves. MAN UTD. 7 33 50 MAN UTD. ManCity. 36 54 0 Wigan. MAN UTD. 73 17 0 Chelsea. MAN UTD. 25 54 11 Liverpool. MAN UTD. 0 34 56 MAN UTD. Bolton. 2 88 0 WestHam. MAN UTD. 11 17 62 MAN UTD. Fulham. 78 12 0 Newcastle. MAN UTD. 0 90 0 MAN UTD. Everton. 6 84 0 Arsenal. MAN UTD. 0 56 34 MAN UTD. Chelsea. 89 1 0 Blackburn. MAN UTD. 0 37 53 MAN UTD. Blackpool. 35 50 5 Average Total.(mins). 35.5 44.8 9.7

And the agreement is very good.Man U actually led for 35 and a half minutes per game compared to the predicted 36 minutes,they drew for 44mins 48 compared to 44:10 and trailed for 9:42 compared to the predicted 9:48.