## Friday, 9 September 2011

### The Expected Points Model.Theory verses Reality.

Expected Points for any game situation are derived from the win and draw probability associated with each team at that particular moment in the game.Because probabilities relate to the longterm,it's not possible to compare the predicted expected points to the actual number of points gained by the teams at the end of the match.For example if the EP was 2.4 that would mean that the average number of points that team would collect from that position if the game was able to be replayed many times over would be 2.4.In reality,of course at the end of that one game the team would actually gain either 0,1 or 3 points.

One way around the problem would be to collect a decent sized sample of games,calculate the EP at a particular time during the game and then see how the cumulative total of expected points compares to the cumulative total of actual points.

I've randomly selected an EPL team,in this case Bolton and calculated the EP for Bolton in every game during 2010/11 where they scored the first goal of the game.I've chosen Bolton's and the game's first goal as the EP reference point to see if Bolton derive any extra impetus from scoring first,whether they underperform from that point or whether they perform as the model expects them to.We are also guaranteed to have reference points spread throughout the game in our sample, thus eliminating any systematic bias such as EP points later in the game correlating more strongly with actual points.

Expected Points compared to Actual Points where Bolton score the game's opening goal.

 Home Team Away Team. Time of 1st Goal.(mins) Expected Points for Bolton after Goal. Actual Points Gained by Bolton. Wolves. BOLTON. 1 1.985 3 BOLTON. Man Utd. 6 1.325 1 Blackpool. BOLTON. 6 1.940 0 BOLTON. Everton. 10 2.138 3 BOLTON. W.Ham. 14 2.320 3 BOLTON. Newcastle. 18 2.408 3 BOLTON. Stoke. 22 2.332 3 BOLTON. Tottenham. 31 2.105 3 BOLTON Arsenal. 38 1.933 3 BOLTON. West Brom. 40 2.447 3 Liverpool. BOLTON. 43 1.801 0 West Ham. BOLTON. 48 2.166 3 BOLTON. Wigan. 54 2.610 1 West Brom. BOLTON. 64 2.221 1 Everton. BOLTON. 79 2.320 1 BOLTON. Wolves. 90 2.845 3 BOLTON. Blackburn. 65* 2.156 3 Total Points. 37.052 37

*Bolton were reduced to 10 men before the 1st goal was scored.The sending off reduced their EP and this was fully accounted for.

The first observation is that scoring the first goal puts a team into a very powerful position.The lowest EP Bolton had after scoring first was 1.3 for a very early goal against a much superior Man Utd side.But overall the first goal gave Bolton an EP of 2 or more in the vast majority of the games.Although the sample size isn't large,they never failed to pick up at least a point in every game where the 1st goal advanced their EP to 2 or beyond.

The model predicted that Bolton would amass 37 points from the 17 games in which thy scored the opening goal and they actually gained exactly that number.The team and match situation was genuinely selected randomly and if I had selected other teams it's inevitable that there would be teams where the predicted and actual results differed.However,this result does give cause to be optimistic that the model is at least reasonably robust.

Once I've automated the process I'll post the figures for different leagues and for different scenarios.It would be interesting to see if some teams do over perform from the norm if they strike with the first goal or if some find it very difficult to match the expected level of performance if they fall behind.

Expected Points are a very potent tool to investigate what is at the very heart of a team's performance come matchday.