## Monday, 3 October 2011

### Predicting Second Half Performance.

One very easy trap to fall into when trying to make sense of soccer statistics is to give far too much prominence to very recent events.A run of very good results from a previously mediocre team may signal a permanent upturn in fortunes,but it's much more likly that the good run is down to random chance.

Similarly,if a game contains a period of rapid scoring,the natural expectation is that the goals will continue to flow or if a game has been goalless for a large proportion of the match,it's tempting to think that the remainder of the game will also be unusually barren......but will it be?

To see if incidents earlier in a game dictate the course a game will take subsequently,I sorted all games from the last five EPL seasons by the total number of goals scored by both teams in the first half,starting with games that were goalless through the first 45 minutes and ending with games that saw five first half strikes.I then saw how many goals were scored in the second period.

There are two competing scenarios that could be played out here.If short term,recent events are more important in determining the course of a game we should expect to see more second half goals scored in games that have goal laden first periods and we should also see fewer later goals in games where scoring is scare before the interval.However,if "unusual" scoring rates are to be expected to occur by random chance,then subsequent events should be more closely related to our pre game expectations.

Average number of second half goals for games where a certain number of first half goals are scored.

 1st Half Goals. Average 2nd Half Goals. 5 1.08 4 1.51 3 1.60 2 1.48 1 1.47 0 1.39

The first point to make is that there are very few games where five goals are scored in the first half,just 13 over the last five EPL seasons,therefore although they are included for completeness they are probably best disregarded.

Of the remaining categories from 4 goals downwards,the general trend would seem to support the idea that first half occurrences are a big factor in what happens post interval.

Games that are goalless have on average the least amount of second half goals.The average number of second half goals then climbs in tune with the number of first half goals,before dropping slightly at 4 first half goals,another relatively small sized sample.

But what of the pre-game expectations for each of these groups of games.A mismatch between the very best and the very worst in the division will tend to have around half a goal a game more than a more competitively balanced game.

So before we can conclude that the increase or dearth of second half goals is likely related to the events of the first half ,we first have to calculate on average how many 2nd half goals we expected to see in these games before they kicked off.

By using a goals based ratings system we can calculate the expected average goals difference in each of the EPL games in the sample,from there we can calculate the average number of total goals in each game.It will range from about 2.5 goals for very closely matched games to just over 3 goals for less balanced games between teams from either end of the table.

The rate of goal scoring increases as a game progresses.Less goals are scored in the first minute than are scored in the second and so on throughout the game,resulting in around 55% of all goals being scored after the interval and 45% before.

Therefore,it's possible to average the pregame 2nd half goals expectancy for each of the groups of games and compare these figures with the actual average number of second half goals scored.

 1st Half Goals. Actual Average 2nd Half Goals. Pre Game 2nd Half Goals Expectancy. 5 1.08 1.57 4 1.51 1.51 3 1.60 1.55 2 1.48 1.52 1 1.47 1.49 0 1.39 1.42

We now see that the pre game prediction of how many goals on average would be scored in each of the 6 groups very closely matches the actual number of 2nd half goals scored.The progression of increasing numbers of goals from one group to the next occurs as a result of each group containing progressively more games that were expected to be more goal laden from the start.

The fact that 4 goals were scored in the first half did not result in an excessive number of second half goals being scored,over and above what was expected from the pre game competitive matchup of all the games contained in the group.

The average 2nd half total goals expectancy for the games where 4 1st half goals were scored was 1.51 goals and that's exactly what happened even after 4 first half goals had hit the back of the net.There was no "early goals creating an avalanche of later goals" effect.

In short,four first half goals is a rare,but expected event,happening in about 2% of games.But that isolated event appears to have little or no effect on what happens in the remaining 45 minutes.