My temptation with any change to the team — be it an injury, transfer, or new manager — is to accept the null hypothesis: no change. This is really the only choice since something is changing in almost every match. There are an infinite number of possible variables that could influence the outcome of the match. If we are going to make predictions about what is going to happen, we have to determine which variables are important and which are not. Hence, for many variables, we must accept the null hypothesis, that those variables do not really matter.
It is qualitatively clear at this point, however, that Dalglish's Liverpool is different. They may be the same players (or at least they were until the last match), but they are certainly playing in a distinctly different style. While we don't yet have enough matches to prove that the Dalglish effect is statistically significant, I feel comfortable introducing a new variable at this point, which I will call the "Dalglish boost", the change in Liverpool performance due to Kenny Dalglish.
We have to be careful in introducing the Dalglish boost because we still do not have a lot of data to go by. Dalglish has only been in change for 6 Premier League matches, and he hadn't even practiced with the team for the first of those. We will assume, then, that the Dalglish boost has been in effect for the last 5 Liverpool matches, which is a paltry number.
If we are to take those 5 matches at face value and assume that Dalglish's Liverpool is a whole new team, then the statistics tell us that Dalglish's Liverpool has the best defense in the league and the 4th best offence, slightly ahead of Manchester City in both categories. That seems a bit too optimistic an assumption for only 5 matches.
We can fix this using the usual statistical techniques for controlling overfitting: we introduce a penalty on the complexity of the model. Now, the Dalglish boost will only enter into the equation if it pays for itself: if the increase in model fit is larger than the increase in complexity.
For the purposes of this analysis, we can adjust the penalty by hand until it demonstrates an acceptable level of conservatism. If we set it very high, then Dalglish's Liverpool is no different from Hodgson's. If we set it very low, then Dalgish's Liverpool is better than Manchester City. I've chosen a penalty large enough that Dalglish's team is settled in between Sunderland and Tottenham. However, with virtually any penalty, we see the same qualitative effect, as I will now describe.
This particular model has a term for each team's offensive power and defensive power. Dalglish similarly gets two boosts: one for offense and one for defense. With the penalty above, we get the following results:
- Dalglish offensive boost: 0.02 goals per game (scored)
- Dalglish defensive boost: -0.15 goals per game (conceded)
This offensive boost is essentially zero. However, a defensive boost of -0.15 is the difference between Sunderland's defense and that of Hodgson's Liverpool. In other words, this model shows a significant Dalglish boost and ascribes it almost wholly to defense.
As I said, this qualitative effect is not particularly sensitive to the penalty chosen above. If you instead decide that Dalglish's Liverpool is now the 4th best team in the Premier League and you choose a penalty that allows the Dalglish boost to get that large, then you get these results:
- Dalglish offensive boost: 0.12 goals per game (scored)
- Dalglish defensive boost: -0.32 goals per game (conceded)
Now, we see a larger improvement in offense. However, the model still ascribes ~75% of the improvement to defensive improvements.
To those who have watched Liverpool play under Dalglish, this should not be entirely a surprise. Perhaps the biggest visible change instituted by Dalglish has been an increase in pressing. Like the best defense in the world, Dalglish's Liverpool presses whenever they lose the ball, even high up the pitch. This decreases from the pressure on Liverpool's central defense, who (one must admit) were a weak point earlier in the season.
Dalglish has also increased the amount of short passing, thus favoring a more possession-based and less direct approach. This clearly improves defense since the opponent cannot score when you're sitting on the ball.
The end result of these changes is that, while Dalglish's Liverpool have been a more potent attacking force, they have also had 3 clean sheets out of those 5 games. According to the statistics, these clean sheets are a more significant change than the increase in goals. In other words, the primary effect of the Dalglish boost has been improved defense.
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