Hodgson, Dalglish, and Statistics

Of all the poor statistical arguments you hear people make, the one that bothers me the most (at the moment, anyway) is when they try to extrapolate recent performance back over the whole season.

If Arsenal beats Wigan 3-0, they say, "if Arsenal had played like this all season, they'd be top of the league," but perhaps they should really say, "if Arsenal had played against Wigan for every match this season, they'd be top of the league." It's not sensible to extrapolate recent performance over the whole season without taking into account who the opponents have been, at the very least.

This error was being made repeatedly a few weeks ago amongst Liverpool fans. They said, "if we'd had Dalglish all season, we'd be top of the league". They would point out that Dalglish's team had earned X points in Y matches, so they suggested that a whole season with Dalglish would have earned (X/Y)*31 points. Argh!

Despite these complaints, it is possible to do a proper analysis of this sort of situation. In fact, I had already reported on what such an analysis shows in this case: no statistical difference with Dalglish versus Hodgson.

Liverpool fans didn't want to hear it, but events since have bourn out that analysis. Liverpool have had a series of poor results. Now fans are admitting that the team just isn't good enough and that they need 4 or 5 new players this summer. This is especially amusing given that Hodgson said exactly this a few months ago and the fans chastised him for it. A better coach, they said, could win the league with this team. Apparently, they've changed their minds about that.

This week, the same statistical error is being made again, but this time by West Brom fans. After West Brom's 2-1 win over Liverpool, pundits are saying that a West Brom with Hodgson would be in the top 5 of the league!

I felt duty bound to do the proper statistical analysis. Here are the results. Unlike with Dalglish, there is currently a nontrivial difference. West Brom are scoring about 0.18 more goals on average (at home only, not away) and conceding 0.26 more goals on average. Unfortunately, these results are more sensitive to how regularization is performed, but the qualitative results are not: Hodgson has made the team stronger in attack and weaker in defense.

Given that, it is hard to imagine that West Brom would be amongst the top 5 in the league. In fact, it's not hard to guess where West Brom would be because there is another team whose characteristics are almost identical to West Brom under Hodgson: Blackpool. The two teams have roughly identical attacking and defending scores as well as the same home versus away performance. So it seems safe to say that, if West Brom had hired Hodgson at the start of the season, they would still be embroiled in a relegation battle now.