Is Tony Pulis Really Liverpool's Nemesis?

I haven't done a quick blog post in ages, but this article from the Liverpool Echo has inspired me.

https://twitter.com/LivEchoLFC/status/852382087667564545

In it, the facts of Liverpool's poor record against teams managed by the current West Bromwich Albion gaffer are rightly laid bare:

Liverpool go looking for their first ever away win in the Premier League against a Pulis managed-team on Sunday when they travel to the Hawthorns, a venue where they have not won since 2011.

Jurgen Klopp’s men won the reverse fixture 2-1 at Anfield in October for a first league victory over Pulis in nine attempts across five years.

But have the Reds deserved to win more of those games than they actually have? Let's take a look.

We don't have expected goals data going back to 2008, but thanks to my database of shots on target in Liverpool games which does go back that far, we can do a similar thing. The following table shows the Reds' matches against teams managed by Tony Pulis, and how many shots on target both sides had.

We can see that 'Pulis FC' have never had more than one shot on target more than Liverpool in any of these matches, and have been out shot (on target) by at least six in six of the fifteen encounters. What's probably the most galling though is 2008/09, where Stoke took a point from both matches despite not having a shot on target in either. This in theory cost Liverpool the title that season, and with shot stats like those surely the Reds deserved to win the matches?

Not all shots on target are equal, but using my database we can see how many points per game Liverpool have averaged depending on how many more or fewer shots on target they have had compared to the opposition. As the sample sizes vary wildly, I have grouped some of the smaller differences together to get the following table:

Using the points per game figures for the exact shot on target differences we can then get an 'expected points' figure for the matches that Liverpool have played against Tony Pulis' teams. They can be seen in the below table.

We can see that in theory Liverpool have 'deserved' to win ten more points against Pulis sides than they've managed to in reality. The worst one here has to be when Kenny Dalglish's Liverpool lost away at Stoke in 2011/12, despite having seven shots on target to their hosts' one. The power of that one being a penalty made the difference.

Over the previous 336 Premier League matches, Liverpool's average shots on target difference per game has been 2.13, yet against the teams of Tony it has been 2.93; 38% better than average, in other words. In my opinion, Pulis has definitely been lucky to get as many good results against the Reds as he has.

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