Last night Swansea, under their new manager Carlos Carvalhal, beat Arsenal. The win moved them out of the relegation zone. This is one piece of evidence that a managerial change produces an increase in points for a club. Broader evidence was produced two weeks ago on Sky's Monday Night Football. In the build-up to the Manchester United versus Stoke City game, Gary Neville and Jamie Carragher said that the evidence from the 2017-18 season suggests that there is a points bonus from changing the manager. The table below is a reproduction of what they used. Five of the six clubs listed improved their points per game under the new manager.
However, there is other evidence to contradict the above. The benefits of managerial change is viewed with scepticism by anyone who read The Numbers Game by Chris Anderson and David Sally. Anderson & Sally draw on work that examines the Dutch league for the period 1986 to 2004. Almost 20 years of data. The work confirms that the points accumulate by sacked managers, prior to their sacking, is unimpressive. It also confirms that the points accumulated by new managers increases. However, they argue that this is not the appropriate comparison. They argue that the appropriate comparison is between clubs who change their manager and those clubs who retain their manager despite a poor run of results. When such a comparison is made then replacing the manager is not the panacea some would claim. The data used by Anderson & Sally, as set out in Figure 53 from The Numbers Game, is reproduced below.