What the data says about results after a managerial change, how long any effect lasts, and why the timing misleads people.
There is a measurable improvement in results immediately after a managerial change, typically lasting a handful of matches. The interesting question is whether the new manager caused it, and the honest answer is mostly no.
Managers are sacked after bad runs, and bad runs are usually a mix of genuine problems and poor luck. Whatever part was luck was always going to correct itself, regardless of who was in charge. Statisticians call this regression to the mean, and it accounts for most of the apparent bounce.
There is a small genuine effect on top: players auditioning for a new boss run harder, and a fresh tactical setup takes opponents a couple of weeks to solve. But it is smaller than the narrative suggests and it fades quickly, so the market's tendency to overreact to a new appointment is itself the opportunity.
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