Interesting stats, but a 40 odd percent win rate does show improved performance as most sacked coaches are running at very low numbers (probably less than 20% - Note I don't have time to actually check).

When the coach changes the tactics, that the opposing team have prepared for, also change. I think this may also account for the dead cat bounce experienced by the teams changing coaches. It is also why it is not a sustainable improvement.

We simply need to be ready for any tactical change the Saints may make, but the best way to do that is control the footy on your terms.