I wonder if Arsenal ( which used to play possession football some time back ) was successful in England on account of this.
Also, teams like Barcelona which play the game with long periods of possession and are extremely successful.
The same for Barcelona - Pep Guardiola, known for being the most successful manager to insist on "possession first" football, was not particularly successful at Bayern (he inherited a team winning all domestic and international trophies in 2013, and only managed to win domestically for the following two years), and is somewhat struggling at Man City.
Famously, Leicester City won the Premier League last year playing the exact opposite of possession football. Someone like Jamie Vardy, capable of quick bursts of speed but with relatively poor skills on the ball, would be embarrassing to watch at Arsenal or Barcelona, but was absolutely lethal for the Foxes last year.
Possession football, like "moneyball" baseball, looks nice on paper but IMHO is a red herring. Technically gifted players will like to hold the ball, and gifted players naturally tend to win more because they are better, so people link this and that and say you have to hold the ball to win. What you really need to be successful is to play a style that suits your players. If you have Messi, Xavi and Iniesta, you play possession; if you have Vardy, Mahrez and Kante, you play counter-attack and long balls in space.
Teams that have beaten Barcelona often just let them have the ball, then wait for them to make a mistake. And teams that are set up for long periods of possession have a hard time quickly switching to defence.
Back to back FA Cups in 2013-14 and 2014-15? I think the rest of your analysis is pretty valid however.
Two things; ok there appears to have been an obvious fallacy in the reasoning, but the data was gathered at the wrong time - the game was changing, TV was becoming fundamental to it, chopper Harris was disappearing and strange things like fitness were becoming important. Secondly and most importantly, the analysis revealed something that was quite widely believed already. Ok it was wrong, but it was believed, and immediately evidence of the success of the strategy was assembled. I see this all the time; confirm someones ideas with data and you will be loved. It's rare that you will be found out, and even when you are it might be 20 years before it happens.
Looks like this season they have taken a leaf out of Leicester's book and gone for the pacy trident of Iwobi, Sanchez and Walcott to launch counters with.