Managers might play a small part in it but they're never going to win a league on their own. Martinez is a good manager but Wigan won't win the league any time soon. If he was manager of Man U for 3 years though I'd expect him to win the league at some point. Arsenal obviously are a lot bigger than Wigan, but they're also some way smaller than the Manchester clubs and Chelsea who are the only three clubs who can realistically win a title in the next few years without something changing drastically. Arsenal not winning the league isn't down to their manager, it's for the same reason as the other 89 clubs that haven't won it recently, they aren't good enough. Wenger, tit as he may be, isn't a bad manager just because he hasn't won a trophy recently. So going back to the point, managers should not be expected to win a trophy every season because there's a lot of competition and only so many trophies. Far too many clubs get too big for their boots and throw a strop when they go a season without a trophy and sack their manager, forgetting that they've actually been doing well for their size or sometimes even over-achieving, and then they inevitably suffer from the disruption that sacking a manager causes. Thankfully, it's that very principle that will keep Leeds out of the top flight for the next few years. They aren't good enough for promotion yet, and every time a manager fails to get them promoted he gets sacked and they try someone else, starting the whole project again.
I'm pretty sure you've missed the point. I was simply saying sacking managers for failing to deliver is has been to the benefit of some clubs in the past and gave the example below; Arsenal had a team capable of winning trophies for at least 2004-2009, they stuck with a manager, he didn't deliver and they won nothing. Chelsea assembled a squad of similar strength after their take over in 2003, then sacked Ranieri for not winning trophies, they hired Mourinho and won trophies. Everything you've posted is replying to points that I haven't made.