The Hammers sit seventh in the Barclays Premier League, having won three of their opening seven fixtures, and Allardyce was backed in the transfer market over the summer - with a change in approach earning plaudits in recent weeks.
It is a far cry from last season when, in the midst of an injury crisis, the club's fans were calling on co-owners Sullivan and David Gold to replace Allardyce - with many pointing at the style of play as their main gripe with the former Bolton and Blackburn boss.
But Sullivan believes the 59-year-old deserves credit for adopting a diamond formation which has brought the best out of the likes of Stewart Downing, as well as new signings Alex Song, Diafra Sakho and Enner Valencia.
"There is a lot of optimism about the place now," Sullivan told the Evening Standard.
"I genuinely believe we have the best squad since we've been at the club
We've signed some high-energy, younger players and we have discovered the 'West Ham way'.
"He (Allardyce) changed the style after that to a diamond formation
Sam made that decision so he deserves the accolades because, had it not worked, he would have been castigated."
Victories over Liverpool and QPR, as well as an entertaining draw at Hull, have followed the new formation as Allardyce starts to win over his detractors.
With a move the Olympic Stadium coming ahead of the 2016/17 season, the pressure will be on to not only keep West Ham in the Premier League but to be a club striving for trophies - and Allardyce will hope to be the man who takes them into their new home.
The owners opted to keep him at the helm at the end of last season despite the clamour to see him sacked but, with Allardyce's current deal expiring in the summer, it will depend on results between now and then as to whether he leads West Ham into a fifth season.
"We have a policy - and it's as much for Sam as us - that we sit down at the end of the season, maybe a bit earlier if we're safe, and judge things over an entire season," Sullivan added.
"We've always done it that way
Last year I was being asked at various times if Sam would be going but my answer was always that we'd look at it at the end of the campaign
We're very loyal to our managers
"We always talk on a Monday or the day after a midweek match and if he has a problem he calls me
We all want the same thing and that is the best for this club
Sam wants to be successful and he's very flexible at looking at ways to achieve that
The change in formation was not my idea - he's the one who made that bold decision to change the strategy."
Source : PA
Source: PA