Any suggestion that Allardyce 'saved' Everton from relegation is nonsense. They were in the relegation zone when Ronald Koeman left, but David Unsworth had gotten the Toffees up to 13th before Allardyce arrived. Big Sam then took them from the precarious lows of two points off ninth to the heady heights of eighth.
Yes, he improved them, in the same way that I could improve a rotten piece of meat by adding salt and pepper. It doesn't mean that I won't wake up with a stomach ache, and it doesn't mean that Everton were good after he took over. They were just better than before.
The search for a replacement begins and the name on most people's lips is that of former Watford manager Marco Silva. Everton tried to sign Silva in November, unsettling the Portuguese manager enough for Watford to part company with him two months later. The Hornets have been blaming Everton for ruining their season ever since.
Silva clearly has talent as a manager. He got Estoril promoted to the Portuguese Primeira Liga and won the Taça de Portugal with Sporting. He then guided Olympiacos to the league title in Greece - not too difficult, admittedly - but it was enough to earn him a move to England.
Going to Hull looked like career suicide, with the Tigers odds-on favourites to be relegated, but Silva actually did a sterling job there, even if he couldn't prevent the inevitable. It earned him a move to Vicarage Road and he had Watford as high as fourth in the table before the Everton inquiry.
Given his admirable record, it may come as some surprise that I don't think he's the right man for the Everton job. Silva would clearly jump at the chance to join Everton, as he did in November before Watford blocked the move. But I find myself reminded of an old piece of dating advice: if he'll cheat on another girl to be with you, he'll cheat on you to be with someone else.
Appointing Silva last November, as a short term fix, made sense. But if Everton's ambitions truly are as big as majority shareholder Farhad Moshiri says they are, they need someone who is going to stick around for the long haul - not one who will jump ship to the first suitor that comes calling.
If it is Marco Silva coming in as the next Everton manager, let’s get behind him. Let’s be positive. He’ll hopefully have an attacking style of football and get the players putting the effort in. At the end of the day, whether you like him or not, at least he’s not Sam Allardyce.— Everton Blue Army (@EvertonBlueArmy) May 14, 2018
After all, Everton have huge ambitions - Moshiri's stated intention is to get them playing Champions League football. He showed his dedication to the cause this season by splashing out on five different signings in excess of £20m, including double that for Gylfi Sigurdsson. Now he needs a manager who will show him the same commitment.
Who could this elusive man be? Arsene Wenger has been mentioned - he seems keen to stay in management - but a young manager would be better. Sean Dyche perhaps, but he thrives better on a small budget. David Moyes has been linked with a return to Goodison Park after leaving West Ham, but that would be playing it too safe.
No, if Everton are serious about their Champions League ambitions then a young manager with European experience would be ideal. No, I already said not Marco Silva! But what about one of his countrymen - Shakhtar Donetsk's Paulo Fonseca.
Fonseca came to Shakhtar Donetsk in a huge transitional moment for the club. Outgoing manager Mircea Lucescu had been in charge at the Donbass Arena for 12 years. With eight league titles and six Ukrainian Cups, he was a Shakhtar legend - essentially the Romanian Sir Alex Ferguson. Stepping into his shoes would be daunting prospect for any manager.
But Fonseca has filled those shoes with ease, seamlessly picking up where Lucescu left off and guiding a team which had become complacent back to the pinnacle of Ukrainian football. He has completed the domestic double in both of his first two seasons, and most bookmakers have installed him as second favourite for the Everton job behind Silva.
He also has the Champions League pedigree that Everton hope he could apply at Goodison Park. This season Shakhtar navigated a difficult group containing Manchester City and Italian title challengers Napoli to reach the knockout stages, where they were beaten by Roma.
Fonseca also has a track record of getting a lesser side into the Champions League. In his case it was Paços de Ferreira, who he guided to an all-time best league finish of third in 2012/13. Fonseca left for Porto that summer and Paços didn't make the group stages, but he returned the following season and led them to another top half finish.
To compare Fonseca's situation at Paços with the current one at Everton would be misleading. Paços had far less money to play with than Everton, but they were also in a weaker league - although cracking the top three in Portugal is no mean feat.
But the fact that he has shown himself capable of working wonders on a small budget under little pressure at Pacos, and equally capable of bringing success under huge pressure at Shakhtar Donetsk, suggests that he is not a one-trick pony.
The only concern over Fonseca is that he has never stayed at a club for long - Shakhtar is the first club he's called home for more than one consecutive season. But unlike Silva, it is his achievements and not his attitude which results in such short spells. It would be up to Everton to convince him that theirs is a project worth buying into for an extended period of time.
It is a risk to appoint a manager with no Premier League experience. Like it was when Liverpool appointed Jurgen Klopp, or when Manchester City appointed Pep Guardiola. Both of those appointments have paid off handsomely. An ambitious club calls for an ambitious appointment, and that's just what Paulo Fonseca would be.
You know what isn't a risk? Sam Allardyce. Sometimes you need to take the plunge to get results.