Under Moyes, Everton were always tough to beat: that is the primary reason he replaced fellow Scot Sir Alex Ferguson at United. Like his predecessor, Moyes prioritises consistent and committed players above flair players.
His Everton side could best be described as a physically strong team with a focus on defensive solidity—as far as you can get from a Martinez team.
Analysts and fans alike are wondering what the Spaniard's first steps will be at Everton.
He has a fundamental belief that football should be played through slick passing and attacking the opposition, and deserves huge credit for assisting chairman Huw Jenkins in laying such sound foundations at Swansea before moving to Wigan.
The former Real Zaragoza midfielder has now been brought to Everton by Bill Kenwright to build upon Moyes' 11 years in charge.
Statistically, Everton and Wigan were quite similar last season. However, that is where the similarities end.
Everton, using a variant on 4-4-2, played a more direct style of football under Moyes and were orientated upon using the full-backs to push on. Wigan, however, utilized a 3-4-3 that morphed into a 3-6-1 when under pressure, using the centre of the pitch to initiate most of their attacks.
Martinez is already trying to mesh these philosophies. During preseason and in training he has toyed with the idea of a 3-5-2 formation, with Everton's full-backs being pushed on as wing-backs.
Leighton Baines and Seamus Coleman are so attack-minded that they were used as marauding full-backs under Moyes. The downside of this tactic is that when caught out of position, the defence could become overloaded.
Graeme Jones, Martinez's assistant manager, has already indicated to Daniel McDonnell of the Irish Independent that this is the direction the club will go in next season.
Seamus and Leighton can be our wing-backs next season. We used to watch them when we were at our previous club, and Seamus would cross while Leighton would be at the back post in the box.
They're like wing-backs anyway and if they can do that from a full-back role too, then we're in business.
With the full-backs pushing on, the initiative then fell to whoever was playing in central midfield to drop deep and cover in the middle as a centre-half slid right or left to fill the full-back void.
Phil Neville filled this defensive midfield role to great effect and has now been succeeded by Darron Gibson, who executes the role with aplomb.
With Everton boasting the likes of Phil Jagielka, Sylvain Distin, Johnny Heitinga and recent capture from Wigan Antolin Alcaraz, Martinez now has the very real option of playing three centre-halves. Add in the fact that the Daily Mail are reporting that the Toffees have lodged a £5 million bid for Ajax defender Toby Alderweireld, and it is obvious that Everton will go 3-5-2 next season.
In theory, this could give them the kind of attacking outlet they did not have under Moyes, whilst also allowing for defensive solidity. The drawback of a 3-5-2, however, is that wide midfielders are no longer necessary.
Baines and Steven Pienaar built a phenomenal relationship last season. Between them, they created 44 percent of Everton's goalscoring chances. Pienaar is a right-footed creative dynamo who, for some reason, failed to make the cut at Spurs.
At Everton, he is at the centre of all the good play and is exactly the kind of player Martinez has used in the past. His inclusion in Martinez's team, regardless of formation, is almost guaranteed. He is the fulcrum upon which their team turned under Moyes and is essential in linking defence and attack during transitions.
Pienaar should be joined in midfield by the defensively-minded Gibson, the workaholic Leon Osman, the irrepressible Marouane Fellaini and the attacking Kevin Mirallas. These five will battle it out for the three central positions, with Fellaini the obvious choice to link midfield and attack.
That leaves Arouna Kone and Nikica Jelavic fighting it out for the lone striker role.
When one takes a helicopter view of the Everton team and places Martinez's philosophy upon it, one can easily see why many fans are optimistic about the chances of their team improving.
The new manager is keen to not overhaul Everton completely, though. He recognises that Moyes' old side just needs tweaking to progress to the next level. Everton only finished lower than eighth twice under the Scot.
As per the Daily Mirror:
It has not been a huge revolution. It has been more adapting to the new way of working and having people that I trust and I know can do the jobs that I need them to.
I have been very impressed with the staff who are already here, but there is another part where we need to do things in a certain way and I need people who can do that straight away without losing six or seven months for them to get to know what I want.
I haven't changed anything, but remember we lost the majority of the staff who were heads of department to Manchester United.
Sometimes you have to change the heads of department because, to bring the players that we need now, they need to have a clear understanding of what I need and what I want and the way I am going to play.
The one thing that Moyes was always criticised for was the one-dimensional nature of his teams. In other words, he had no Plan B. In three short months in charge, Martinez has already established a different style of play and used at least four different formations.
The elephant in the room for Martinez, however, is Manchester United's looming shadow. Having been rebuffed by Barcelona and Cesc Fabregas, United are now trying to poach Fellaini and Baines from their manager's old club, report multiple media sources including the Independent.
Everton's fans are understandably up in arms. They did not chant, "Who the **** are Man United?" (per the Daily Express) at Moyes' last game in charge for nothing.
Fellaini is valued at around £23 million, so United's bid of £35 million for both would value Baines at just £12 million. The club have flatly refused that initial offer. However, the Guardian is reporting that £40 million might just be enough to pry the pair away.
Bryan Oviedo has deputised for Baines on the left side of defence and could, in time, inherit the England international's position. For the moment, though, he looks raw.
The real problem for Everton will be Fellaini. The Belgian international scored 11 goals last season and was the Toffees' main threat. If he leaves, there will be a huge void in midfield. None from Gibson, Pienaar, Osman or the impressive Ross Barkley can be relied upon to score regularly.
Mirallas, Fellaini's international teammate, could fill that gap—even though he is a completely different style of player.
This season will be all about Everton coming to terms with life without Moyes: coping with a different style of play, a new manager and another coaching setup.
However consistent they were under Moyes, Everton never won a trophy which is something Martinez can claim to have done after his Wigan team out-fought, out-thought and out-played high-spending Manchester City in last season's FA Cup final.
Moving towards the Martinez style of play will probably result in a more inconsistent Everton than the one of recent years.
But in time, and with shrewd investment, Everton could become the Premier League's dark horses.
Their shot at the top four this season relies upon keeping Baines and Fellaini. If they can do a Daniel Levy and fend off interest from a bigger fish, even for a year, they can achieve much.
If the two leave, as is now looking a distinct possibility, Everton will not be hit as badly as many expect.
Progress will not be measured in points, it will be measured in style. Under those terms, and with the possibility of cup success, Everton could surprise everyone.
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