First off I'd just like to say I'm not calling for Martinez to go, my stance is always give a manager 3-4 seasons for a fair analysis so if we finish the season with signs of progression then another season is a fair deal, if we stand still then I think 3 seasons to make progress is enough to judge fairly whether that is happening.
Implications if Martinez were to go at the end of the season:
A lot of players have faith in him, we could easily see Lukaku Stones McCarthy not interested in playing for Everton under another manager.
The progress of young players could be hampered. Deulofeu Barkley Galloway may not have the faith of a new manager.
His exit could see the end of young world class talent coming to Everton. Lukaku Deulofeu Besic deals were all teed up by Martinez, could another manager offer the same proposition to attract these players?
Lastly he has shown in his time here that he is capable of winning any game on his day. Arsenal United and Chelsea have all been dismantled at Goodison in a manner never seen in the prem before. Tie that to his trophy winning pedigree at Wigan and getting rid of him may result in getting rid of the one manager who could inspire a series of individual performances to win a trophy.
Potential benefits if he were to go (obviously impossible to predict what a new manager would bring):
A new manager could bring in a new keeper and instantly improve the defensive solidity of the side.
A new manager may believe in the importance of a progressive midfielder who can dictate play and make Everton take the game to teams on the front foot rather than the counter.
A new manager may instruct the players to press without the ball and not excuse luxury defensive performances from the likes of Kone Barkley and Deulofeu.
A new manager may play players in their correct position meaning an even more influential Ross and the rehabilitation of Mirallas.
A new manager may create a team and squad that does not fall to pieces as soon as one vital cog is missing.
With Deulofeu Lukaku and Barkley in the side the offensive potential of this team is one of the best in the league. If we can even only adequately match the defensive aspect we'd be a proposition that could properly challenge for fourth considering the weakness of other teams in the league. Next year could be a crucial one as it may be Van Gasls last year and Chelsea will be outside the top 4. If we stay with Martinez and continue midtable the landscape could switch to see Mourinho back on top with Chelsea, Guardiola at Utd or City, and Wenger buying another world beater.
Pros and cons both ways but fans have to accept that in this league now you get a few seasons as a window for success before the vultures dismantle it. If this season is a dud this team will probably get dismantled. Does Martinez deserve to rebuild it if he couldn't get success out of world class talents like Lukaku Barkley Del and Stones?