Ok, let's start from the back and move forward...
Keeper:
Martinez signed Joel who was criticised early on for lacking confidence and for coming from Wigan. Incidentally, my biggest criticism of Martinez was the time it took him to make that change, as Howard had been diminishing for the last few years of Moyes time.
Defence:
Its easy to blame Martinez again for this, but again, it was a defence he inherited from Moyes, and 1 which had its best years behind it. For all the Criticism Martinez gets for the state of the squad he left, he had 1 hell of a building job to do when he took over, with Moyes team reaching the end of another cycle, and we all know Martinez was brought in to manage the team on a budget, much like Moyes had, and all prior to Moshiri taking over.
He gets none of the credit for the team performances in year 1, because it was built on Moyes defence, but he's never excused for the eventual decline of said defence after that, even though, Alcaraz and Mori aside, it was still by and large a Moyes defence, who apparently forgot how to defend because Martinez hypnotised them all.
Fitness:
I won't have it that the every single 1 of the players were so unfit under Martinez that it took an entire preseason and 6 months of the current season to undo all that bad work. All players reset in the summer and rebuild again from July onwards. The fitness or lack of, in the back end of Martinez era was as much a symptom of a lack of confidence and an apparent lack of effort from the players who he fallen foul of near the end. Barry implied as much in his interview. Now if you are talking about intensity, that's a different story, and a matter of tactics and conditioning for a different style of play.
Set Pieces:
It always makes me laugh at the thought that Martinez didn't practice any set pieces, but not as much as the thought that professional players who had practiced them for rest of their entire careers suddenly forgot how to do it in less than the space of 1 year. I suppose these players, like Rooney and Ronaldo who stay behind for hours after training to practice taking free kicks would've been brought to task by Evil Bobby as well,had they had the misfortune of playing under his dictatorship.
Midfield:
Our midfield has improved because we have signed 3/4 quality midfielders with our improved budget, instead of signing the likes of Naismith, Cleverley, McGeady, Gibson, Barry, Deulofeu, Besic etc for a combined total of about the price we signed Lookman for. Add to that the gradual emergence of our golden generation, who I'm convinced Martinez was looking to introduce as soon as they were ready.
Attack:
Rom is still scoring our goals.
Team Spirit:
There was an obvious falling out and the team suffered massively for it. Poor run of results, lack of confidence and form and a fan base who love to hound out anyone for failing their expectations, is a toxic mix.
Martinez didn't help himself with his relentless positivity, his loyalty to players who clearly weren't as loyal to him in return, and a stubbornness in continuing down a path that was failing him.
But he's not our manager any more. Leave him alone and stop comparing every decent result against 1 of his poor ones. It helps noone.
P. S. Last year we battered Stoke away. Just saying.
I'm going to begin this reply by saying you imply that my post is primarily anti-Martinez - which in some ways it was - but it's more about the improvements that can be seen by the team he left behind after 3 years in the job and the team we have now under a new manager. You can only improve on things which were lacking in the first place. If things were good, there would be no room for improvement. The difference between what Martinez left us with and what he have now is undeniably large.
Anyway. Keeper first. I said Joel had improved massively. He has. This could be down to personal development or a change in training or both. Who knows. I'm not sure what your first point is here because you didn't really say anything other than Martinez signed him - which we can both agree on because it's a fact and not opinion.
Defence. You say that the team that Martinez inherited from Moyes was nearing the end of it's cycle, which implies that they were past their best and left Martinez with a massive rebuilding job.
This isn't really true considering 4 years later, 3 of the back 4 (Coleman, Jagielka & Baines) are still playing under Koeman, and playing much better than they were during the last 2 years of Martinez's tenure. Admittedly Jagielka is now more of a squad player with a limited part to play but that has only happened this season. In fact the only thing that Martinez changed from the Moyes defence was replacing Distin with Stones (whom, it could be argued, was mismanaged but that is no longer relevant). So we have 3 of the same back 4 Moyes left behind still playing yet we are a much more defensively sound team. If it's not the players then it's the manager/tactics that has improved.
Fitness. New manager steps in with a new fitness coach and a new fitness regime that focuses on intensity and suddenly we are much fitter. Barry admitted in his interview that the standards of near enough everything slipped under Martinez. Koeman won't let that happen. That is an improvement.
Set pieces. It's established that Martinez did not pay much attention to set pieces. It was evident from the woeful way we defended them and tried to utilise our own. New manager and suddenly we aren't as bad. Perhaps Koeman realises them for what they are - opportunities. It takes practice to upkeep skills. I learned to ride a bike when I was young. I haven't been on one for a long time. If I suddenly got on one today I probably wouldn't fall but I wouldn't be very stable either. Maybe that's a poor analogy but my point is that if enough time is spent in practice on set pieces (both attacking and defending) then they wouldn't have been as poor as they were. We have improved.
Midfield. I acknowledged that our improvements were perhaps more to do with recruitment than tactical changes. Maybe things would have been different if Martinez had Gueye but I - and probably many others - doubt it would have made an overwhelming difference.
Attack. Rom does score our goals. Correct. He is our striker. But as I said, we've improved in terms of how direct we are now in and around the box. This is perhaps down to confidence but that would be the confidence instilled in our team by a new manager.
The fact is that Martinez was probably ultimately responsible for whatever happened behind the scenes in terms of confidence. Whether it was, as you say, his relentless positivity in the face of disappointment or his tactical stubbornness, it clearly left a void between himself and the team.
Our new manager is probably our greatest improvement overall. Look at the game against Stoke, where he changed tactics drastically at half time in order to combat a difficult Stoke side. When did Martinez do that? That, in my eyes, is a massive improvement. We have a manager who is pragmatic and realistic and unafraid to tell the team when they haven't been good enough. That is improvement.
I've tried to keep this post in line with the theme of "improvements" as it fits the thread, but I won't be drawn into any further Martinez talk because he has his own thread now.
I agree with a lot of what you said mate, but we have to look at the negatives from last season in order to see the positives this season, that's how we measure improvement. Unfortunately our last manager was responsible for a lot of those negatives.