Arsène Wenger allowed himself a nostalgic smile as he recalled how routine player checks on a Friday produced some impressive results in the old days. Building up to the weekend, everyone was weighed and underwent various tests, and when Arsenal had a team of powerhouses, the scales were put under a fair amount of strain. “Petit, Vieira, Parlour,” Wenger said. “It was quite something there.”

These days the checks produce rather different numbers. It would not surprise too many in football to discover that the Premier League team who came in with the lowest figures in weight and height on the opening weekend of this season were Arsenal. Wenger’s starting XI averaged 5ft 10in, some three inches less than the tallest teams (Chelsea, Crystal Palace, QPR, Stoke and West Ham). An average weight of 10st 12lbs was way below QPR’s hulking 12st 7 lbs.

Such data is useful only up to a point. Put Lionel Messi’s height and weight next to Cristiano Ronaldo’s and the contrast would be extreme, without being any kind of sensible reflection on their qualities. Besides, Wenger felt inclined to joke about his present team being comparatively lean. “Because our diet is better,” he quipped.

But there is a serious element to the question of whether Wenger’s preference for small, nimble players has an effect. That certainly seemed to be the case in the high-profile games last season when Arsenal were far too easily outmuscled and rendered impotent. It was a particular problem away from home against the strongest clubs, and was manifested in some shocking scorelines. There seemed to be an obvious frailty – physical and mental – that left Arsenal reduced. They were pulverised each time they visited a rival from the top five. Might that be in part down to being smaller and less powerful than their opponents?

The fact that Arsenal had an excellent away record against teams lower in the league suggests that their emphasis on technique was generally enough to overcome routine challenges. But when it came to the sharp end, reliance on technique alone was clearly not enough.

Arsenal travel to Goodison Parkon Saturday, one of the scenes of their horror shows last season. That defeat at Everton – a comprehensive 3-0 win for Roberto Martínez’s team in April – exposed the soft underbelly that Premier League managers tend to target. The image of Romelu Lukaku bulldozing through, with waves of blue attacks spreading anxiety through Arsenal’s ranks, is still very clear in Wenger’s mind. “We were a bit bullied,” he says. “In the quality of our performance – and even more than that in mental resistance, the steel on the day – that was one of our low points.”

Arsenal need to make a radical improvement in terms of their levels in the trickiest away assignments. It was interesting that when Wenger reflected on why his team were perceived as fragile he pondered how the choice of a player of Mikel Arteta’s physique as a holding midfielder might be part of the explanation. “Maybe because we use more technical players in the middle of the park, especially Arteta,” he said. “You always want to improve technically and sometimes when you want to do that you go a bit more for skill, which can be more lightweight.”

Wenger is still “open” to buying a defensive midfielder which would instil more power and height in that department. All the players on Arsenal’s radar this summer in that position – Sami Khedira, William Carvalho and Adrien Rabiot – are around 6ft 2in, which gives a completely different dynamic to when Wenger picks two from Arteta (who is out of Saturday’s game with an ankle injury), Mathieu Flamini, Aaron Ramsey or Jack Wilshere (all 5ft 10in or under). Although Calum Chambers is an option in defensive midfield with more physical presence, the youngster is needed at the back for now.

Is it risky to go for smaller players in the Premier League? “First of all it is not a target,” Wenger said. “When we buy a player we do not look how heavy he is but how good he is.”

A trip to Goodison Park does not come at the ideal time between the Champions League qualification matches against Besiktas. Any sign of fatigue will be pounced on. Wenger knows how much of a test this is of Arsenal’s mettle. He thinks Martínez’s team are even better placed to challenge for a Champions League position this season, now that they have exerted their ambition by recruiting players in the £30m bracket.

Last season Wenger was worried that Everton would make the top four at Arsenal’s expense after the game at Goodison. “Because it was not in our hands any more,” he said. “It was only their defeat against Crystal Palace at home that allowed us to get there.”

He added: “It was very tight last year. We finished with 79 points and I think it’s the first time since I am in England that with 79 points that you finish fourth. Look at the tables – that never existed before. Even if the Premier League was more interesting than ever last season, the top four teams took more points together than in any other year. For Everton, it’s the first time a team on 72 points don’t get in the top four. It was very difficult last season.”

Martínez is not banking on another exhibition against Arsenal. “I’m not sure we are going to surprise them as much,” he said. “I felt last season we were very good in everything we did. Remember that was the first time we scored the first goal against Arsenal. Whoever is clinical on the day has got a big advantage, because last season whoever scored first had a big advantage and I think it will be the same again.”

After all that punishment against the Premier League’s highest achievers last season, Arsenal have to find a way to make themselves feel somehow bigger.