One day during the many months that Bournemouth spent analysing the man who would eventually become their coach, they saw his Rayo Vallecano team run through a routine that looked familiar. If at first they could not quite put their finger on why, when they got the chance to ask him about it, everything fell into place. Yes, Andoni Iraola told them, it’s one of Eddie Howe’s. Iraola, described as a “sponge” by his former coach Joaquín Caparrós, soaking up everything he saw and heard, had learned from the Englishman, just as he had from Marcelo Bielsa, Ernesto Valverde and Patrick Vieira. From everyone.

Howe had learned from him, too, a lot shared. Howe, a frequent visitor to Spain, travelled to Madrid shortly before becoming Newcastle manager to see Atlético and Rayo. Rayo lack the basic resources elite teams consider standard, but there was good reason to go. He watched Iraola train, spent time with him and returned even more impressed. Analysts and sporting directors came from England’s big clubs, too, a quiet chatter commencing; something was happening over there, a coach emerging who was different.

Related: Bournemouth’s ruthless O’Neil sacking is a gamble history shows could work | Ben Fisher

Now Bournemouth have brought him to the Premier League. If sacking Gary O’Neil shocked, in Iraola they see an upgrade. Unable to match other clubs financially, you have to find other ways to compete. Here is an innovative, analytical coach who has done just that, charged with building a team, an identity.

Iraola was not always sure he wanted to be a coach. Born in Usurbil, a town of 6,308 people in the northern Gipuzkoa province, a full-back who gave up a law degree and played 510 games for Athletic Bilbao, he had quite fancied opening a bookshop. Others were more certain and it can appear almost inevitable, a product of his place, his personality, the experiences accumulated.

Bournemouth have signed Justin Kluivert from Roma for an undisclosed fee. The 24-year-old winger, who was capped twice by the Netherlands in 2018, has agreed a "long-term contract" at the Vitality Stadium. He becomes the club's first signing since the appointment of Andoni Iraola as head coach."

We are delighted to have made Justin our first signing ahead of the new season," said Bournemouth's chief executive, Neill Blake. "Justin is an exciting and versatile attacking player who has an eye for goal. He is pacy, direct and boasts a high level of technical ability."

Kluivert, the son of the Netherlands legend Patrick Kluivert, began his career at Ajax before moving to Serie A in 2018. He scored nine goals in 68 appearances for Roma and spent last season on loan at Valencia following similar spells with RB Leipzig and Nice.

Astonishingly, his arrival alongside those of Unai Emery and Julen Lopetegui to join Mikel Arteta means Spain’s smallest province – at 1,980 square km, Gipuzkoa is dwarfed by Dorset – provides four Premier League managers. Iraola and Arteta played alongside Xabi Alonso, another top-flight manager, at the same youth club, Antiguoko. As a player, Iraola stood out for his reading of the game; an atypical right-back at whose feet moves began, never one to make a noise and more passer than runner, he was an ever-present over 12 seasons and under seven coaches in Bilbao.

He learned from the Europa League winner José Luis Mendilibar; Bielsa, under whom he and Carlos Gurpegui were the captains and a conduit to the squad; and Valverde, his coach in the under-19s, B team and twice in the first team. Joining New York City at 33, where he was fascinated by the NFL and perfected his English, opened his eyes to a new position in midfield and a different perspective under Vieira – vital, he admits, in the process towards becoming a coach, an idea forming.

Enough, at least to try it out – even if just putting out the cones back at Antiguoko – and then get drawn in. “He might have not always been keen and being a coach is a huge sacrifice, but football is a drug,” says Galder Cerrajería, who coincided with Iraola at Athletic and later played under him at Mirandés. “And you could always see he would be a coach in the way he observed what they did. He already was one, like an assistant on the pitch.”

There were only two people on the 2018 pro licence course run by the Spanish federation whom fellow graduate Gica Craioveanu says he would have bet on making it: Lionel Scaloni and Iraola. “It was his personality, his knowhow,” the former Romania international says. “He likes modern, attacking football, reads the game, sees opponents clearly, and does it all with a light touch.”

That summer Iraola got his first job, at the Cypriot side AEK Larnaca, signed by the sporting director, Ander Murillo, a former teammate at Antiguoko and Athletic. He was only 36, the experience more a lesson than a demonstration of the ability he showed upon returning to Spain to take charge of Mirandés then Rayo.

Mirandés had just been promoted to the second tier and had the 20th biggest budget out of 22. Despite spending six of the opening 10 weeks in the relegation zone, they finished 11th. They also defeated top-flight Celta, Sevilla and Villarreal on an extraordinary run to the Copa del Rey semi-finals.

At Rayo, a club where the captain said it was “problem after problem”, he won promotion to the first division. To a backdrop of crisis, with the second-lowest expenditure in primera, essentially the same team as in segunda and coaching staff having to buy basic materials out of their own pocket, they spent much of the season on the edge of Europe, eventually finishing 11th and reaching a first cup semi-final in 40 years.

“Next year, Rayo-Liverpool!” the chant ran and it would be repeated: Iraola’s side reached the final day of 2022-23 with a chance of a second ever European place. They had beaten Real Madrid with a budget 18 times smaller. In four games under Iraola they remained undefeated against Barcelona. Eight of the starting XI that defeated Xavi Hernández’s team this past season had been there in the second tier, its total cost less than £10m.

But it wasn’t just what his teams had done, it was how they had done it: “intense pressure, high block, vertical, daring, open, quick”, in the words of the Mirandés defender Carlos Julio Martínez. In Mirandés’s cup run, they put two past Celta, three past Sevilla, four past Villarreal. “We were a whirlwind,” Cerrajería says. The defender Sergio González says: “We weren’t scared of anyone or anything. There was humility, but the coach transmitted huge ambition, and you watch Rayo and it’s very clearly an Andoni Iraola team, everything worked out, mechanised.”

Unlike the typical small, promoted team, Rayo did not park the bus; instead, they took it for a ride, and it was wild. “He doesn’t want the game to be under control: he wants things to happen,” says their midfielder Mario Suárez. “Rob in the opposition’s half, direct, open the pitch, get into the area.”

The pitch is divided into sectors, individual responsibilities imposed. The analysis is profound, data analysed and acted upon, the apparent anarchy nothing of the sort. Organised chaos may be one way of putting it and it’s a description Iraola likes. In fact, he says: “I prefer too much chaos to too much organisation. I prefer to play at a high pace, even if it means a touch of hastiness, than play at a lower pace and have a bit more control.” Only one side won the ball more than them in La Liga last year; only one team lost it more too.

An admirer of German football, of Marco Rose especially, Iraola and his highly rated assistants Iñigo Pérez and Pablo de la Torre built a physical team set up in a 4-2-3-1 where the No 8 is vital, the forwards run and run and the full-backs fly, where the opposition are invited into a trap then hunted down: relentless, attacking by stampede, always going at you, with and without the ball. Xavi called them the biggest pain in the arse in La Liga.

The stats reinforce the eye test. This past season the three players with the most high-intensity sprints in Spain play for Rayo: the winger Álvaro García and the full-backs Fran García and Iván Balliu. Only Bayern Munich forced more high turnovers leading to shots in Europe’s big five leagues. In Spain, only Barcelona and Athletic, spent more time in the opposition’s half. Only Athletic put more balls into the box. No one played more long passes. Alejandro Catena, a central defender, completed more than anyone else. Only four teams made more chances, only five had more shots, only two goalkeepers made fewer saves.

Iraola talks about “volume”. As Álvaro García puts it: if there are “lots of crosses, lots of people arriving in the area, lots of attacks … if there are three crosses in the same move, one will come off; it’s a matter of time”.

Breathless and brilliant, over the past two years there has been nowhere in football more fun than Vallecas. Iraola engages, too. One day, he was cycling around the neighbourhood when a fan stopped him. Rayo were not playing well, and the supporter wanted to know why. Iraola got off, listened and explained. He had refused to leave mid-season and before he departed a banner said: “Thanks for making us dream.”

There may be no team in Spain with an identity so defined, and that was an attraction to Bournemouth. The metrics in which Rayo stand at the top are ones where Bournemouth stand near the bottom.

“We never changed our style,” Suárez says. “There would be adaptations depending on opponents but the idea remained. The players know exactly what to do. It’s an enjoyable, attractive style, but you have to run a lot. He focused on the physical data but that work was always done with the ball. He manages players well, respects them, gives them space. He virtually never goes in our dressing room at the training ground. And when there’s a bad run, he never loses the plot.”

Some words recur in conversations with those who have worked with Iraola. “Brave” is one, “clear” another but “introvert” comes up, too, even “timid”, and that profile is one players appreciate. “There’s no smoke‑selling,” one says; no bullshit, in other words.

An hour after finishing talking about his former coach, Martínez sends a follow-up message, keen to stress something he already mentioned: “We thought: ‘Bloody hell, Andoni Iraola is a legend at Athletic, he played 500 first division games, but he’s so humble, so normal.’ It was like we’d known him our entire life. He never wore that label: ‘super player from primera’. We respected him so much. He’s a spectacular coach.”

Cerrajería says: “I would define him as ‘normal’, and that’s not so normal. He has good people around him too, and he understands players, empathises … He was intelligent, he watched coaches, saw what they did, took it all on. He would take on 10 or 15 drills from Bielsa, eight or 10 from Valverde, eight from Caparrós. Do a mix, bring it altogether. And everything he said would happen, happened.”

Cerrajería stops, laughs. “Bloody hell,” he says, “here I am putting him on a pedestal, and he hardly ever played me!”