It was Schmidt vs Schmidt on Sunday. Or at least it could have been, if Roger, the Leverkusen manager, hadn’t been forced to watch proceedings from behind a glass screen in a VIP box at the Coface-Arena, nursing the odd bottle of beer. The trip to Mainz 05 marked the start of the 48-year-old’s five-week ban (three suspended) for refusing to leave the touchline the previous week. Disappointingly for all Airplane fans, initial reports suggest he didn’t transmit instructions down to the bench with a two-way radio (that would have been in violation of the sanctions). In any case, it was all over for Roger by half-time, with Martin – the other Schmidt – confirmed as victor.

The home side were 2-0 up going into the break against a Leverkusen team missing plenty of key players. Yunus Malli scored his second goal of the afternoon, via a penalty, to make it three just before the hour, and Javier Hernández’s goal merely made the scoreline a tad less embarrassing for the visitors. There were no excuses, Christoph Kramer said after the final whistle: “We shouldn’t make [the ban for Schmidt] bigger than it is, it was us who messed up today.”

The defeat meant Leverkusen slipped to sixth in the table and lost ground in the Champions League race; the team looked so jaded after their 3-1 win over Sporting on Thursday night that you have to fear for them in coming weeks. To make matters worse, midfielder Kevin Kampl, one of the best performers alongside centre-back Jonathan Tah in the current campaign, was ruled out until the end of the season with a fractured leg. Leverkusen, you sense, are but one more managerless defeat away from another Rudi Völler meltdown, accompanied by newspaper reports bemoaning the team’s lack of character and leadership. The coach’s petulance during the defeat by Dortmund might well prove telling at the end of the season.

Schmidt (Martin), though, could well be the new Schmidt, as far as coaching plaudits are concerned. The win over Leverkusen confirmed his Mainz side (insert the words “plucky”, “courageous”, “spirited” and “underdog” in random order) as the team of the moment and took them all the way up to fifth place, equal on points with Borussia Mönchengladbach and only three behind third-placed Hertha, the most lovable impostors in the German capital since folk hero Wilhelm Voigt.

Smaller teams outpacing much bigger, financially powerful sides is by no means a new development in the Bundesliga but Mainz doing so well with two thirds of season over is still an arresting sight. A year ago, when Schmidt – then the club’s under-23 coach – was promoted to take over from the luckless Dane Kasper Hjulmand, Mainz were one point clear of the relegation zone. They finished in 11th spot but looked destined for another campaign battling against the drop. They sold two of their best players, Shinji Okazaki (to Leicester City) and Johannes Geis (to Schalke) for a combined €22m, and replaced them, as they always do, with a bunch of unheard of prospects. After spending most of the campaign safely in nowhereland, they’ve now shot up the table with a bunch of high-profile wins over Schalke, Gladbach and Leverkusen. You feel silly doubting them now. Mainz are masters of backing the right, unfashionable men, from Jürgen Klopp and Thomas Tuchel on the bench to André Schürrle and midfielder Malli (a €10m target for Borussia Dortmund) on the pitch.

The Colombian striker Jhon Córdoba, a €1.6m signing from Granada and Yoshinori Muto (€5m, FC Tokyo) are the latest star performers who can be sold for a vast profit next summer. Few operators have consistently bought as well in that kind of market as the Mainz sporting director Christian Heidel, which explains why Schalke 04 have moved heaven and Earth to snap him up. The 52-year-old will move to Gelsenkirchen next summer after 24 years in charge at FSV.

Heidel’s and Mainz’s biggest achievement, however, has been to take the moneyball principle one step further. They don’t just produce a high number of players in their excellent academy and buy well from all corners of the globe, they also produce their own managers. Klopp started his career as player-manager there, Tuchel was promoted from the under-23s and managed to outdo his predecessor.

In Schmidt, a former extreme skier who ruptured his cruciate ligaments seven times (two playing football, three on the piste, two riding his mountain bike) and broke plenty of bones in pursuit of his dangerous hobbies, they seem to have unearthed a third gem. Qualifying for the Champions League would put him firmly among and perhaps even above the former greats who made their name in the capital of Rhineland-Palatinate. Like Klopp and Tuchel before him, he had never coached at senior level before Heidel gave him a chance.

Schmidt, who never played higher than amateur level – he worked as a race car mechanic and occasional ski instructor before becoming youth coach at FC Thun – hails from the Canton of Valais, where Switzerland’s mountains are at their tallest. He spent his childhood summers tending to his grandfather’s cows and is a fully paid-up member of the village yodelling club. The new Fifa president Gianni Infantino grew up just down the road and remains a childhood friend.

Every day, Schmidt looks at webcams on the Belalp, his local mountain, and studies the snow reports. “It’s good for me, it’s my anchor,” he told Münchner Merkur. “It stirs feelings of home. One mountain photo is like a holiday to me. The mountains are my source of energy.” During the winter break, he took his team up the Belalp in a long trek through the snow in mountain boots. They ate local delicacies at 2,700m and spend the night in tents. Afterwards, Schmidt introduced the players to his family.

“Of the four components – technique, tactics, fitness and mentality – three are being taught throughout the season. But we miss out on mentality a little,” he told Neue Zürcher Zeitung. Going up the mountain was meant to be a transgressive experience, a process designed to “create a mental image that we can work with in the season, to remind ourselves what we are capable of doing when we’re in tough spot.” As a small club, “doing things differently are the only weapons we have,” he added. “But of course they will say we should have practised more football if we lose the next three games.”

Mainz didn’t do that though. Schmidt has built on tactical knowhow accumulated under Tuchel and made them even more hard-working. They run more and sprint more than any other side in the league. Against Gladbach a couple of weeks ago, who are by no means slouches, Mainz notched up an outlandish 125km collectively and set a new record with 262 sprints. Their former best was 214. No team comes remotely close. Schmidt modestly claims that as manager, he is responsible only for 1% of the team’s output.

If the run of results manages to keep up with the that of the feet, one of Mainz’s jokes from last year will soon look a lot less or even more funny, depending on your sense of humour. The club’s official Twitter account tweeted a mock-up of Schmidt and his assistant Sandro Schwarz in Dortmund training outfits, with the dates “2020” and “2025” over their respective heads and “coaching academy” beneath them. That was on 19 April, the day that Tuchel was confirmed as the future BVB coach.

On Wednesday night Mainz’s mountaineers will attempt to climb the tall mountain of an away trip to Pep Guardiola’s Bayern Munich. A win would make their story much bigger, just as Tuchel’s “boyband” rang in the hype after the away triumph over Louis van Gaal’s Reds in 2009. But even if Mainz lose, they’re still on course: for another quite incredible, gravity-defying season.

Results: Köln 0-1 Hertha Berlin, Hamburg 1-1 Ingolstadt, Wolfsburg 0-2 Bayern Munich, Stuttgart 1-2 Hannover, Werder Bremen 2-2 Darmstadt, Augsburg 2-2 Borussia Mönchengladbach, Borussia Dortmund 3-1 Hoffenheim, Mainz 3-1 Bayer Leverkusen, Eintracht Frankfurt 0-0 Schalke.