Geometry, football and the World Cup final

By Conor BolandSpain will play Argentina in the Fifa World Cup final on Sunday. The highly anticipated match takes place in New Jersey’s MetLife Stadium, with the teams vying for the most coveted prize in football.Attacking flair and physicality will no doubt play a role. But we could also see an underappreciated element of football come to the fore: geometry.In their 2-0 World Cup semi-final win over France, Spain formed neat passing triangles around the French players. This sometimes made it look as if Spain had extra people on the field.Wherever a Spanish player received the ball, two teammates appeared at different angles – with their French opponents seemingly always arriving a fraction too late.The triangle mattered not because it was neat, but because it gave Spain choice and France uncertainty. Each pass forced a French defender to commit to one possible future: press the ball, block the inside route, or protect the space behind. By the time that choice was made, the ball had often moved and the geometry had changed again.Spain were not simply finding space. They were controlling when and where the next space would appear.Spain’s passing triangles repeatedly forced French defenders to commit to one possible future. Forcing choicesPut three attackers in a straight line and one defender can often block both supporting players. But move one supporting player sideways and the passing lines separate.The defender must choose which route to close. Press the ball and a pass can go around them. Protect the inside route and the outside may open. If another defender steps across, a Spanish player can attack the space left behind.A useful football triangle does not need equal sides or 60-degree angles. Its best shape changes with defenders’ positions, body orientation, ball speed and the space available.A narrow triangle is easy to squeeze because one defender may block both lanes. A wide one makes the pass travel farther, giving an opponent more time to intercept it.In their semi-final match against France, Spain found the middle ground again and again – close enough for quick combinations, but far enough apart to stretch France’s press.Argentina are competing with Spain for the ultimate trophy in world football. A pitch made of probabilitiesFootball geometry is a problem of time as well as space. A passing lane is not open simply because no defender is standing in it. The key question is whether the ball reaches the receiver before an opponent reaches the interception point.A diagram shows where players are – but a useful model of the game asks where players can get to. Research using player-tracking data estimates control of the pitch from players’ position, direction, speed and acceleration. The result is a constantly changing map of who is most likely to reach each area first.Pedro Porro’s 58th-minute semi-final goal offered a compact example when, after exchanging passes with teammate Dani Olmo, he continued his run to score Spain’s second. The first pass shifted the defenders’ focus. Porro’s movement created a new angle for the return.A living networkThree-player combinations make this idea even harder to defend. Spain’s strength was not just one triangle, but the speed with which several overlapped. A midfielder could be one corner of multiple shapes, connected to a defender, full-back, winger and another midfielder.Passing-network research describes players as points and passes as links. Yet a final network diagram for a given football match misses something important: Spain were rebuilding those links with every movement and first touch they made.The value of a pass is not only where the ball goes, but how it changes what could happen next. That is why ten sideways passes are not automatically better than one pass that removes two defenders.The shape that conquered basketballTriangles are not unique to football. Under head coach Phil Jackson (1987-1998), US basketball team the Chicago Bulls made frequent use of a tactic called Tex Winter’s triangle offence. This places three players on one side of the court to create passing, cutting and scoring routes.The sport was different but the principle was the same: triangles preserve alternatives. Close one route and another remains; follow the ball and space opens elsewhere.In their match against Spain, France’s problem was not simply a lack of running. Pressing works only when several defenders move together and close connected passing options.After the match, Kylian Mbappé said there had been “a lack of communication” in France’s pressing. Spain kept moving before France could reorganise.A triangle on a tactics board does nothing by itself. Its power depends on players scanning before receiving, opening their bodies, and using the first touch to preserve the option of more than one next action.The deeper contest was between Spain’s speed of reconfiguration and France’s speed of recognition. Spain kept changing the problem faster than France could solve it. The triangles were visible – but their real advantage was control over what could happen next.Will we see a similar approach deployed in the final? Argentina will no doubt be closely studying their opponent’s tactics from other matches. But geometry will still play a prominent role – and may even prove a deciding factor.This article is republished from The Conversation under a Creative Commons license. Read the original article here.