Action and Reaction

Every movement changes the game. Step through a tactic, then drag any player, change his run or his rating, and watch which passes open and close. The positions are made up to show a coaching idea; everything the board measures is worked out from them, and you can see the maths.

How the timing works, step by step: Who gets there first? Timing a pass, and the cost of waiting

Layers

Who owns the space Passing lanes Free players Space behind the line Runs

Blue, attacking left to right
Red
Open passing lane
Too close to call
Best release
Free player
Who gets there first
Back line, and the space behind it
Run: where he'll be in 2 s

Where should he stand?

Player skill

Rate a player from 1 to 5. The rating sets his top speed and how quickly he reacts; 3 is average.

Measured from the positions

Show the maths

Your definitions

These are judgement calls, not facts. Change them and watch the answers change.

Players keep running while they react Passes over 30 m go in the air (up to 70 m; only the last 5 m can be contested) The pass travels at m/s A player can block or take anything within m without moving Too close to call: within s either way A free player is one nobody can reach within s

How to read it

Positions are hand-placed to show a coaching idea. They are not from a real match.
Everything under "Measured" is worked out from where the players stand and how they are running, so it changes when you move one.
The shading shows which team would get to each part of the pitch first.
The gold dashed line is the defending team's last outfield player; the shaded strip beyond it, and the number on it, is the space behind their back line that a runner or a ball over the top can attack.
Arrows show each player's run: where he'd be in two seconds. Select a player standing still and a handle appears beside him; pull it out to give him a run.
While the sandbox plays, the arrows show where each player is heading that second under the rules below: Red's nearest player goes to the ball, the rest of Red slide across with it and drop back as it comes forward, and Blue's players follow your runs or drift sideways or forward into space.
Best release is the teammate furthest forward with an open lane who is free or running onto the pass. If his lane is too close to call, the board says so.

How it works

Everything comes down to one question: who gets there first? A player can block or take anything within reach (1.5 metres) without moving. Further away, he needs time to react, then time to run. While he reacts he keeps going the way he was running, so a defender already moving towards a pass is quicker to it than one moving away. This is the arrival-time idea behind pitch control, from William Spearman's paper "Beyond Expected Goals" (MIT Sloan Sports Analytics Conference, 2018). A player rated 3 uses the defaults from Laurie Shaw's open Friends of Tracking code: a top speed of 5 metres a second and 0.7 seconds to react. The ball travels at 15 metres a second.

A passing lane is open if no opponent can reach any point on the line of the pass before the ball does, and too close to call if the closest one is within 0.3 seconds either way. Spearman's model allows about 0.45 seconds of uncertainty in when a player arrives; at a 0.3-second margin the slower player still gets there first about one time in four, so anything closer is a coin toss, not a verdict. The board says so rather than pretend to know.
A pass to a runner goes where he and the ball meet, from solving \(\lvert \mathbf p + \mathbf v t - \mathbf a \rvert = u t\) for the time \(t\): a through ball.
Offside is judged when the pass is played: in the opponents' half, ahead of the ball and of the second-last opponent.
Passes in the air (with that switch on) can only be contested in the last five metres, where the ball comes down.
The optimiser tries every spot a player could reach in about two seconds and keeps the ones that meet the rules.

In the sandbox, Play runs ten seconds, a second at a time, by four simple rules. They are coaching rules of thumb, not predictions of what players would do:

The player on the ball plays the best release, into the receiver's path if he's moving, but not straight back to the player who just passed to him unless nothing else is on. With no pass on, he carries it forward if nobody can reach him within 1.5 seconds, and otherwise shields it.
The defending side's quickest player to the ball goes to press it, goal-side.
The rest of the defending side keep their shape and slide with the ball: half as far across as the ball moves, and 40% as far up or back.
The attacking side's other players follow the runs you give them. Without one, they keep their place in the shape (within 8 metres of where they started, moving up as the ball does) and, inside that, step each second to the spot within 3 metres that's furthest from any opponent: sideways or forward, never back, not onto a teammate, at least 4 metres inside the touchlines, and onside.

Nobody runs faster than his rating allows, and play stops when a defender gets within reach of the ball.

The timing, the margins and pitch control are explained step by step in who gets there first? Timing a pass. The other ideas underneath are on the site too: positions as vectors and the dot product in passing as a vector and the dot product, "who's nearest" in nearest neighbours, and searching for the best option in what are we optimising?

Where it goes wrong

The positions are made up. The plays show coaching ideas; they don't prove anything happens in real matches.
The ball travels in a straight line at a steady speed: no bounce, curl or slowing down, and no first touch.
Players only move when a step or you move them. Real defenders react all the time.
There are no percentages, on purpose. A lane is open or shut by the rules above; a chance of the pass arriving would need a model fitted to real passes, which this isn't. Who gets there first? shows what the published uncertainty in arrival times would make of a margin.
Only rating 3 comes from a published model. The spread from 1 to 5 (4.0 to 6.0 metres a second, 0.9 to 0.5 seconds) is ours.
Offside is the simple version: no "interfering with play", and a level player counts as onside.