Real swerve comes from spin, airflow and pressure differences across a moving ball. No browser game simulates that, and none needs to. What players recognise as bend is something much simpler: a sideways displacement that grows through the flight.
The interesting part is how it grows, because that single choice determines the entire strategy of every free-kick game you will play.
Three ways to model curve
Linear drift
Offset grows evenly with time. Easy to write, and it feels wrong — the ball appears to travel along a diagonal rather than to bend. Rare in good games.
Sine arc
Offset follows a sine curve, so the ball bulges out and comes back to the original line. Used for shots that swerve around something and finish where they were aimed. It looks great and makes aim the sole determinant of the finishing point.
Accelerating swerve (the common one)
Offset grows with time raised to some power above 1, so almost nothing happens early and a lot happens late. This is what Free Kick Master uses, with an exponent of about 1.6 and a maximum of 130 pixels.
What an exponent of 1.6 actually means
| Flight progress | Share of total bend | Sideways offset |
|---|---|---|
| 25% | ~11% | ~14 px |
| 45% | ~27% | ~35 px |
| 70% | ~56% | ~73 px |
| 90% | ~84% | ~109 px |
| 100% | 100% | 130 px |
More than half the bend happens in the last 30% of the flight. That is why a curved shot looks dramatic — and why it is useless for beating an obstacle that sits at the halfway point.
Consequence 1: curve cannot beat a wall
The wall check happens at 45% of the flight, where maximum curve has produced about 35 pixels of movement against a wall 82 pixels wide either side of centre. Curve is not a wall-avoidance tool; aim is.
What curve does is let you aim somewhere that would otherwise be a miss, and still finish inside the goal. That is the whole trick: Free-Kick Walls: How Blocking Is Actually Decided covers the check itself.
Consequence 2: curve beats the keeper
The keeper commits when you strike and dives toward a side based on the ball's final position. But because the swerve is late, a heavily curved shot spends most of its flight looking like it is going somewhere else — and in our game the keeper's reading chance is deliberately lower than in the penalty game (16% rising a couple of points per attempt, against 24% rising 3.5) to reflect that.
So curve is genuinely the anti-keeper tool, and the scoring rewards it: up to 40 points, which is as much as the entire placement bonus.
Consequence 3: aim and finish are different things
This is the mental model that makes free-kick games click:
- Aim decides the path — what the ball clears on the way.
- Curve decides the finish — where it ends up, up to 130 pixels from the aim point.
Players who treat aim as the finishing point either get blocked (aiming at gaps) or miss wide (aiming at the post and then curving past it). Separating the two fixes both.
How to calibrate curve in any game
Four attempts is enough to learn an unfamiliar curve model:
- Attempt 1: zero curve. Establishes where your aim actually lands.
- Attempt 2: maximum curve, same aim. The distance between the two finishing points is the game's maximum displacement.
- Attempt 3: maximum curve, aim displaced by that amount in the opposite direction. Should land where attempt 1 did. If it does, the model is an accelerating swerve.
- Attempt 4: watch the path, not the ball. If it bulges and returns, it is a sine model and aim alone determines the finish.
Knowing which model you are facing tells you immediately whether aiming wide is a plan or a mistake.
Is any of this like a real free kick?
More than you might expect, in structure if not in mechanism. A real bending free kick does swerve late, because the aerodynamic force acts over the whole flight and its effect on position accumulates. And the real tactical idea — start the ball outside the wall and bring it back — is exactly what an accelerating swerve model reproduces.
What is not realistic is the input: you are stopping a meter, not striking a ball across its surface with the inside of your foot. The decision is faithful; the execution is an abstraction. Football Arcade Games vs Simulation Games explores that distinction.
Why designers pick an exponent above one
The choice of exponent is the whole feel of a curve mechanic, and it is worth seeing what the alternatives produce.
| Exponent | Bend at the halfway point | Feels like |
|---|---|---|
| 1.0 (linear) | 50% | A diagonal, not a curve. Reads as a mis-hit. |
| 1.6 (ours) | ~33% | A late swerve, like a struck ball bending in. |
| 2.5 | ~18% | Almost nothing, then a violent hook at the end. |
Anything much above two looks unnatural and makes the mechanic unusable, because the player gets no visual feedback until the ball is already past the obstacle. Anything at or below one does not read as bend at all. The 1.5–1.8 range is where a sideways offset starts looking like a curling football, which is why games converge there.
It also has a happy side effect for gameplay: an exponent in that range makes curve useless against a midway obstacle and decisive at the goal line, which produces exactly the "start the ball away from the wall and bring it back" decision that makes free-kick games interesting. The mechanic and the strategy come from the same number.
