Football

Passes, kicks, field geometry, and game stats.

About sports math

Sports math applies real formulas to the games students follow: batting average and ERA in baseball, shooting percentages in basketball, passer rating in football, xG and group-stage points for soccer, plus golf and volleyball stats and the physics of speed, distance, and projectile motion.

Each sport pairs a plain-language formula with a calculator and links to the Formula Library, turning stats and game situations into approachable practice for ratios, percentages, and algebra.

Sports Math

Football

Passes, kicks, field geometry, and game stats.

9 formulas

Stats

Pass Completion Percentage

\text{Completion \%} = \frac{\text{Completions}}{\text{Attempts}} \times 100

Share of pass attempts that were caught.

Stats

Yards Per Carry

\text{YPC} = \frac{\text{Rushing Yards}}{\text{Carries}}

Average rushing yards gained each time the ball is handed off.

Angles & distance

Field Goal Angle

\theta = 2\arctan\left(\frac{w}{2d}\right)

Approximate the angle between the goalposts as seen from the spot of a kick (w = post width, d = distance).

Trajectory

Punt Height Model

h(t) = -\frac{1}{2}gt^2 + v_0 t + h_0

Height of a punt (or kick) over time uses the same quadratic shape as any projectile near Earth.

Angles & distance

Red Zone Corner Route

c = \sqrt{a^2 + b^2}

A receiver running a corner route forms a right triangle: one leg along the sideline, one toward the middle.

Stats

Yards Per Pass Attempt (YPA)

\text{YPA} = \frac{\text{Passing Yards}}{\text{Attempts}}

Average passing yards gained each time the quarterback throws.

Stats

Third Down Conversion %

\text{3rd\%}=\dfrac{C}{A}\times 100

Share of third-down plays that earn a new set of downs.

Stats

Red Zone Touchdown %

\text{RZ TD\%}=\dfrac{TD}{T}\times 100

Share of possessions inside the opponent 20-yard line that end in a touchdown.

Stats

NFL Passer Rating

\text{PR}=\dfrac{T_1+T_2+T_3+T_4}{6}\times 100

NFL index that blends completion rate, yards per attempt, touchdown rate, and interception rate into one quarterback number.

About sports math

Each sport pairs a plain-language formula with a calculator and links to the Formula Library, turning stats and game situations into approachable practice for ratios, percentages, and algebra.

9 formulas

Stats

Pass Completion Percentage

\text{Completion \%} = \frac{\text{Completions}}{\text{Attempts}} \times 100

Share of pass attempts that were caught.

Stats

Yards Per Carry

\text{YPC} = \frac{\text{Rushing Yards}}{\text{Carries}}

Average rushing yards gained each time the ball is handed off.

Angles & distance

Field Goal Angle

\theta = 2\arctan\left(\frac{w}{2d}\right)

Approximate the angle between the goalposts as seen from the spot of a kick (w = post width, d = distance).

Trajectory

Punt Height Model

h(t) = -\frac{1}{2}gt^2 + v_0 t + h_0

Height of a punt (or kick) over time uses the same quadratic shape as any projectile near Earth.

Angles & distance

Red Zone Corner Route

c = \sqrt{a^2 + b^2}

A receiver running a corner route forms a right triangle: one leg along the sideline, one toward the middle.

Stats

Yards Per Pass Attempt (YPA)

\text{YPA} = \frac{\text{Passing Yards}}{\text{Attempts}}

Average passing yards gained each time the quarterback throws.

Stats

Third Down Conversion %

\text{3rd\%}=\dfrac{C}{A}\times 100

Share of third-down plays that earn a new set of downs.

Stats

Red Zone Touchdown %

\text{RZ TD\%}=\dfrac{TD}{T}\times 100

Share of possessions inside the opponent 20-yard line that end in a touchdown.

Stats

NFL Passer Rating

\text{PR}=\dfrac{T_1+T_2+T_3+T_4}{6}\times 100

NFL index that blends completion rate, yards per attempt, touchdown rate, and interception rate into one quarterback number.