StudyQuest
Sports Math

Football

Passes, kicks, field geometry, and game stats.

9 formulas

Stats

Pass Completion Percentage

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

Share of pass attempts that were caught.

Stats

Yards Per Carry

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

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

Angles & distance

Field Goal Angle

θ=2arctan⁡(w2d)\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)=−12gt2+v0t+h0h(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=a2+b2c = \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)

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

Average passing yards gained each time the quarterback throws.

Stats

Third Down Conversion %

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

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

Stats

Red Zone Touchdown %

RZ TD%=TDT×100\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

PR=T1+T2+T3+T46×100\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

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 World Cup Seattle 2026 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.