Math Through Sports
Salary caps, contracts and ticket revenue
8 min · A cap is a budget. Every signing spends money that then cannot be spent again.
- Financial literacy
- Percentages
The stat
A cap is a budget. Every signing spends money that then cannot be spent again.
Learn the number
A salary cap is a hard budget: the total a team may pay its players. Sign one player for more and there is less for everyone else. That is opportunity cost.
Contracts are usually quoted as a total and a length. The useful figure is the average per year: total divided by years.
Revenue works the same way in reverse. Ticket revenue is price × tickets sold — and raising the price does not help if it empties enough seats.
Read the stat
A team has a $200 million cap and has already committed $164 million to 48 players. A star wants $30 million a year.
- Space left: $200m − $164m = $36m.
- After signing him: $36m − $30m = $6m for the rest of the roster.
- As a share of the cap he alone takes 30 ÷ 200 = 0.15, or 15%.
- If 5 more players are still needed, $6m ÷ 5 = $1.2m each.
The signing fits, but leaves $1.2m per remaining spot — the cost is the roster you can no longer afford.
Your turn
A stadium seats 20,000. At $40 a ticket it sells out. At $55 it sells 15,000. Which price earns more ticket revenue?
Explain what it means
Budgets force trade-offs and the trade-off is the real decision. "Can we afford him?" is the easy question; "what do we give up?" is the one that decides seasons.
Make a prediction
Take a real cap situation. Predict whether the team re-signs their star or lets him go, and write down which other positions the money would otherwise fill.
Review what happened
When the deal is announced, check the average per year and the cap share. Did the rest of the roster get thinner in the way you expected?
Check your understanding
0 of 4 correct
Every question has to be right for this lesson to count as complete. Miss one and you can try it again.