Pennant ChaseActivity 02BasketballGrades 7–12

The 240-Minute Problem

Five players on the floor for forty-eight minutes is 240 player-minutes per game. That number does not change no matter who you draft. Neither does the fact that there is only one basketball.

NameTeamLeague

Part One · Before the draft

The constraint

Start with the arithmetic that governs everything else. Fill in the blanks:

5 players × 48 minutes = ________ player-minutes per game

If you play 9 players, the average player gets ________ minutes.

A team takes roughly 85 shots a game. Across 5 starters that averages ________ shots each.

Now the consequence. You are about to draft players whose historical numbers were produced under specific conditions — a certain number of minutes, a certain share of their team's shots. If you draft four players who each took a quarter of their old team's shots, they cannot all take a quarter of yours.

In one sentence: what makes a basketball player worth drafting?

Rank the three stats you plan to draft on — 1 is most important
Rank	Statistic	Why this one?
1
2
3

Two formulas to have ready

True shooting percentage — scoring efficiency counting twos, threes, and free throws together:

TS% = PTS ÷ ( 2 × ( FGA + 0.44 × FTA ) )

The 0.44 is there because not every free throw ends a possession. A TS% around .500 is ordinary; .600 is excellent.

Per-36 rate — what a player would produce with a starter's playing time:

Per-36 = ( stat ÷ minutes ) × 36

This is how you compare a bench player to a starter without the minutes doing all the talking.

Part Two · The draft

Build the roster

Draft log
Pick	Player	Pos	Real PPG	Real FGA/g	Why you took him here
1
2
3
4
5
6
7
8

The overdraft check

Add up the "Real FGA/g" column for the five players you intend to start.

Total shot attempts my five starters "want": ________

Shot attempts actually available per game: about 85

Difference: ________

If that difference is large, whose shots are going to disappear — and how do you think the simulation will decide?

Part Three · During the season

Keep the log

Team tracking log
Date	W	L	PPG	Opp PPG	Team FG%	Reb/g	TO/g

Efficiency table

Fill this in twice — once at midseason, once at the end. Compute TS% yourself; don't look for it in a stat page.

Your rotation, by efficiency
Player	MIN/g	PTS/g	FGA/g	FTA/g	TS%	PTS per 36

Part Four · After the season

Explain what happened

Rank your rotation by points per game. Rank it again by TS%. Rank it a third time by points per 36 minutes. Which player moves the most between the three lists, and what is each list actually measuring?
Your leading scorer took the most shots on the team. Would the team have scored more if some of those attempts had gone to your most efficient player instead? Estimate the difference using TS%, and then say why the real answer is more complicated than your estimate.
Compare each starter's points per game in your league to his real historical season. Who lost the most, and does the shot-attempt arithmetic from Part Two explain it?
Build a league-wide table of team TS% and wins. Do the same for rebounds and for turnovers. Which of the three lines up best with winning?
You drafted three strong rebounders. Did your team get three players' worth of rebounds, or did they take them from each other? Show the numbers.
Given everything, write the drafting rule you'd hand to next year's class. One sentence, and it has to be a rule someone could actually follow during a draft.

Final write-up: your revised theory of what makes a player valuable

Extension

What is the engine doing?

Basketball is the easiest sport to reason about, because possessions are countable. Roughly a hundred of them per team per game, and each one ends in a shot, a turnover, or a trip to the line.

Work through the chain

Who shoots? A player who took 25% of his old team's shots probably gets picked about 25% of the time on your team — a weighted lottery. Test it: does the share of your team's shots each starter takes look like his historical share, rescaled to fit?
Does it go in? Once the shooter is chosen, the engine needs a make-or-miss probability. His shooting percentage is the obvious starting point. What would a strong defensive team have to do to that number, and how much?
Who gets the rebound? Another weighted draw — but among ten players, not five, and offense and defense are not equally likely to win it. How could you check the split from your own box scores?
How long did it take? Pace has to come from somewhere. Where would a simulation get the number of possessions in a game?

The sim engine primer works through the probability math behind steps 1 and 2.

Your model of one possession, start to finish

Teacher guide

Running The 240-Minute Problem

Timing

One period to launch, 10–15 minutes a week for tracking, two periods at the end. Basketball seasons simulate quickly, so this is the easiest of the three to fit into a short unit — ask for a season length that lands where you need it.

The point of the unit

This is an allocation problem wearing a jersey. Minutes and shot attempts are fixed; talent is not. Students who draft a roster full of stars watch those stars' per-game numbers shrink, and the arithmetic in Part Two predicted it before the season started. That's the moment worth building the assessment around.

The secondary target is rate versus volume. True shooting percentage is the cleanest tool in school sports analytics for showing that the biggest number is not always the best number, and computing it by hand — including the odd 0.44 — is a nice exercise in trusting a formula you can interrogate.

Where classes get stuck

The 0.44. Someone will ask. The honest answer is that it's an empirical estimate of what fraction of free throw attempts end a possession, since and-ones and technicals don't. That it's an estimate rather than a law is a feature — ask what would happen to their rankings if it were 0.40 or 0.50.
Per-36 taken too literally. Students conclude a 12-minute bench player would score 28 a game with starter's minutes. Push back: rates measured over small samples are noisy, and playing more usually means facing better opponents.
Efficiency worship. The opposite error, once TS% lands. A player who shoots 70% on three attempts a game is not more valuable than a 58% player taking eighteen. Volume matters too — that tension is the real lesson, not a winner.

Differentiation

Lighter: Skip TS% and use points per shot attempt (PTS ÷ FGA). Same idea, one operation.
Heavier: Have students build a full minutes-allocation model — assign all 240 minutes across the roster, project each player's per-36 production, and predict team points per game. Then compare the prediction to what the season actually produced. The gap is a genuinely good discussion.
Economics tie-in: This is opportunity cost, diminishing returns, and constrained optimization with real data. Runs well as a joint unit with an econ class.

Setting up the league

Email guy@pennantchase.com for a free class league — sport, class size, weeks available.
Send a spreadsheet of logins to have accounts created in bulk. The site blocks repeated sign-ups from one IP address, which is exactly what a class on a school network looks like.
Some school district mail servers block mail from pennantchase.com. If no reply arrives, ask IT to allow the domain or write from a personal address.
You choose the number of teams, which historical players are eligible, and how many games the season runs. A narrow player pool — one decade — makes comparisons cleaner.