🔢 MathGrade 6Lesson 35
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Sports Statistics Analysis

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Learning Objectives

  • 1Compute common sports rates such as batting average, points per game, and win percentage
  • 2Find the mean and median of a small set of player or team statistics
  • 3Compare two players or two teams using ratios and percentages
  • 4Interpret a stats table or bar chart to answer real-world sports questions
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Mini Lesson

Sports run on numbers. Coaches, analysts, and fans use statistics to compare players, scout opponents, and decide who plays. In this lesson you will work with the same kinds of stats real teams track — batting averages, points per game, win percentages, ratios, and team totals — and use ratios, decimals, and percents to answer sports questions.

The big four sports rates

  • Batting average = hits / at-bats. A player with 30 hits in 100 at-bats has an average of 0.300 (read as "three hundred").
  • Points per game (PPG) = total points / games played. A player with 240 points in 20 games scores 240 / 20 = 12 PPG.
  • Win percentage = wins / games played x 100. A team with 15 wins in 20 games has 15 / 20 x 100 = 75%.
  • Field-goal percentage = made shots / attempted shots x 100. 12 of 20 = 60%.

Step-by-step: comparing two players

  1. Write each player’s raw numbers: Player A — 240 points in 20 games. Player B — 180 points in 12 games.
  2. Convert to a per-game rate so the games-played gap does not fool you: A = 240 / 20 = 12 PPG. B = 180 / 12 = 15 PPG.
  3. Compare the rates, not the totals: B scores more per game even though A scored more in total.
  4. Decide what the comparison shows: per-game rate is the fair scoring stat; total points just rewards playing more games.

Mean and median

A mean (average) is the sum divided by the count. For points 8, 12, 14, 18, 18 the mean is (8 + 12 + 14 + 18 + 18) / 5 = 70 / 5 = 14. The median is the middle value once the list is sorted. With 5 values, the median is the third one — 14. Mean and median often match closely, but a single huge game (an outlier) can pull the mean up while the median barely moves.

Example

A player has 36 hits in 120 at-bats. What is the batting average?

Answer:0.300

Batting average = hits / at-bats = 36 / 120 = 0.300. In sports talk, that is read "three hundred" — a strong batting average.

Ratios and team totals

  • Ratio of wins to losses: Team Red has 18 wins and 6 losses. Ratio = 18:6 = 3:1 (3 wins for every loss).
  • Total points: add every player’s points to get a team total. Team Red = 80 + 65 + 55 + 40 = 240.
  • Comparing two teams: a bar chart with one bar per team makes the gap obvious at a glance.
  • Sanity check: if a number looks impossible (like a 1.500 batting average), recheck the formula — the bigger number must always be on the bottom of the fraction.
Player Scoring StatsA four-row stats table for players Avery, Blake, Casey and Drew, listing games played, total points and points per game. Blake's row is highlighted as the top PPG at 15.0 even with the fewest games.Player Scoring StatsPPG = total points / games played.PlayerGamesPointsPPGAvery2024012.0Blake1218015.0Casey1819811.0Drew1521014.0Top PPG = Blake at 15.0 with the fewest games.
Compare per-game rates, not totals.
Total Points by TeamA bar chart comparing Team Red at 240 points and Team Blue at 200 points; Red scored 20% more than Blue.Total Points by TeamRed 240 vs Blue 200 — Red scored 20% more.050100150200250240Red200BluePointsPercent more = (40 / 200) x 100 = 20%.
Bars make the gap obvious at a glance.
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Tip: always show units. "12" means nothing, "12 PPG" or "12 points per game" means everything. Units stop you from comparing the wrong things.

Vocabulary
batting average
Hits divided by at-bats; usually written to three decimal places.
points per game
Total points divided by games played; a fair per-game rate.
win percentage
Wins divided by games played, times 100, written as a percent.
mean
The sum of all values divided by the number of values.
median
The middle value of a sorted list.
ratio
A comparison of two quantities, like wins:losses.
outlier
A value much larger or smaller than the rest of the data.
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