Mathematics in Sports and Cricket Statistics

Cricket is a game of numbers. Commentators quote averages, strike rates and required run rates every few balls, and a tournament place can be decided by the second decimal of a net run rate. In this article we unpack the mathematics behind cricket statistics, work through real-style calculations, and see how maths shapes other sports too.

Batting Statistics

Batting Average

A batter's average measures how many runs they score per dismissal:

$$ \text{Batting average} = \frac{\text{total runs}}{\text{number of times out}} $$

Not-out innings add runs but not dismissals, which is why the formula divides by dismissals rather than innings.

The most famous number in cricket is Sir Donald Bradman's Test average of 99.94. He scored 6996 runs in 80 innings, and was not out in 10 of them, so he was dismissed 70 times:

$$ \frac{6996}{70} \approx 99.94 $$

In his final Test innings at The Oval in 1948, he needed just 4 runs to finish with an average of exactly 100, but was bowled for a duck by Eric Hollies.

Strike Rate

In limited-overs cricket, speed matters as much as total runs. The batting strike rate is runs per 100 balls:

$$ \text{Strike rate} = \frac{\text{runs}}{\text{balls faced}} \times 100 $$

A batter who scores 45 runs off 30 balls has a strike rate of \( \frac{45}{30} \times 100 = 150 \).

Bowling Statistics

Bowlers are measured by three related numbers:

• Bowling average = runs conceded ÷ wickets taken (lower is better).
• Economy rate = runs conceded ÷ overs bowled (runs per over).
• Bowling strike rate = balls bowled ÷ wickets taken (balls per wicket).

The Overs Trap

Cricket writes overs in a special notation: 3.4 overs means 3 complete overs plus 4 balls, which is not 3.4 overs in decimal. Since an over has 6 balls, 3.4 overs is

$$ 3 + \frac{4}{6} = 3.667 \ \text{overs} = 22 \ \text{balls} $$

Forgetting this is the most common mistake students make in cricket maths.

Worked Example 1: A Bowler's Figures

A bowler finishes with figures of 3.4 overs, 25 runs, 2 wickets. Find the economy rate, bowling average and bowling strike rate.

Step 1: Convert overs to balls.

$$ 3 \times 6 + 4 = 22 \ \text{balls} $$

Step 2: Convert balls to true overs.

$$ \frac{22}{6} \approx 3.667 \ \text{overs} $$

Step 3: Economy rate.

$$ \frac{25}{3.667} \approx 6.82 \ \text{runs per over} $$

(Using 3.4 as a decimal would wrongly give 7.35.)

Step 4: Bowling average.

$$ \frac{25}{2} = 12.5 $$

Step 5: Bowling strike rate.

$$ \frac{22}{2} = 11 \ \text{balls per wicket} $$

Run Rates in a Chase

The current run rate is runs scored divided by overs faced, and the required run rate is runs still needed divided by overs remaining. Suppose a team chasing 180 in a T20 has made 92 runs in 11 overs. They need \( 180 - 92 = 88 \) runs from \( 20 - 11 = 9 \) overs, so the required rate is

$$ \frac{88}{9} \approx 9.78 \ \text{runs per over} $$

compared with a current rate of \( 92 / 11 \approx 8.36 \). The gap tells the batters they need to accelerate.

Net Run Rate: The Tournament Tie-Breaker

When teams are level on points, they are separated by net run rate (NRR):

$$ \text{NRR} = \frac{\text{total runs scored}}{\text{total overs faced}} - \frac{\text{total runs conceded}}{\text{total overs bowled}} $$

Two rules matter:

• If a team is bowled out, it is counted as having faced its full quota of overs (for example, 20 in a T20).
• Overs must be converted properly from cricket notation to decimals.

Worked Example 2: NRR After a Successful Chase

Team X bowls first and restricts Team Y to 165 in 20 overs. Team X then chases the target, reaching 166 in 18.3 overs. Find Team X's NRR from this match.

Step 1: Convert 18.3 overs to decimal.

$$ 18 + \frac{3}{6} = 18.5 \ \text{overs} $$

Step 2: Run rate scored.

$$ \frac{166}{18.5} \approx 8.973 $$

Step 3: Run rate conceded.

$$ \frac{165}{20} = 8.25 $$

Step 4: Subtract.

$$ \text{NRR} = 8.973 - 8.25 \approx +0.723 $$

Team Y's NRR from this match is the opposite, about \( -0.723 \). Notice that finishing the chase faster boosts NRR, which is why teams sometimes try to win quickly near the end of a group stage.

Over a whole tournament, NRR is not the average of match NRRs. You must add all runs and all overs first, then divide, a classic example of why averages of ratios can be misleading.

The Duckworth–Lewis–Stern Method

When rain shortens a limited-overs match, a fair target is needed. Simply scaling by overs is unfair, because a team with 10 wickets in hand can score much faster in its final overs than one with 2 wickets left.

English statisticians Frank Duckworth and Tony Lewis solved this using the idea that a team has two resources: overs remaining and wickets in hand. Their method was first used in international cricket around 1997 and later improved by Australian statistician Steven Stern, becoming the DLS method. Resource percentages come from a mathematical model fitted to thousands of past matches.

The basic idea for a revised target (when Team 2's resources are less than Team 1's) is

$$ \text{Team 2 par score} = \text{Team 1 score} \times \frac{\text{Team 2 resources}}{\text{Team 1 resources}} $$

with the target being one run more. For example, if Team 1 made 250 using 100% of its resources and rain leaves Team 2 with 80%, the par score is \( 250 \times 0.8 = 200 \), so the target is 201. (The real DLS tables are more detailed than this simple illustration.)

Maths Beyond Cricket

• Ball tracking systems such as Hawk-Eye use several cameras and coordinate geometry to reconstruct a ball's 3D path, then fit a curve to predict where it would have gone for LBW decisions.
• Football analysts use "expected goals" (xG), a probability that a shot from a given position becomes a goal.
• Athletics uses speed–distance–time: a 100 m sprint in 9.58 s means an average speed of about 10.4 m/s.
• Squash and hockey teams use statistics to plan tactics against specific opponents.

Did You Know?

• Wasim Akram was the first bowler to take 500 wickets in One Day Internationals and finished with 502.
• Usain Bolt's 100 m world record of 9.58 s, set in Berlin in 2009, included a stretch where his speed was over 12 m/s, well above his average.
• Many franchise teams now employ full-time data analysts who use regression and probability models to pick players.

Key Takeaways

• Batting average divides by dismissals; strike rate is runs per 100 balls.
• Always convert cricket overs (like 3.4) into balls or true decimals before calculating.
• Economy rate, bowling average and bowling strike rate describe different aspects of a bowler's work.
• Net run rate compares runs per over scored and conceded, adding totals before dividing.
• DLS sets fair targets in rain-affected matches by modelling overs and wickets as resources.

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