AFCAT Numerical Ability · Average

Batting Averages, Runs Needed and Run Rates

A batting average is runs divided by innings (or by dismissals), a run rate is runs divided by overs, and every cricket question is a total of runs read against a count.

All Average notes

Why this matters

Two AFCAT past-year questions are cricket ones, from 2016 and 2017, and the bank adds about fifty more like them. Most are EASY. The marks go on the divisor: dismissals rather than innings when some innings were not out, the overs still left rather than all the overs, wickets rather than matches for a bowler.

Concept 1 of 3: Batting average and the next innings

Runs pile up into a total. After one more innings, the new average is the new total over one more innings.

Definition

Runs so far = average × innings.
After the next innings: $\dfrac{\text{runs} + \text{new score}}{\text{innings} + 1}$ .
Part of a run of matches: runs in the last $k$ = all the runs − runs in the first ones.
With not-out innings, the batting average divides runs by dismissals: innings − not-outs.

Batting average

\text{batting average} = \dfrac{\text{runs}}{\text{innings}} \quad \left(\text{or } \dfrac{\text{runs}}{\text{dismissals}}\right)

Worked example

A batsman averages 36 over 14 innings. He scores 66 in the 15th. Find his new average.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

AFCAT · 2016 · AFCAT (II) 2016 — Numerical Ability · 02-213Easy

Example 1 · Average · Cricket Scores

The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, the average for the last four matches is

Not-outs change the divisor

1,000 runs in 25 innings with 5 not-outs is a batting average of

1000 \div 20 = 50

, not

1000 \div 25 = 40

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Concept 2 of 3: Runs needed for a target, and how many innings

A target average is a target total. The next score has to fill the gap between the runs already made and the runs needed.

Definition

Score needed = new average × $(n + 1)$ − old average × $n$ . Shortcut: new average + $n$ × the rise.
Unknown number of innings: if a score of $x$ moves the average from $A$ to $A'$ , then $An + x = A'(n + 1)$ , so $n = \dfrac{x - A'}{A' - A}$ .
A bowling average is runs conceded per wicket. Taking $w$ wickets for $r$ runs after $w_0$ wickets: $Aw_0 + r = A'(w_0 + w)$ .
Several matches at a fixed score $s$ : $An + sk = A'(n + k)$ ; solve for $k$ .

Score needed in the next innings

x = A'(n + 1) - An

Worked example

A batsman averages 30 over 16 innings. How many must he score in the 17th to average 33?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

AFCAT · 2017 · AFCAT (II) 2017 — Numerical Ability · 02-211Moderate

Example 2 · Average · Cricket Scores

A man whose bowling average is 12.4 takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him before his last match is

Count the innings still to come

To average 33 after 17 innings he needs

17 \times 33

runs in all, not

16 \times 33

Drill 16 more on runs needed for a target, and how many innings

Concept 3 of 3: Run rate, required rate and economy

A run rate is a speed: runs per over. An overall rate is total runs over total overs, never the plain average of two rates.

Definition

Overall run rate = total runs ÷ total overs.
Required rate = runs still needed ÷ overs still left.
A bowler's economy rate = runs conceded ÷ overs bowled.
A target rate over the whole innings sets a target total first: 6 an over for 40 overs is 240 runs.

Run rates

\text{run rate} = \dfrac{\text{runs}}{\text{overs}}, \qquad \text{required rate} = \dfrac{\text{target} - \text{runs so far}}{\text{overs left}}

Worked example

A team scores 4.5 an over for the first 15 overs of a 40-over innings. What rate does it need in the remaining overs to reach 260?

Practice this conceptself-check · 3 quick reps

The same idea in a practice question:

Practice questionModerate

Example 3 · Average · Cricket Scores

A cricket team's run rate in the first

20

overs is

5.5

runs per over. If they want to achieve an overall run rate of

6.2

runs per over in a

50

-over match, what should be their run rate in the remaining

30

overs?

Do not average two rates

12 overs at 5 an over and 4 overs at 9 make 96 runs in 16 overs, a rate of 6, not

(5 + 9) \div 2 = 7

Drill 11 more on run rate, required rate and economy

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Batting average and the next innings
Batting average
$\text{batting average} = \dfrac{\text{runs}}{\text{innings}} \quad \left(\text{or } \dfrac{\text{runs}}{\text{dismissals}}\right)$
Runs needed for a target, and how many innings
Score needed in the next innings
$x = A'(n + 1) - An$
Run rate, required rate and economy
Run rates
$\text{run rate} = \dfrac{\text{runs}}{\text{overs}}, \qquad \text{required rate} = \dfrac{\text{target} - \text{runs so far}}{\text{overs left}}$

Watch out for (3)

Not-outs change the divisor
→ Batting average and the next innings
Count the innings still to come
→ Runs needed for a target, and how many innings
Do not average two rates
→ Run rate, required rate and economy

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