Measuring Audience IV: Advanced Issues
JMC 222 Media Planning
Department of Media & Communication
Hanyang University
Estimating Reach n+
Reach n+
Media planner needs to know not only a schedule’s overall reach and
GRPs (= reach x average frequency), but also cumulative reach per # of
exposure (= reach n+)
Reach 1+: % of audience exposed to the media at least once
Reach 3+: % of audience exposed to the media at least three rimes
Estimating reach n+ allows to see how reach builds up per units of GRPs
– understanding the patterns is important for making strategic decisions
Estimating Reach n+
Reach n+ (cont’d)
Growth patterns of reach n+ by GRPs (Network TV)
Upper limit
Reach 1+ shows a
concave pattern,
which changes to a Sshape as frequency
increases
Estimating Reach n+
Reach n+ (cont’d)
Growth patterns of reach n+ by GRPs (Cable TV)
Upper limit
Cable TV’s reach
grows slower than
network TV’s, and has
a lower upper limit due
to the number of
channels
Estimating Reach n+
Reach n+ (cont’d)
Growth rate of reach by media
Reach
Network TV
Cable TV
Print Media
Radio
300
GRPs
Knowing how much
reach is possible per
some units of GRPs is
needed
Estimating Reach n+
Reach n+ (cont’d)
Reach estimates/GRPs by media
GRPs
Reach
Frequency
Network TV
100
300
25-50
55-70
2.0-4.0
4.3-5.5
Cable TV
100
300
15-40
40-55
2.5-6.7
5.5-7.5
Radio
100
300
3-10
17-20
5.0-16.7
11.5-21.4
Internet
100
300
10-50
65-80
2.0-10.0
3.8-4.6
Print Media
100
300
10-60
30-70
1.7-5.0
4.3-5.0
Estimating Reach n+
Two ways of estimating reach n+
Using real data is desirable, but could be done only after enough real
data are collected
Could be misleading if the data are insufficient and/or flawed
Fitting curves to available data
Finding a mathematical model with the smallest errors for the data
given
Estimation using probability distributions
Media exposures are viewed as probability-related phenomena
Estimating Reach n+
Probability models
Binomial probability distribution
It is assumed that events are probabilistically independent of one
another (i.e., Event A’s chance won’t affect B’s chance, or vice versa)
What would be the chance that an event X occurs y times in n trials?
 n  y n− y
P( y) =   p q
 y
P(y): Probability of an
event in a repeated trial
p: Probability that the
event would occur
q: Probability that the
event would not occur
Estimating Reach n+
Probability models (cont’d)
Binomial probability distribution (cont’d)
Ex) Vehicle X’s rating = 16.67%
Ad inserts = 4 times
What is the probability that the ad is seen 2 times?
P(4E2) = 4C2 x (.1667)2 x (.8333)2
= [4!/(2!)(2!)] x .0278 x .6944 = 6 x .0193
= .1158
= 11.58%
Estimating Reach n+
Probability models (cont’d)
Binomial probability distribution (cont’d)
Calculating the probability of ad exposures is the same as calculating
the probability of flipping a coin or throwing a dice
Binomial distribution has two problems:
1) BD uses an average monthly rating, and does not consider the fact
that ratings constantly change
2) BD ignores individual variation in the probability of exposures
Estimating Reach n+
Probability models (cont’d)
Sainsbury Formula
How to estimate the combined reach of vehicles A and B?
Rc = R(A) + R(B) – R(A&B) = R(A) + R(B) – R(A) x R(B)
= 1- [1-R(A)] x [1-R(B)]
Net reach of n vehicles (R1, R2,…, Rn)
= 1.0 – [(1.0 – R1)(1.0 – R2)(1.0 – R3) … (1.0 – Rn)]
Estimating Reach n+
Probability models (cont’d)
Sainsbury Formula (cont’d)
Net reach of 3 vehicles
Program
Rating
A
10
B
15
C
20
Reach = 1.0 – [(1.0-.10)x(1.0-.15)x(1.0-.20)]
= 1.0 - .612 = .388 = 38.8%
GRPs = 10 + 15 + 20 = 45
Frequency = 45/38.8 = 1.2
Estimating Reach n+
Probability models (cont’d)
Sainsbury Formula (cont’d)
An application of the “binomial probability distribution model.”
Assumption: Media duplication is a random process (?!)
Advantage: Easy to use, allows rough comparisons of different
schedules.
Disadvantage: Tends to overestimate reach (thus underestimate
frequency).
Solution: Deduct 10% of estimated reach.
Estimating Reach n+
Probability models (cont’d)
Beta binomial distribution (BBD)
It is assumed that individuals are not homogeneous in terms of exposure
probability, which follows a continuous distribution
P(x): Probability of an
event in a repeated trial
T  x
T −x
P(x) =   p (1− p)
x 
T: the total # of
insertions in the
schedule
p: the composite
vehicle audiences
Estimating Reach n+
Probability models (cont’d)
Beta binomial distribution (BBD) (cont’d)
Magazines
A
B
C
Total
%Audience
13.85
9.80
11.70
35.35
Step 1: Calculate composite audience
(.1385 x 1 + .0980 x 1 + .1170 x 1)/3 = .1180
Insertion
1
1
1
3
Estimating Reach n+
Probability models
Beta binomial distribution (BBD) (cont’d)
3 
p ( x = 0 ) =   ∗ . 1180
0 
0
∗ (1 − . 1180 ) 3 − 0 = . 6862
3
p ( x = 1) =   ∗ . 1180 1 ∗ (1 − . 1180 ) 3 − 1 = . 2754
1 
3 
p ( x = 2 ) =   ∗ . 1180 2 ∗ (1 − . 1180 ) 3 − 2 = . 0368
2
3 
p ( x = 3 ) =   ∗ . 1180
3 
3
∗ (1 − . 1180 ) 3 − 3 = . 016
Estimating Reach n+
Probability models (cont’d)
Other estimation models
Conditional beta binomial distribution (CBD)
Sequential aggregation model
Dirichlet Multinomial distribution model
Canonical expansion model
Hyper-beta distribution model
Every probability model is based on assumptions, not on universal truths
The more accurate, the better
Cannot answer the question of “why?”
Any question?