At the 2010 AMSRS conference, a paper was
presented dealing with the difficulties of using purchase intent scores to
estimate sales for a new product.

The claim was made we can’t simply take
these scores, however much we may modify or recode them, and use them for this
purpose. So an approach was described,
whereby the purchase intent scores for a similar/comparable product that

__had__been launched were used to devise a calibration factor for the scores obtained for the test product.
That’s not a bad idea … however, it’s
not quite so simple.

Purchase intent, properly considered,
measures only the respondent’s likelihood that they will

__try__the product. There is no guarantee that, once having tried, the respondent would go on to adopt the product into his/her repertoire (i.e. keep on buying it).
Indeed, if the product turns out to be
a ‘dog’, then there is very little likelihood that the respondent will ever
purchase that product again.

*[Why are dogs used to represent something bad? I know some very nice dogs.]*
So, properly considered, purchase
intent scores are only one part of the estimation process. This is why, some considerable number of
years ago, “trial-repeat” modelling arose.
It’s an old approach, but I have yet to find one better.

The underlying premise of trial-repeat
modelling is that the steady-state long-run market share achieved by a (new)
product will be the product of the long-run levels of trial and repeat
purchasing it attains.

Thus (slightly simplified):

*M*

_{R}= T_{R}* R_{R}
where:

*M*= steady-state long-run market share_{R}*T*= long-run cumulative trial rate

_{R}*R*= long-run repeat purchase rate.

_{R}
Further (again, slightly simplified):

- Trial comes through initial purchase
- Initial purchase depends on the level of awareness (brought about by advertising and promotion) and on the availability of the product in stores.

Thus:

*T*

_{R}= T_{P}* A* D
where:

*T*= long-run probability of trial_{P}*A*= long-run level of awareness

*D*= long-run level of distribution.

All the above
parameters are reasonably readily able to be estimated, except

*R*- the long-run repeat purchase rate._{R}*T*can be estimated from the proportion of respondents who indicate at the initial interview of a product test that they would buy or choose the test product.

_{P}*D*and

*A*can be specified based on experience or by some other means.

*R*- the long-run repeat purchase rate – can actually be viewed as the equilibrium, or steady-state solution of a first-order, two-state Markov chain.

_{R}
In the table
below, R

_{1}is the probability that someone would be in a state of not having bought the test product, and would move into a state of having bought the test product. R_{2}is defined similarly.
Some people will stay permanently in
the ‘not buy’ state and others will stay permanently in the ‘buy’ state. And some will be in a constant state of flux,
moving periodically from ‘not buy this time’ or ‘buy this time’ to ‘not buy
next time’ or ‘buy next time’.

In the long term, for a group of people
it can be shown that mathematically things settle down to a steady state
situation, R

_{R}, the long-run repeat purchase rate mentioned above.
In fact,

*R*turns out to be_{R}__exactly__computed as[1]:
•

*R*_{R}_{ }=*R*/ (_{1}*R*+ 1 -_{1}*R*)._{2}
Where do

*R*and_{1}*R*come from?_{2}
In some
simulated test market models, where respondents are interviewed both before and
after the product is placed with them to try, estimates of

*R*and_{1}*R*are based on the behaviour (or preferences) at the follow-up interview:_{2}*R*is the proportion of those respondents who_{1}__did not__buy/choose the test product at the initial interview, who__did__buy/choose at the follow-up interview.*R*is the proportion of those respondents who_{2}__did__buy/choose the test product at the initial interview, who__did so again__at the follow-up interview.

But if we are
not actually undertaking a full-scale simulated test market modelling study,
what do we do?

From a one
stage product test (i.e. where product is not actually placed with respondents),
we actually have some information in the answers obtained to the purchase
intent questions.

We can assume,
for example, that:

• “I would definitely buy this product” = 70%
probability of purchase

• “I would probably buy this product” = 30% probability
of purchase.

An estimate of

*R*_{1}_{ }can then be computed directly from this information, perhaps with some additional tweaks.*R*can take an assumed value, normally around 25% to 35% (depending on the category) and the trial-repeat calculations then worked through to give the long-run market share estimate_{2}*M*._{R}
In reality, we
should not make fixed assumptions about

__any__of the various parameters discussed above. Ideally, we would conduct a number of Monte Carlo simulations, where values for each parameter are sampled from a specified distribution. That’s not too hard to do, and it gives us the option of providing an estimated product sales figure that sits between an upper and lower bound, or (better) 25^{th}, median and 75^{th}percentile estimates (based on the estimated values for*M*, in combination with population data, and weight and frequency of purchase)._{R}
My experience
in doing this over very many projects is that the eventual actual sales often
lie pretty much in the middle of that range, i.e. more or less coinciding with
the median forecast.

[1] William Feller,

*An Introduction to Probability Theory and its Applications: Vol 1*, 3rd edition, Wiley 1968.
## No comments:

## Post a Comment