The document discusses improving forecast accuracy through collaboration between forecasting and business teams. It frames forecasting as a repeated game where initially neither team has incentives to collaborate, but over time cooperation can emerge as the dominant strategy to build trust and reputation. Key recommendations include empowering stakeholders, transparency, fairness, and avoiding blame to encourage collaboration instead of defection.

1. http://www.andreaterzaghi.eu
The art of Forecast
Improving forecasting accuracy
Andrea Terzaghi
October 2011

2. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 1
Top-down and Bottom up
Forecasts may be of two different types: top-down and bottom-up:
o Top-Down forecasts typically set objectives to operative managers and consider a
stretch (and a risk) compared to the currently possibilities of the organization in the
reference market. The driver is typically the Shareholders expectations
o Bottom-Up forecasts try to understand the real possibilities of the organization in the
reference market with no bias from Top Management.
Normally companies have a mixed approach to forecasts but I will focus here on the
methodologies to improve bottom-up forecast accuracy: once the base line has been set and
understood with a bottom-up forecast, Top managers can ask for stretch clearly understanding
the consequences of their decisions.
Why Forecasting accuracy is so important
Bottom-up forecasting process allows an organization to
see a bit further into the future and to plan for it.
Estimations and insights are useful to correctly and timely
allocate resources (or de-allocate them before it is too late)
to meet Business Objectives and shareholders
expectations. Top Management can take informed
decisions to steer business in new directions. Typical
decisions are for example investments cuts (or even
unfortunately personnel) or investments approvals to
reach new markets or develop new technologies.
Forecasting activities are crucial in Top Management decision making process. An error in
forecasting can be disruptive for the business and for Top Managers credibility and reputation.
Every top manager is worried about the quality of the forecasting process and many consulting
firms move in this space to sell a lot of stuff to troubled organizations.
The usual solutions to improve forecasting accuracy
The traditional solutions to improve forecasting accuracy follow two mainstreams:
1. Implement better “forecasting” software and abandon old fashioned approaches that
use MS Excel. Excel is considered suitable for small organizations with low complexity
and suggests an artisan “not so professional” approach.
2. Increase mathematical sophistication of the forecasting models: the usual thinking
follows the logic of “the more mathematics there is, the more precise the calculation
will be”.
They are true to some extent.
1. Excel is a very powerful tool and it is very flexible, too flexible. It can be considered as
a white piece of paper: to extract the best from it, skilled people are needed; it does not
provide usable user-friendly interfaces for reporting purposes to stakeholders and
features to gather data from the field in a structured way. All these activities are time
Your forecasts are always
wrong!
- Undisclosed -

3. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 2
expensive and source of errors: people managing the tool have to have skills both as an
IT expert and as a Business expert: they are normally considered a bit geek. At the end
the Excel forecasting spreadsheets become a sort of “black box” for the rest of the
organization and may contain undetected errors.
2. Mathematical sophistication is of course necessary but only to some extent:
 Good quality of data is needed in order to provide good quality of outputs: not all
the companies are in a situation in which they have high quality of data to be used.
If poor approximate data is used, no matter how sophisticated is the mathematical
approach, poor quality of results is obtained. There is a risk of “smoke curtain”:
because of the highly sophisticated mathematical approach, people may be
deceived and think that the output is highly accurate even with poor quality input
data. This is a really serious error and may mislead the business. Too many cases
can be found in literature and in everyday life in any industry, from Oil&Gas to
Banking.
 Highly sophisticated mathematical models are not easily understandable by most
of the people. They may provide correct outputs that contradict common sense. It
would be very tough to validate them and use the result in a Business decision.
Pragmatic approach to mathematical sophistication is crucial: the calculation has
to be as accurate as possible but it must be possible to replicate it at 90% accuracy
using only common sense, a piece of paper and a pen.
The real pathway towards Forecasting accuracy
My key point is: forecasting deals with future and in particular with the expectations of
people around future. The process deals with people and their psychology. It is not a
mathematical trick; it is a matter of humanities.
Those aspects have to be carefully considered in shaping the forecasting processes. Some key
elements have to be put in place:
1. Transparency: forecast results and expectations (business objectives) have to be
communicated capillary to the organization to all stakeholders
2. Ownership of the forecast: any stakeholder who is responsible for the attainment of
a specific business objective has to feel that it is his own objective and feel empowered
to get it.
3. Clarity and fairness in the calculation: the way in which objectives are calculated
have to be clearly understood and accepted by all the stakeholders, the calculation
methodology should not make any difference among stakeholders
New forecasting tools have to go in the direction of providing Transparency and Clarity in the
calculation methodology, Mathematical sophistication may improve the accuracy but destroy
the sense of ownership of the stakeholders: they do not understand which “levers of business”
have to be actioned to get the result.
In my experience the only reason for poor forecasting performances is:
Disconnection between the forecasting department and the operative managers who do
not feel any ownership of the business objectives

4. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 3
Forecasting and game theory
Forecasting is a negotiation between those two actors: the finance department and the
operative manager and can be treated with game theory. The very simple model of Prisoner’s
dilemma can be used.
Let’s consider the two players, the Forecast Department and the Operative Manager, in
particular, for sake of simplicity, a Sales Manager who has a bonus payout linked to his
performance against the forecast.
They have two possible behaviors: “Collaborate” or “Not collaborate - Defect” with the other in
the preparation of the forecasting document for the Top Management.
Ideally, 4 scenarios are possible and for each of them will have different benefits for both
players.
In detail:
o Forecast Dept. collaborates, Business does not collaborate: this scenario happens
when the Forecasting department input in the Forecast any figure and any assumption
provided by the Sales Manager without challenging it and, on the other hand, the sales
manager is not transparent enough about sales expectations and market dynamics:
typically the sales manager provides low sales expectations (sandbagging) to ensure to
have an easy forecast: most likely actual sales will be higher providing great bonuses to
the Sales manager, blame to the Forecasting department because they were fooled by
the Business and resulting in a underestimated forecast.
o Forecast Dept. does not collaborate, Business collaborates: this scenario happens
when the Forecasting department connects to the Business but does not trust them,
thinking they are sandbagging, and input in the Forecast a different value (typically
higher) from the one proposed. Again, this generates poor forecasting, blame to the
Business because they do not reach the objectives and consequently their bonus is
Prisoner’ Dilemma
The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two purely
"rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no
means of speaking to or exchanging messages with the other. The prosecutors do not have enough evidence to
convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge.
Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to:
betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining
silent. Here is the offer:
o If A and B each betray the other, each of them serves 2 years in prison
o If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
o If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison
sentences they get, and that their decision will not affect their reputation in the future. Because betraying a partner
offers a greater reward than cooperating with him, all purely rational self-interested prisoners would betray the
other, and so the only possible outcome for two purely rational prisoners is for them to betray each other.

5. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 4
reduced. Finance Department has a simple story to explain the variance: “it’s all Sales
managers’ fault!”.
o Forecast Dept. and Business does not collaborate: this is similar to the previous
scenario with Business that does not know what the Forecasting is doing, has not
transparency, does not buy in the forecasting methodology and the KPI that are used,
does not loose time in talking with them, on the other hand, Forecasting department
does not trust the Business, does not talk with them, does not share information and
hypothesis, take much less time and effort to discuss the forecast hypothesis, does not
enter any negotiation process with them. Because of the lack of knowledge from
Finance Department, objectives are erroneously set and can be easily reachable for the
Business, thus raising (only by chance) the possibilities to get a bonus out of it. This is
the worst possible scenario for forecasting accuracy and, of course the situation is of
reciprocal blame between the two departments.
o Forecasting Dept. and Business collaborate: this scenario happens when the
Forecasting Dept. share hypothesis, KPI, data, reports, put a lot of effort in sharing data
and in the negotiations, on the other hand the Business people have to spend a lot of
time with the Finance guy, reducing the selling time, provide transparency on the
business insights and receiving an objectives that is challenging but reachable, thus
having the bonus payout that is good but not over performing.
To simplify:
Business
Collaborates
Business DOES NOT
Collaborate
Finance Dept.
Collaborates
Finance: effort, no need to
explain because variances are
small
Business: effort, Bonuses
average result
Output: accurate
Finance: effort, fooled, need to
explain
Business: no effort, great
Bonuses
Output: underestimation
Finance Dept.
DOES NOT
collaborates
Finance: less effort, no need to
explain (blame Business)
Business: effort, fooled, poor
Bonuses, complains with
Finance for stretched
hypothesis
Output: overestimation
Finance: less effort, no need to
explain (blame Business)
Business: no effort, if lucky
great Bonuses. complains with
Finance for wrong forecasts
Output: random result
In a basic scenario in which the players have to play just one time, are selfish and have no fear
in social blame, both parties are incentivized to “not collaborate” with the other:
o If Business does not collaborate, they will benefit of a forecast with lower or wrong
targets thus increasing their bonus payout
o If Finance does not collaborate, they will benefit because of a reduced effort to prepare
the forecast, reduced time to prepare reports, no time for negotiations, reduced time in
Forecast preparation. If the forecast is not accurate, Business is to blame.
The two are called “dominant strategies” as for each of them is better to “not collaborate”
regardless of the strategy used by the counterpart.

6. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 5
Forecasting is a repeated game
The reality is a bit more complex because Forecast exercise is run multiple times between the
same actors: this changes the approach of the game. Each stage (forecast) is a part of a wider
repeated game in which the decisions (strategies) taken in a previous run impact the future
outcome as the counterpart will react to the strategy applied.
Repeated games theory clearly states that, even in Prisoner’s Dilemma, it is possible to reach
Win-Win situation in which Collaboration (and behaving not in a selfish way) is more
convenient. This creates a Social Norm in which the players decide to collaborate because they
know that the punishment will have a very high cost due to non-forgiving playing strategies
applied from the other player in case of Defection.
Repeated games
In game theory, a repeated game (supergame or iterated game) is an extensive form game which consists in some
number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied
2-person games. It captures the idea that a player will have to take into account the impact of his current
action on the future actions of other players; this is sometimes called his reputation. The presence of
different equilibrium properties is because the threat of retaliation is real, since one will play the game again with
the same person. It can be proved that every strategy that has a payoff greater than the minmax payoff can be a
Nash Equilibrium, which is a very large set of strategies. Single stage game or single shot game are names for non-
repeated games.
The most widely studied repeated games are games that are repeated a possibly infinite number of times. On
many occasions, it is found that the optimal method of playing a repeated game is not to repeatedly play a
Nash strategy of the constituent game (look at the Repeated prisoner's dilemma example), but to cooperate and
play a socially optimum strategy. This can be interpreted as a "social norm" and one essential part of infinitely
repeated games is punishing players who deviate from this cooperative strategy. The punishment may be
something like playing a strategy which leads to reduced payoff to both players for the rest of the game (called a
trigger strategy). There are many results in theorems which deal with how to achieve and maintain a socially
optimal equilibrium in repeated games. These results are collectively called "Folk Theorems". An important feature
of a repeated game is the way in which a player's preferences may be modeled
Cooperation with trigger strategies in the repeated
Prisoner’s Dilemma
In case in which both players use a not-forgiving trigger strategy:
o Collaborate in every period unless someone has Defected in the past
o Defect forever if someone has Defected in the past
The result is:
o Cooperation is the best response to Cooperation
o Defection is the best response to Defection
It is possible to have a long-lasting “Collaboration – Collaboration” (Win-Win) situation

7. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 6
So in a repeated Forecasting game, rules of the game changes dramatically: now the reputation
of the people involved as professionals is put on the table: since there are so many occasions to
collaborate both parties are pushed collaborate as in any organization who collaborates is
better considered that who do not collaborate. Moreover:
o Business side has a pressure not to tell lies and be transparent, in order to avoid
putting at risk his reputation and being considered as a “sandbagger” and not trusted
anymore, a bit like in the fable: “The Boy Who Cried Wolf
1
”.
o Finance department has a clear pressure to listen and accommodate in the finance
prospects the input form the Business side, in order to avoid the risk of being
considered a useless source of wrong messages to the Senior Management.
Negotiation and continuously adjustment of own strategies based on past behaviors of the
other side are necessary for both parties to create equilibrium and a win-win situation.
The Negotiation mechanism between Finance Department and Business Department is easily
described:
o Finance department does not betray Business in order to avoid to have an “enemy” in
the organization complaining against them, this will rise their effort in Forecasting
preparation with no significant increase in Forecasting accuracy.
o Business does not betray Finance Department with a short term benefit (higher
bonuses for 1 round) to avoid the risk of not receiving any bonus in the future.
The build-up of a clear and transparent reputation for any stakeholders is crucial: Business
owner performance against Forecast has to be published, messages about lack of transparency
of the Forecasting Department as to be spread in the organization.
Final recommendations to improve forecasting accuracy
To summarize the real winning point is to create a collaborative and trustful scenario among
players:
a. Forecasting is not a recipe cooked in the headquarter office with a top-down approach,
Forecasting is an organizational process to capture bottom-up the contribution of all
stakeholders to increase accuracy
b. Ownership of each single KPI should be clear and the owner has to be empowered in
reaching the target
c. Transparency about the complete set of objectives and their attainments should be
provided. Reporting is a key aspect in the forecasting process: it builds the reputation
of each stakeholder in the forecasting process.
d. Fairness has to be demonstrated by Finance Department in order to keep the conflict at
low level and develop the trust among parties
e. No blame for business owners that missed an objective should be generated. This will
reduce the conflict among the stakeholders and allow collaboration behavior to emerge
f. A clear non-forgiving strategy has to be declared at the beginning of the game from
both sides.
g. Run the forecast game between the players as often as possible implementing for
example Rolling forecast approach with monthly reviews. This will enhance
cooperation and communication among parties
1
http://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf

8. The Art of Forecast, Improving forecasting accuracy – Andrea Terzaghi – October 2011 – 7
In this environment tools and mathematical sophistication are useful but not necessary. The
risk of lacking money and reputation from the Business will be the best incentive to improve
forecasting accuracy.
Final Disclaimer: Business environment such as the attitude of the people involved and the
values that the Company promotes in the organization have certainly an impact on the above
considerations enhancing/reducing the benefit of the measures taken. Life is always more
complex than any mental model you want to apply to it.
Bibliography:
A great book that inspired this paper is “Thinking strategically – The
competitive Edge in Business, Politics, and everyday life” where the basis of
“game Theory” are provided and applied to so many different situations such as
for example Baseball matches and so on, that allows the reader to “think out of
the box” and look at reality with a new perspective.
http://amzn.to/1T4V0pr
Other sources:
o Wikipedia Prisoner’s Dilemma: http://en.wikipedia.org/wiki/Prisoner%27s_dilemma
o Wikipedia Repeated game: http://en.wikipedia.org/wiki/Repeated_game
o MIT, Repeated games and cooperation, Acemoglu and Ozdaglar http://economics.mit.edu/files/4754
o Econometrica, Prediction, optimization an learning in repeated game, Nachbar:
http://www.uibk.ac.at/economics/bbl/lit_se/lit_se_ws0506_papiere/nachbar_pred_op_rat.pdf