Decision Tree Analysis: choosing between options by
projecting likely outcomes.
How to use tool:
Decision Trees are excellent tools for helping you to
choose between several courses of action. They provide a
highly effective structure within which you can lay out
options and investigate the possible outcomes of choosing
those options. They also help you to form a balanced
picture of the risks and rewards associated with each
possible course of action.
Drawing a Decision Tree
You start a Decision Tree with a decision that you need to
make. Draw a small square to represent this towards the
left of a large piece of paper. From this box draw out
lines towards the right for each possible solution, and
write that solution along the line. Keep the lines apart
as far as possible so that you can expand your thoughts.
At the end of each line, consider the results. If the
result of taking that decision is uncertain, draw a small
circle. If the result is another decision that you need to
make, draw another square. Squares represent decisions,
and circles represent uncertain outcomes. Write the
decision or factor above the square or circle. If you have
completed the solution at the end of the line, just leave
Starting from the new decision squares on your diagram,
draw out lines representing the options that you could
select. From the circles draw lines representing possible
outcomes. Again make a brief note on the line saying what
it means. Keep on doing this until you have drawn out as
many of the possible outcomes and decisions as you can see
leading on from the original decisions.
An example of the sort of thing you will end up with is
shown in Figure 1:
Once you have done this, review your tree diagram.
Challenge each square and circle to see if there are any
solutions or outcomes you have not considered. If there
are, draw them in. If necessary, redraft your tree if
parts of it are too congested or untidy. You should now
have a good understanding of the range of possible
outcomes of your decisions.
Evaluating Your Decision Tree
Now you are ready to evaluate the decision tree. This is
where you can work out which option has the greatest worth
to you. Start by assigning a cash value or score to each
possible outcome - how much you think it would be worth to
you if that outcome came about.
Next look at each circle (representing an uncertainty
point) and estimate the probability of each outcome. If
you use percentages, the total must come to 100% at each
circle. If you use fractions, these must add up to 1. If
you have data on past events you may be able to make
rigorous estimates of the probabilities. Otherwise write
down your best guess.
This will give you a tree like the one shown in Figure 2:
Calculating Tree Values
Once you have worked out the value of the outcomes, and
have assessed the probability of the outcomes of
uncertainty, it is time to start calculating the values
that will help you make your decision.
Start on the right hand side of the decision tree, and
work back towards the left. As you complete a set of
calculations on a node (decision square or uncertainty
circle), all you need to do is to record the result. You
can ignore all the calculations that lead to that result
from then on.
Calculating The Value of
Uncertain Outcome Nodes
Where you are calculating the value of uncertain outcomes
(circles on the diagram), do this by multiplying the value
of the outcomes by their probability. The total for that
node of the tree is the total of these values.
In the example in Figure 2, the value for 'new product,
thorough development' is:
0.4 (probability good outcome) x £500,000 (value) =
0.4 (probability moderate outcome) x £25,000 (value) =
0.2 (probability poor outcome) x £1,000 (value) = £200
Figure 3 shows the calculation of uncertain outcome nodes:
Note that the values calculated for each node are shown in
Calculating The Value of Decision
When you are evaluating a decision node, write down the
cost of each option along each decision line. Then
subtract the cost from the outcome value that you have
already calculated. This will give you a value that
represents the benefit of that decision.
Note that amounts already spent do not count for this
analysis - these are 'sunk costs' and (despite emotional
counter-arguments) should not be factored into the
decision. When you have calculated these decision
benefits, choose the option that has the largest benefit,
and take that as the decision made. This is the value of
that decision node.
Figure 4 shows this calculation of decision nodes in our
In this example, the benefit we previously calculated for
'new product, thorough development' was £210,000. We
estimate the future cost of this approach as £75,000. This
gives a net benefit of £135,000.
The net benefit of 'new product, rapid development' was
£15,700. On this branch we therefore choose the most
valuable option, 'new product, thorough development', and
allocate this value to the decision node.
By applying this technique we can see that the best option
is to develop a new product. It is worth much more to us
to take our time and get the product right, than to rush
the product to market. It is better just to improve our
existing products than to botch a new product, even though
it costs us less.
Decision trees provide an effective method of
decision-making because they:
clearly lay out the problem so that all options can be
allow us to analyse fully the possible consequences of a
provide a framework to quantify the values of outcomes and
the probabilities of achieving them
help us to make the best decisions on the basis of
existing information and best guesses.
As with all decision-making methods, decision tree
analysis should be used in conjunction with common sense -
decision trees are just one important part of your
decision-making tool kit.