# The Packages Option Generator: scoring

The Packages Option Generator uses the scores of each of the shortlisted measures and their barrier scores or a set of pairwise synergy scores. These are summed and divided by the number of measures in the package to give a final score out of 100, which is rounded to the nearest integer.

If the user chooses to package based on overcoming barriers, for a package with r measures, the formula is:

*Score _{mn..r} = (Score_{m} + Score_{n} + ... + Score_{r} + Bar_{m} + Bar_{n} + ... + Bar_{r})/r*

Score_{m} is obtained in the initial option generator as explained in Single Measure Option Generator: scoring.

Bar_{m} is based on the barriers table in the First Principles section for measure *m*. The 6-point scores (0 to -5) are summed over the four barriers: finance, governance, political acceptability, stakeholder acceptability. (The legal and technical barriers are excluded, since packaging is not expected to resolve them.) The formula is thus based on the assumption that a pair of measures with fewer barriers in total is likely to be more effective.

If the user chooses to package based on seeking synergy, for a package with r measures, the formula is:

*Score _{mn..r} = (Score_{m} + Score_{n} + ... + Score_{r} + Syn_{mn} + ... + Syn_{qr})/r*

Score_{m} is obtained in the initial option generator as explained in Single Measure Option Generator: scoring.

Syn_{mn} is a synergy score for the pair of measures *m, n* which is dependent on the objectives, problems or indicators which the user selects in the initial option generator, and the weights assigned to each. The formula for calculating Syn_{mn} is

*Syn _{mn} = ΣW_{a}Syn_{mna}*

where *W _{a}* is the weight given to objective

*a*by the user normalised so that

*ΣW*1, and

_{a}=*Syn*is the synergy score for measures

_{mna}*m*and

*n*for objective

*a*. The values for

*Syn*were derived from a model-based analysis in which ten types of measure were tested alone and in pairs in terms of their impact on four performance indicators of accessibility, delay, accidents and carbon emissions. Synergy scores for each pair of measures for a given performance indicator were based on the extent to which the performance of the pair exceeded (for positive synergy) or was less than (for negative synergy) the sum of the performances of the two individual measures. In calculating the formula above, each measure is assigned to one of the ten types, and each objective, or problem, or indicator, is associated with one of the four performance indicators.

_{mna}In this formula, a synergy score is included for each pair of measures in the package; thus for a package of 2 measures there is one synergy score, for a package of 3, three, for a package of 4, six and for a package of 5, ten. This is a simplifying assumption based on earlier work which suggested that synergies were largely additive across larger packages of measures.