## Averaging Performance Measures

During the development of a Performance Based Contract (PBC) one area that consistently trips people up is the concept of averaging.  Typically, performance measures take into account multiple timeframes (e.g. days in a month), multiple events in a time period (e.g. number of deliveries in a day) or even multiple events in multiple timeframes (e.g. a number of repairs in a single day, and then those days in a month).  So how do we take into account these multiples into a single number for payment to our contractor?

The default position of most practitioners reflects our education.  That is to use a simple mathematical average or mean of all the values. Here the equation is simply:

Average = total score for all events (or timeframe (e.g. days)) divided by number of events (or timeframe)

I refer to this approach as Input Averaging since it uses the Contractor’s input score to average. While this approach is easy to understand and simple to use, it does have a disadvantage; that is, depending on the payment curve (i.e. the relationship between performance and payment), this approach may mask poor performance by treating the value received by the buyer for all events equally.

Other simple approaches, although less common, base the final score on either the minimum or maximum input score over the events (or timeframe).  While it is simple to apply and easy to understand, what happens to the final score if the minimum score is delivered on the first day, what incentive is there for the contractor to deliver any better performance during the timeframe? Alternatively, if the maximum score is delivered on the first day, what incentive is there for the contractor to continue to deliver this level of performance during the timeframe? I refer to these approaches to averaging as either Minimum Averaging or Maximum Averaging.

The less common approach to averaging is to treat each event (or timeframe) against the payment curve. That is to calculate the payment for each event resulting in what I like to call Output Averaging. In this approach the final score is based on an average of the payments corresponding to each event or timeframe. I believe this approach is more representative of the average ‘value’ delivered to the buyer.  Unfortunately, this approach is more complex to apply including using to trigger other contract consequences such as Stop Payment or Termination where the average input payment levels are traditionally used.

To assist in understanding these differences consider the following example.  A contractor is to deliver a product to the buyer on-time, every-time.  The measure is simply the number of days late between the contracted delivery date and the actual delivery date.  In this case the relationship between performance and payment is represented as follows:

• on-time (e.g. 0 days late) or less (e.g. early) results in 100% payment
• 1 day late results in 75% payment
• 2 days or greater results in 30% payment

So consider a single day with 3 deliveries, the first delivery being on-time (i.e. 0 days late), the second being 1 day late and the third being 2 days late.

Based on this example the Input Averaging approach would result in a final score of 1 day late based on the simple mathematical average of the delivery times (e.g. 0 days + 1 day + 2 days divided by 3 deliveries) resulting in an 75% payment.

The Minimum Averaging approach would result in an “average” of 0 days and 100% payment while the Maximum Averaging approach would result in an “average” of 2 days and 0% payment.

Alternatively, the Output Averaging approach would be the average of the payment score for each delivery in the day, in this case resulting in payment of 68.3% based on 100% + 75% + 30% divided by the 3 deliveries.

So how do you choose which is the best approach?  My thoughts are the choice should best balance the value received by the buyer with the simplicity of the approach.

That said, there are specific circumstances where you would combine the approaches. For example, you could use the Minimum / Maximum Averaging for a range of events (e.g. minimum quantities held by a contractor over a range of items or products) on a single day, but then use Input / Output Averaging for all days within a month. This approach provides a good balance of protection to the buyer and simplicity, but also fairness to the contractor

So in summary there are 4 types of averaging used in a PBC as follows:

• simple mathematical average (input average)
• payment averaging (output average)
• minimum value
• maximum value

Each approach has their own advantages and disadvantages that should be considered when developing your performance measure.

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