Probability of Award (The goal of the formula is to calculate our probability of beating a competitor and winning work)

[Manders0629]

Looking for some insight into a formula that I've been using (see also: inherited) at work that I want to understand more.

The goal of the formula is to calculate our probability of beating a competitor and winning work (aka Pwin).

There are two primary inputs/steps in the formula:
1. Calculate the percentage difference between our cost and the predicted cost of the competitor
2. Calculate the Z-score. This is done by dividing the above referenced cost difference by the % error associated with the competitor's cost prediction, revealing an absolute value:

=abs(cost difference/error%)

Where I'm confused is: how/why does dividing the cost difference by the competitor cost prediction error reveal a z-score?

Thank you!

 

[Dr.Peterson]

Looking for some insight into a formula that I've been using (see also: inherited) at work that I want to understand more.

The goal of the formula is to calculate our probability of beating a competitor and winning work (aka Pwin).

There are two primary inputs/steps in the formula:
1. Calculate the percentage difference between our cost and the predicted cost of the competitor
2. Calculate the Z-score. This is done by dividing the above referenced cost difference by the % error associated with the competitor's cost prediction, revealing an absolute value:

=abs(cost difference/error%)

Where I'm confused is: how/why does dividing the cost difference by the competitor cost prediction error reveal a z-score?

Thank you!

Can you give an example, using either real or fake (but reasonable) numbers, so we can be sure exactly what you mean by all this? I'm not sure what it means, without seeing how you carry it out.

That includes what you do with the result. What do you do when it tells you a certain probability, and is there any way of checking whether you were right? (That is, if it were complete nonsense made up by your predecessor, would anyone know?)

All I know is that z-scores are not probabilities.

 

[BigBeachBanana]

Looking for some insight into a formula that I've been using (see also: inherited) at work that I want to understand more.

The goal of the formula is to calculate our probability of beating a competitor and winning work (aka Pwin).

There are two primary inputs/steps in the formula:
1. Calculate the percentage difference between our cost and the predicted cost of the competitor
2. Calculate the Z-score. This is done by dividing the above referenced cost difference by the % error associated with the competitor's cost prediction, revealing an absolute value:

=abs(cost difference/error%)

Where I'm confused is: how/why does dividing the cost difference by the competitor cost prediction error reveal a z-score?

Thank you!

[math]\text{z-score}=\dfrac{x-\text{mean}}{\text{standard deviation}}[/math]
Step 1 is calculating the numerator. The difference between the cost and the predicted (mean/expected) cost. <- This measures how far your cost compares to your competitor's.

Step 2. The % error is synonymous with the standard deviation. Dividing the difference by the standard deviation normalizes the data so you can find the probability using the standard normal distribution.

A positive z-score says the data point is above average. A negative z-score says the data point is below average.
Since the difference between the cost and the predicted can be negative, they're taking an absolute value to ensure it's always positive. I'm not sure of the justification for taking the absolute value.