## Friday, November 21, 2014

### Figure of Merit

"Figure of Merit".... everybody got this, or should I say more?

Some say FoM, of course.

Definition
A figure-of-merit is a metric used to compare like objects or concepts where the metric itself may have no dimension or units of measure (UoM); or the FoM dimension is meaningless for day to day operations. You can also think of a FoM as a weight applied to separate the value or utility of one thing from its peers.

A FoM may have no dimension because it is a ratio of two similarly dimensioned metrics, so the dimensions cancel in the ratio; it may have dimensions that are meaningless  for anything other than that's how the metric got formed -- like days-squared.

Sometimes, when you have no other way to compare something, a FoM, even if you make it up  gives you a way to separate things and make decisions.

Examples
Day to day in the PM domain, we run into a lot of stuff that needs to be compared -- one strategy over another, or one competitor over another, etc -- and there's no one metric that quite does it.

Enter: FoM

You might look at a number of factors and baseline competitor A as a "10" -- a dimensionless FoM. All others are compared to the baseline. If competitor "B" is evaluated as a 20, or some such, and bigger is better, then B is twice as "good" or valuable as A on the basis of a figure of merit.

You might look at the utility of one thing over another. Utility is perceived value; it may not be objective -- quality, like art, is in the eye of the beholder, etc. -- and it may not be functional: what's the perceived value of silver over black? (My wife won't buy a black car .... so, a black car on the sales lot has no value to her )

To look at the utility of something, you give it a score -- a FoM -- probably dimensionless. And, then everything else is compared to it. (Silver gets a 10; black gets a 0)

And then there's the quantitative stuff, like risk variance. Risk is often judged by how far an outcome might be from the accepted norm or average value. But, this implies a direction ... how far in what direction? Maybe it doesn't matter. Perhaps you've got a situation where the direction is immaterial and it's all about distance.

In that case, as in + or - from the average value, the way to get around direction is to square the distance -- now, everything is positive but, alas, the dimension is now squared, as in days-squared.

That's ok, just think of the variance is a FoM: smaller is better! Who actually cares what a days-squared is? Nobody, actually.

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