We are actually trying to measure performance - something quite difficult actually.

Yes, we measure by the stage time, but for overall scoring the problem is:

What do we use as an INDEX?
 - You actually have an unknown challenge when you set up a match.
 - What is a good time for each stage?
 - Will the performances be closely "packed" - i.e. only tenths or hundreds of a second apart?
 - Or will they vary by several seconds for each performer?
 - Will the stages measure shooting speed, transition speed or foot speed?

The normal solution for testing physical and mental abilities and contests is to have a large sample of people perform the test, then compare the individual with the larger sample. As such we often use either a total score or a percentile method.
If the component parts are essentially equal (each of 10 parts worth 10%) OR if the scores for each section can be accurately WEIGHED (some parts worth 5 %, others 12%, etc), a total score method works well.
If the parts are NOT equal and you cannot readily WEIGHT each portion, a percentile method or ranking system is more accurate.

Many think of scoring a cowboy match as simply scoring a single race - sort of like a relay. In that case, the one that crosses the finish line first wins. We usually also measure the performance by using the total time of the race. Total time can be a relatively "linear" measurement that works well for most races.

But what if the conditions under which the race is run is different?
What if one race is run up hill while other competitors run down hill? Would it be as simple to measure as taking the total time? Would total time then be "fair?" Such situations are no longer simple, linear measurements

Many see total time as the solution, but I have some reservations about that.

A cowboy match is actually more complex than a simple race because the contest can contain many different elements. For example some stages are simple "stand and deliver" with essentially no movement. Others require much more movement or may involve using props or unusual staging. Standing at a table with pistols holstered and long guns handily on the table is quite different than having to run between locations, shoot and pulling and returning long guns from scabbards. As an analogy, think of a decathlon competition. The contestants have to perform a variety of different challenges with differing skills.

For example, you may have to run a 100 meter spring, run hurdles, throw objects for distance and run a long distance run. Consider just doing different running challenges such as the 100 meters dash, hurdles, and a mile run.
Of course, the surest way to win such a competition is to win all the events, but what if you don't. Say you win the 100 meter dash by 0.5 seconds, the 200 meter hurdles by 2 seconds, but lose the mile by 3 seconds. You had significant wins in the shorter races but a close lose in the mile. Even though you won two out of three of the events decisively, you would lose overall due to a close lose in the mile.
This example shows a major flaw in total time scoring.
This is also the strength of the rank scoring system.

Some folks have figured this out so they know they can "Make up" for some "bad" stage performances. Of course, they prefer the Total Time method in part for this reason.

What is the weakness of rank scoring?

First, if you do NOT have an adequate sample (enough folks for a good distribution), rank scoring does not work well. You have to have quite a few folks to establish a good distribution or the results can be inaccurate. Certainly if less than 30 folks shoot, the distribution may inadequate as the index will have big gaps such that you cannot measure the relative merits of each stage unless the person wins essentially all the stages.
For this reason, I use and recommend using Total Time for scoring with smaller matches.

Another weakness of rank scoring relates more to match design.
If a stage is designed to be quite short or have a bonus on a short stage, getting a miss or not getting the bonus will result in getting a BIG difference in rank points so that the one stage becomes what I call a "Match Maker". You do well in this stage and it pretty well determines the match. By keeping this in mind when designing a match, this weakness can be maximized OR minimized.

An interesting sidelight is that Rank Scoring actually encourages accuracy more than Total Time does for such stages. Many competitors know this and shoot a Total Time match slightly differently because of of that. Some actually shoot a little more "recklessly" in a total time match. Not a bad thing, just different than many folks realize.

Further Complications
This is actually further complicated by how we score misses. We generally accept that a miss is a 5 second penalty added to the stage time. But some have pointed out that while this works pretty well, it is rather arbitrary because as miss in a fast stand and deliver has a greater percentage penalty than for a longer stage with more complications or movement. Also, if you think about our fantasy sport, very possibly the first miss may be more critical than one in the middle. And what if the last shot is a miss and the other fella still has bullets? Also, what if the person you missed shoots like Evil Roy and the other competitor missed someone who is not only slow but inaccurate. So if we figured out some method that a miss would be a PERCENTAGE of the stage time penalty, it still wouldn't be perfect or make everyone happy.

So in many ways the scoring is like the old joke:
Measure with a Micrometer, (Measure to 1/100 of a second)
Mark it with Chalk, (5 seconds per miss)
Cut it with an Ax (wide variance in stages)

Plus for most of us, our performance varies against our competition. No matter the scoring method, sometimes we beat our close competitors, sometimes they do.

Summary.
Both Rank or Total Time scoring systems have some advantages and disadvantages. Due to their strenths and weaknesses, I prefer Rank for larger matches and Total Time for smaller matches.

So go out and have as much fun as you can!
Don't let the little details distract from our FUN!

Here are some Excel spreadsheets I use to score matches. They are not perfected yet, so you have to do a litte more manually that I would like. (Excel files that were zipped)
Rank Score Sheet      Total Time Score Sheet