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PAX: The Great Leveler

-- by Jack Desert July 2020 --

Is PAX really The Great Leveler? Perhaps the following thought experiment will help you decide:

1. The Greatest Driver of the Day

Imagine you have a hundred cars show up at a race, all different makes and models. You are tasked with assigning each a handicap such that whoever wins today be dubbed The Greatest Driver of the Day.

In a perfect scenario, each car would be given a handicap based on its performance capability. You might measure this performance capability directly (200m time, skid pad G's, braking distance) or you might compute it based on some relevant data points (power, mass, tire size, tire rubber softness). You could even put an unbiased (ha!) driver in the cars, and time her on course.

Now you've assigned each car a handicap (which may have taken most of the day) let's get on to the good stuff!

The race goes on, a winner is declared and touted The Greatest Driver of the Day.

2. The Greatest Driver From Each Performance Group

The next week you decide to do it again. The same 100 cars show up, which makes your job easier. You already know the handicaps! But this week, instead of one trophy to give out there are ten! You could give out trophies for overall places 1 through 10. OR you could break the 100 cars into groups of 10 each, and offer a trophy to the winner of each. Let's say you opt for the latter..

The fastest 10 cars (based on handicap) are in group A. The next fastest 10 cars are in group B. And so on through the letter J.

A:
  CAR   HANDICAP
  1     1.00
  2     0.99
  3     0.99
  4     0.98
  5     0.98
  6     0.95
  7     0.94
  8     0.93
  9     0.93
 10     0.92

B:
  CAR   HANDICAP
  11    0.91
  12    0.90
  13    0.88
  14    0.88
  15    0.87
  16    0.87
  17    0.86
  18    0.86
  19    0.85
  20    0.84

C:
  CAR   HANDICAP
  21    0.83
  ...

As luck would have it, within each group of ten NOT ALL THE HANDICAPS ARE THE SAME. That is, cars #1, #11, #21, #31, #41, #51, #61, #71, #81, and #91 are the most performant cars in their respective groups. If you are lucky enough to be in one of these cars, you have a better chance of winning your group!

So the race goes on, with ten winners declared:

  • The Best Driver of Fast Cars (group A)
  • The Best Driver of Nearly as Fast Cars (group B)
  • The Best Driver of Somewhat Slower Cars (group C)
  • ...

By multiplying raw times by the average handicap in a given group, they also declare one of those group winners the Overall Winner. So ten happy winners go home, one of them doubly happy for being both group and overall winner.

3. The Greatest Driver From Each Car-Type Group

Week three arrives, and those same 100 cars have arrived at your venue again, begging to race. Except one of the non-winners from last week has a request: He wants to be in a group of similar type vehicles. He doesn't understand all the fancy math you did to compute the handicap for his vehicle (a 1969 Camaro---rear-wheel-drive) and doesn't understand why it is in the same group as 1997 Maxima---front-wheel-drive.

So to concede his request, you change up the groups from last week. An attempt is made to group similar performance capabilities in the same group, but to also match vehicle type. Obviously this will mean that on average, each group will have a greater performance disparity between its fastest and slowest car. But it makes the Camaro driver happy, because now he's being beaten by a 1972 Barracuda---rear-wheel-drive, which for him generates friendly competition and camaraderie rather than resentment :)

4. SCCA Classing & PAX System

And this brings us round to discussing the current (as of 2020) classing & PAX systems used by the SCCA for autocross (Solo II) events. Cars are presumably grouped both by ability and by type. Grouping them by ability leaves the least disparity between slow cars and fast cars in a given class. In my opinion, grouping them by type generates camaraderie and friendly competition, but leaves more disparity between slow cars and fast cars in a given class.

PAX is basically the maximum handicap of the cars in a given class. You may have heard PAX called The Great Leveler. But given that it is based on a less-than-perfect classing system, we might want to redub it The Crude Leveler That Did the Best It Could.

Given that it's a crude leveler, let's point out a few false statements:

  • "Each car has the same chance of winning its class today."
  • "Each car has the same chance of winning PAX today."
  • "Cars A and B had the same PAX time today, so those two drivers must be equally skilled."

5. How To Win Your Class or Win PAX

As any crook knows, imperfect systems exist to be taken advantage of. In reality we are not forced to show up on race day with a randomly chosen automobile from a stack. Rather, we know ahead of time what the PAX factor is for a particular car before we show up. So if there are two cars in your driveway, you will obviously choose the one that has the best chance of winning based on the current class & PAX system. If you are smart and/or in need of a place to shovel some cash, you may seek to add a car to your collection that has a good chance of winning with the current class & PAX system. As new cars come out each year, you might need to reconsider what you're driving each year in order to keep bettering your odds.

If you are not smart, not in need of a place to shovel some cash, or willing to get by on something less than winning, any car will do.

Results by Jack Desert
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