Hm, my last post has stirred up a bit of a hornet's nest in private e-mail,
about the relative ranking of driver X versus driver Y.
That's fine - discussions like these have been going on since sport was
invented. Hogan or Woods? Fangio or Villeneuve Sr? Richard or Gretsky?
But in making some counter points to some folks, I've stumbled onto a way
of graphically representing driver ability.
The trick here is to recognise that the ability of a given driver is not a
fixed value - it's a *range* Depending on the kind of day the driver is
having, their mental state, their physical state, and so on and so forth
their performance is going to vary.
So if we assign a given performance a percentile, based on how much close
to the maximum performance of the car the driver extracts on a given run,
and then run this through a season's worth of performances, you wind up
with a bar, like so:
0% 100%
|<-----Driver X----->|
Now the actual distribution of individual runs on that bar is not going to
be linear. Instead, it's going to be a bell curve, which is to say that the
majority of the scores of individual runs are going to fall near the middle
of the bar, and there will be a couple of great runs near the upper end,
and a number of crappy runs near the bottom end.
Now as a driver improves, two things cam happen. Firstly, the bar can shift
right - that is, the driver has improved the maximum capability they can
extract from the car. This would correspond to a "step up the pyramid" as I
described earlier. The other thing that can happen is the bar can shrink as
the driver's performance becomes more consistant.
So consider the following model:
0% 100%
|<-----------X----------->|
|<-----Y----->|
|<-------Z------->|
|<------A---->|
|<------B-------->|
|<---C--->|
|<---D--->|
Driver X is a rookie - the range is very wide, as there's no consistancy.
Sometimes, he's not bad, but other times, he just plain sucks.
Driver Y is the same rookie with some experience under his belt. He hasn't
really improved his maximum potential at all, but he no longer sucks so bad
- not making rookie mistakes any more.
Driver Z is driver Y with more experience. The max potential is up a little
bit, the lower end is up a little bit, but the consitancy is the same or
maybe a little worse.
Driver A has been to an Evo School, or has been doing National-level
competition for a while. The max is up, the min is up, and the range is
narrower, so more consistant.
Driver B is talented, but streaky. When he's good, he's very good. When
he's bad, he's not much better than a rookie having a good day. On average,
he's a little slower than Driver A, and a lot slower than C or D, but
occasionally he's the equal of C and D and better than A.
Driver C is an "A" level driver. On average, better than most.
Occasionally, better than the best. But also occasionally beatable by
lesser drivers when his bad day and their good day coincide.
Driver D is a Daddio or Ames. On average, better than everyone.
Occasionally so good as to be unbeatable by mere mortals. But sometimes,
they can be caught by C, B, or even very rarely, by A.
Now _where_ individual real people fit into this model I don't intend to
argue, because there's no winning it. I tend to place McIver into "Driver
C"'s range, but other people are certainly capable of having other
opinions. They may make his bar longer, or shorter, or father to the left
or right. It really doesn't matter. Different drivers will have different
bars, located in different spots, with different widths. Concentrate on
that.
But anyway, the point is, with _so_ much fluctuation and variablility in
driver ability (as modeled here) try and class a car based on one data
point. Or two. Or even 5.
This is the ultimate nature of the problem. It is complex, complicated, and
not easily modeled with a small number of samples. And overall, the noise
of differing driver performances masks the differences between cars, for
broad ranges of car types.
DG
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