Every time I go for a walk on the local track, this Burning Question hits me.
A friend thinks it is due to auto racing in Europe and the steering wheel is on the other side of the car. I am half buying into this.
Steering wheels in mainland Europe are on the same side they are here. Only Britain (of European states) has RHD.
In Europe most road courses are run clockwise, but as far as ovals are concerned I can’t think of one anywhere in the world which is run clockwise.
Just a WAG, but if my right leg is stronger than my left, I guess I would prefer it got to go further and faster (just a bit, though).
Since chariot races in ancient Rome were quite common, surely someone must have written and given enough of a description that it can be determined.
Brooklands, the first purpose built oval-type track (there’s a small kink in the back straight) runs anticlockwise.
Most Formula One tracks are run clockwise, with only 3 in the current calendar being run counterclockwise. Formula One being the grand European racing thing.
As for walking tracks (the OP has me confused about what’s being asked), most I have seen run in one direction some days and in the opposite some others.
There’s an Australian oval that is run clockwise, but the name escapes me at the moment.
Ovals are generally going to be run so that the driver is toward the inside for multiple reasons: so he’s got more space between himself and the wall, because at the lower levels, cars are converted from street cars that will have the wheel on that side (that’s why American ovals are run counter-clockwise) and because the more weight that’s on the inside, the faster the car will run on the banking.
I’m pretty sure that stock car racing originated in the States.
In the States and most of the world when oncoming traffic, pedestrian or vehicular , approaches you go right. Its been like that since Napoleon. Its affect our choice of going right rather than left around an obstacle as well. So when you approach an oval track, you are inclined to go right and hence counter-clockwise. That would explain roller rinks.
Since we pass oncoming traffic “left to left”, naturally we position the steering on the left for better visibility with respect to possible collision.
When stock car racing started in the States, communication between the driver and the pit was crucial so the counter-clockwise direction for oval racing was pretty well a lock
Then there is the coriolis theory but that’s a bit of a stretch…
There’s short-oval racing in Britain, which runs clockwise, ranging from Hot Rods (hot hatches) through to full-contact Bangers (which, unlike American demonlition derbies, are run as actual races).
A clockwise circuit which did at one time have a high speed oval is Monza. I’m sure there’s others.
This would make a lot of sense. Post-war, stock car racing was brought to Britain, but has evolved into a very different creature, as a short-oval contact formula. Clockwise.
You’ve forgotten Northen Ireland and the Irish Republic.
Cecil’s article gave examples of many phenomena, but omitted one: the circumambulation of pilgrims around the Ka‘bah in Mecca is also counterclockwise. But this is anomalous in the field of comparative religion; Hindu and Buddhist pilgrims circumambulate around their shrines clockwise. In most traditions, clockwise circumabulation is symbolic of the sun’s apparent movement around the sky. As for why Muslims go counterclockwise around the Ka‘bah, I don’t rightly know, but I’ve heard Sufis saying it places people’s hearts closer to the center, the heart being on the left side of the body and the left side facing in.
NI is part of Britain (the European state), even if it’s not part of Great Britain 
This may or may not be relevant, but the reason skating rinks tend to go counter-clockwise is that 80 or 90% of people find it easier to turn left (right foot crossing ahead of left) than to turn right. This is related to the “regular” vs “goofy” phenomenon.
Motorsport in general originated in France and Britain, though.
That doesn’t really mean an awful lot, though. Given the history of Europe since then, it’s hardly surprising that there’s been big influences at times from American racing on trends in Europe.
This doesn’t sound like it has anything to do with it - weight-bearing has no relevance, and it doesn’t explain the differences between different national, or if we’re honest about it continental (F1 vs America), differences.