I run my horse to the left barrel first because when I was training him, he turned better to the right. So it made more sense for me to run the pattern with one left turn and two right turns because we could complete the right turns faster.
However, now in his training, he turns equally well both ways and I do run the pattern both ways, but most often I'll stick to going to the left barrel first because that's the way he is most used to.
He will also run the poles either way and I continually run them different every time, because it keeps him from "assuming" what he is supposed to do and actually listen to my cues instead.
Many times, barrel racers will just train to go to the right barrel first because that's "what everyone else does". And it is true that most horses tend to be better at left turns, however, once fully trained and seasoned, most horses turn equal both ways. But to make the most of training a barrel horse, it often is beneficial to figure out which way they turn better and make that your two turns in the pattern.
How do you barrel race and not know what leads are?
That seems a little harsh, since there was a point in my life that I barrel raced and didn't know what a lead was, as I am sure there was a point in your life when you didn't know what a lead was either. I've come a long way from then but everyone has to start somewhere. The least you could do was explain what a lead was, instead of just leaving this single comment.
And I guess I have never heard the term "backwards" in regards to running to the left barrel first. Maybe it is a regional thing? We call them lefties and righties.
Okay, what is a lead?
As spastic_dove stated, the lead is so named because it is based off of what leg is "leading" the horse when he is galloping. When the horse is in the left lead, the right hind leg hits the ground first, followed by both the left hind leg and right front leg at the same time, and then the front left leg is the last to make contact with the ground. Just the opposite would happen with a right lead (left hind leg --> right hind leg + left front leg --> right front leg) in the 3-beat cadence.
Leads are beneficial because when you ask a horse to do precise maneuvers, whether it is turns in barrel racing or circles in reining or running down the fence after a cow preparing for a turn, the horse can better complete that maneuver.
For example, a horse is more balanced when doing a circle in a clockwise direction (to the right) if he is on his right lead. And better when doing a counterclockwise circle on the left lead.
So when you train for barrel racing, you should also train your horse to switch leads in a flying lead change between barrel 1 and 2. A flying lead change is when the horse changes the lead without slowing down (staying at the gallop). A simple lead change is when you break down to a slower gait (trot or walk) and then ask the horse to begin galloping again on the different lead.