I'm not really sure why you are comparing a totally different person riding with a different skill set on a different horse, in a different discipline to you riding your horse and how safety statistics equates. You're trying to combine two sets of statistics...
There are no studies that have only one variable in riding, nor can there be. It is not possible to ride even the same horse on 2 different days and have only one variable change.
That is why studies use statistics, and review large numbers of riders and horses and scenarios - it is to even out changes due to those many variables.
If you fall on your noggin, then yes - a helmet reduces your risk. How much? No one knows. There are too many variables in a fall. However, statistics indicate it may be a 50% reduction.
But to understand how that one factor impacts your total risk, consider two scenarios:
1 - You have a 50% chance of falling on your head that day. The helmet reduces your risk in a fall by 50%, so the helmet reduces your overall risk by 25%.
2 - You have a .1% chance of falling on your head that day. The helmet reduces your risk in a fall by 50%, so the helmet reduces your overall risk by 0.05%.
In the first case, almost everyone would agree wearing a helmet is very important. In the second case, many would argue the total risk reduction is too small to care about - that your overall risk that day is largely determined by other things.
If, as we both agree, the helmet reduces your risk during a fall by some number - and 50% is reasonable - then your risk reduction for that day is determined by your risk of falling times 50%.
During an eventing competition - which is one of the 2 scenarios used by the original poster - the risk of falling is pretty high. How does it compare to the risk of falling off my gelding in an arena?
Well, in 3+ years, I've never fallen off my gelding, not even when he was trying to get me off his back. Of course, when he spent 10 minutes trying to unseat me, I was in an Australian-style stock saddle. I ended the ride with big bruises on each thigh, and the D ring in the front was twisted from how hard I pulled on the grab strap, but as a green rider with a previous injury on a horse that wanted me off, I stayed on.
Even with my mare, I've only come off twice in 4 years - both when she bolted during a dismount. I hurt my back the first time without a helmet, and my arm the second time with a helmet. But if I do fall, a helmet will reduce my risk - which is why I usually wear a helmet. Others choose not to, and I understand their choices even while making a different one
...I'm not really sure where you think I am telling you how to manage your choices...
You are not, and I really appreciate that. The OP was: "I just want to talk about the importance of helmets. I heard of people riding without helmets (or with cowboy hats) and it drives me crazy."
A number of posters on this thread have suggested laws making it illegal to ride without a helmet, at least for minors. That is trying to use government to control our choices as parents.
You are not, and I respect your courtesy to others. When someone suggests making it a law, they are saying, in effect, that I'm too stupid a parent to be allowed to determine acceptable risks for my daughter, and I resent being called stupid - particularly when I've studied the issue more than most have.
You are explaining why you make the decisions you do, and are doing so in a polite and intelligent way.