I am going to bust a couple of myths about hook eye direction.
Myth 1 - The direction of the hook eye affects the angle of pull on the fly, and angle of pull will affect how well the fly "hooks" the fish.
Myth 2 - The direction of the hook eye affects the hooking gape. A down eye hook will have less hooking ability and should be avoided in small flies because it narrow the hooking gape.
Reality - The direction of the hook eye does not affect the angle of pull on the fly and makes very little difference in the ability of the fly to "hook" a fish.
Gary Borger on pg. 178 of Designing Trout Flies
demonstrates why the angle of a hook eye has no effect on the angle of pull on the hook. The angle of pull is determined by where the rod tip is in relationship to the hook and not by the angle of the hook eye to the shank. For example, one would think that a down eye hook would cause the angle of pull to be "down" on the hook, but the angle of pull is actually up if the rod tip is above the level of the hook when the hook set occurs.
The slight offset of the hook eye provides no significant "lever" force to affect the angle of pull. Imagine the tip of a crowbar as the angled hook eye. When you push on the long end of the long end of the crow bar, the force of the push is magnified by the longer lever arm of the crow bar. But if you reverse the crow bar and push on the angled tip, you will have difficulty moving the long arm of the crow bar because the long lever arm is now working to reduce the force. The same thing occurs with an angled hook eye; there can be very little force generated by pulling on the short angled eye (short crow bar head) against the long shank (long arm of the crow bar) of the hook to move the hook point.
Some fishers also think that a down eye hook somehow "narrows" the hooking gap and negatively affects the hooking ability of the pattern. That is not true either. The gap is the distance between the hook shank and the point and is not determined by the direction of the eye. What narrows the hooking gap is the material that is tied onto the hook at the location of the gap.
Mustad has perpetrated this fallacy by writing that the hook eye position affects hooking.
"The position of the eye is an important factor when it comes to improving the hooking potential of artificial lures. “Straight” is the standard eye position. Here are three other variants:"
Hook Anatomy « Mustad
The reason Mustad says that is the "penetration angle" of a hook. If you place a hook agains a flat table top, a down eye hook has a shallower "penetration angle" due to the angle of the hook eye; and Mustad argues that a shallower angle is less likely to hook the fish.
I used to believe that penetration angle was important, but as I read more, I've changed my view. Therefore, I have some disagreement with what Mustad has written about how important the eye position is in hooking. I think any effect is very very minor. The reason is that hooking (penetration) angle does not stay constant.
Once the hook point penetrates flesh, the hook pulls on the flesh deforming it and simultaneously the hook rotates in line with the angle of pull of the line. The eye of the hook no longer rests nicely at a 90 degree angle to the flesh as it does on a table top.
The angle of pull on the shank and the hook point are pretty much equal when the hook eye does not rest on against a flat surface. I believe that this angle of pull drives the hook point further into the flesh at pretty much the same angle which is determined by the angle of pull on the eye rather than the angle of the eye of the hook.
If the hook point is sharp, hook eye position does not matter much. The hook point will enter the flesh regardless of the difference in hook eye position. Hooking gap and offset have a greater effect in my view because they affect the probability that any fish flesh comes to lie against the hook point.
Need more proof? Let's examine what actually happens when a fish takes a fly.
When the fish's mouth is closed on the fly, it doesn't matter how the eye of the hook is angled. There is no "mouth" or opening for the fly to lie at perpendicular to a flat table. The jaw is closed so the hook of the fly is flat to the upper and lower jaw. The fish has turns and the fly is pulled along inside the closed mouth. This is why the fish is most often hooked in the side of the mouth at the junction of the upper and lower jaw.
Experience tells us this where most of the flies hook the fish. And it doesn't matter whether the fish is hooked on a dry, a nymph or a streamer. It doesn't matter whether the hook eye is up, straight, or down. It doesn't matter whether the fish takes the fly head on like a dry or or from the side. So something else is going on.
When the fish closes its mouth on the fly, the fly rotates
so that the fly lies flat or in a horizontal rather than in a vertical position. The hook point is directed sideways and when you strike, it lodges in the side of the mouth at junction of the upper and lower jaw. So the position of the hook eye makes little difference. This is also why an offset hook point works. The offset hook point juts out against the surface of the mouth, when the mouth is closed against the fly.
I think hook eye position is more about the aesthetics of the fly and the ease of tying the fly than any effectiveness in hooking.