How useful is archery?

I love archery. It might be because I'm a bit of a coward and wouldn't want to do any hand to hand combat but there's just something about a volley of arrows that makes me shiver. In the films, archery is devastating. All of the knights of Minas Tirith are cut down by rounds of orc fire from Osgiliath. The elves at Helms Deep kill countless Uruk-hai with their sharpshooting. Legolas can bring down pretty much anything with nothing but arrows and a bow.

Removing as many enemies as possible with bows, before they get too close with their pointy and sharp things, makes sense in real life and also in LotR SBG so I wanted to include as many archers as possible in my force and if you want decent archers there's only one race you can count on: the elves.
Not only do elves have the best shoot value in the game (3+ for ordinary warriors and 2+ for Thrandril and possibly 1+ for Legolas) but their bows also have a higher strength than most, without compromising their full move (like the crossbows of the Uruk-hai).

However, after playing with my Mirkwood force for a while, I was disappointed with the lack of impact archery has on the game. I was confused by how even Legolas, with his automatic hit rule, can fail to kill even the most poorly armed goblin, when in the books he can kill a fell beast with one shot.
Now, I'm a bit of a nerd and I wanted to see, statistically, how likely one is to kill any enemies with bow-fire so I pulled out the GCSE maths revision guide from a couple of years ago and brushed up on some probability.

An elf warrior has a shoot value of 3+ so will hit on a roll of a 3, 4, 5 or 6 meaning one has a 4/6 chance of hitting an enemy. So far that seems reasonable. But then one must roll to see if that hit killed the enemy, bounced off his armour or just didn't do enough damage to cause death. We must go to the would chart.

Let's take a standard orc warrior and see what the probability of killing him is, assuming we hit him. A unshielded orc has a defence of 4 and an elf bow has a strength of 3. This means that to kill the orc, one must roll a 5 or 6. This means our elf has a 2/6 chance of killing the orc (still assuming we hit it).
Well a 2/6 chance seems reasonable, seeing as the orc is covered in armour and has thick, calloused skin. But we have to take into account the probability of both: a) rolling above a 3 to hit and b) wounding the enemy if we do hit to accurately calculate the chance of killing one orc, with one shooting elf. We do this by multiplying the two probabilities together.

The probability of hitting the orc, is 4/6.
The probability of killing a hit orc is 2/6.
Therefore the probability of hitting and killing an orc is 4/6 x 2/6.
This equals 2/9 or 22% which seems rather low.

This means you need to shoot that orc with 5 elves to be statistically confident you'll kill him, and remember we're shooting with the best archers in the game against the most average of the enemies troops. If the orc has a shield then the probability of hitting and killing him is 11% so you'll have to shoot him with 10 elves to be confident you'll kill him! That just seems ridiculous. 10 of the best archers in the game to kill 1 of the weakest.

One could argue that due to the range of archers that the number of turns they have, unchallenged, to attempt to thin out the enemy balances out the poor odds of killing anything. In that case, let's assume that the archers have 3 turns of fire until engaged by the enemy and that we have 10 elf archers. Each turn we can expect to kill 1 shielded orcs or 2 unshielded orcs, provided we have a clear line of sight. In that case we can expect to kill 3 shielded orcs or 6 unshielded orcs depending at whom we shoot before they engage us. That still seems fairly low for the best archers!

Think about if you were playing as Mordor and your orc's hit on a 5+ and have a bow strength of 2. You have an 11% chance of killing an unshielded Warrior of Rohan with a single orc and his bow. If you try and hit an elf or a sheilded man you have a 6% chance of killing them. You would need 19 orcs to be statistically likely to kill one elf. Doesn't seem worth it.

In conclusion, I wish archery was more devastating! I know there are people who will argue that bow fire is boring and hand to hand combat is more exciting but in my opinion a few deadly volleys before the orc horde comes crashing in to the lines of men and elves is just as exciting, if not more so.
I'm sorry for the lack of anything interesting in this post, I've recently bought some Galadhrim Knights so I'll be posting some pics of them soon and maybe a painting guide. Thanks for reading!