Ogres vs archery

I felt like crunching some numbers a few days ago. What I found is quite interesting.

I compared the use of 5 ironguts vs archers to 4 ironguts and a butcher vs archery. For the archers I took glade guard as I have the army book at home.

First I looked at how many shots are required to take out 1 irongut, assuming long range. Taking a unit of 5 ironguts 1 shot from a glade guard has 2/3(to hit roll)*1/3(to wound roll)*2/3(armour save)= 0,148148 chance to wound the ironguts. This means that 1 in 6,75 shots will wound. This means 20,25 shots are needed to kill an irongut. To cause a panic test 2 ironguts have to be killed, counting a total of 40,5 shots

When exchanging an irongut for a butcher the following happens:

The butcher takes 2/3(to hit)*1/6(to wound) to wound. This comes down to 36 shots to kill him.

Because the unit consists of 4 rank and file models and a character it has to spread its hits. The ironguts now take 80% of the total hits on the unit. This means that effectively a number of 20,25/0,8= 25,3125 shots are required to take down an irongut. The butcher will take 25,3125- 20,25= 5,0625 shots away from the irongut. The butcher suffers on average 0,5625 wounds.

To cause a panic test 2 models have to be killed. Since the butcher takes 20% of the shots, 10,125 shots, 1,125 wounds, not enough to kill him, 2 ironguts have to be killed. It now takes 25,3125*2=50,625 shots to take these out due to the butcher siphoning off 10,125 shots.

In conclusion:
A unit of a maximum of 4 rank and file models(ironguts) and a character(butcher) offers a significant increase in shooting hit absorption capabilities compared to a unit of 5 rank and file models.(in this case (50,625-40,5)/40,5= 0,25=25%)

This percentage becomes greater should the unit drops in size as the character now takes away more hits.
For ogres, especially butchers this is a good thing. They have a bucketload of wounds and the ability to regenerate them on top.

These are my two cents, do with them what you will. Comments are much appreciated.

Ogur Spearchewer

Certainly an important point you make there. If I want to protect a unit from light archery I put in a tyrant, 2 butchers and 2 maneaters in a unit. If they want to take out that unit with shooting they have to go on all week. Of course opponents understand that and start shooting on my 1x3 ogre units instead, but they are disposable (especially with the new panicking

I wondered why I was shrugging off incoming fire   My standard setup for IG units is either 4 + butcher or 4 +tyrant+butcher in 2000 point games - plus I often shield them with bull units.  My IG units always make it across the field intact and cause havoc.

Very interesting number crunching.  I'll have to ensure that my opponent remembers to randomize hits against the butcher, instead of just having guts or bulls soak up all the damage.

Yeah, I quite often use Bulls as missile screens and place characters in the units to begin with to make it more difficult to cause Panic. When the units start getting too shot up I move the characters back to the combat unit in the second line.