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How to handle 30 RXB and The Guiding Eye 
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Malekith's Best Friend
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Howdy.

I've played a few games now trying out a unit of 30 RXB. I used a character in there with The Guiding Eye to further boost them. I'm very pleased with the results, but I got to thinking "How should I deploy them? As a horde from the start, or as a 2x15 line and then reform when the enemy is about to charge? What gives the most shooting? And when should I use The Guiding Eye?"

I did what I always do in these situations: Bring out the maths!

There are 4 possible scenarios. I'm assuming that the enemy's infantry is rushing towards my RXB.

1) I deploy as horde and get the first turn. I can then do the following:
    ¤ Move + shoot at long range (40)
    ¤ Shoot at long range (40)
    ¤ Shoot at short range (40)
    ¤ Stand and shoot (40)

2) I deploy in a line and get the first turn. I can then do the following:
    ¤ Move + shoot at long range (60)
    ¤ Shoot at long range (60)
    ¤ Reform + shoot at short range (40)
    ¤ Stand and shoot (40)

3) I deploy as a horde but the enemy gets the first turn. I can then do the following:
    ¤ Shoot at long range (40)
    ¤ Shoot at short range (40)
    ¤ Stand and shoot (40)

4) I deploy in a line but don't get the first turn. I can then do the following:
    ¤ Shoot at long range (60)
    ¤ Reform + shoot at short range (40)
    ¤ Stand and shoot (40)



I now calculate how many hits I will cause on the enemy during the battle. For those of you who aren't at home in the world of statistics, I can say that this is the important number. Regardless of what T and AS your opponent has, the case that gets the most hits is going to be the best case, since it will cause the most wounds too. The only thing that differs between troops is how many wounds that will be caused, but the relative difference will be the same. I will not bother you with my calculations, so if you don't believe me, just do them yourself. But I do have lots of experience with maths, so don't worry ;)

Note also that I'm involved in a discussion in a different thread about weather you can stack Armour Piercing or not. Conveniently, the answer to that question does NOT affect this result.


Results:
Case 1 (Horde + first turn): I cause 68,94 hits before the enemy reaches me. The Guiding Eye is best used when you are "shooting at close range".

Case 2 (Line + first turn): I cause 75,44 hits before the enemy reaches me. The Guiding Eye is best used when you are "shooting at long range" before I reform.

Case 3 (Horde + enemy goes first): I cause 61,28 hits before the enemy reaches me. The Guiding Eye is best used when you are "shooting at close range".

Case 4 (Line + enemy goes first): I cause 64,44 hits before enemy reaches me. The Guiding Eye is best used when you are "shooting at long range" before you reform.


As you can see, it should be best to deploy your RXB in 15x2 and reform when the enemy gets close. Some interesting things though. If you do NOT have a character with The Guiding Eye in the unit, the same calculations show that if you do not get the first turn, you will cause exactly as many hits if you are deploying in a line as you do with a horde. If you do get the first turn though, you are better off deploying as a line.

If you buff your unit with +1 to hit (Metal spell) nothing changes (well, you do more hits of course), except that in case 1 it is now best to use The Guiding Eye when shooting at long range. As I mentioned before anything that affects the "to wound" roll or any save will not change the relative difference between these cases. naturally you will do less wounds on Chaos Warriors than on Goblins, but the above conclusions still hold true. The only thing that can change them is if the enemy can reach you faster than I anticipated. Cavalry or Trolls Could close the gap faster, thus allowing fewer shots to be fired before reforming. That would favour a horde deployment. It could be wise to deploy your RXBs late in the deployment to make sure they are not right across the table from a huge bunch of smelly Ogres, alternatively to deploy it more than 24 inches away from the enemy deployment zone, giving your an extra round of shooting if the opponent should go first.

The Guiding Eye should in short be used when you can fire as many bolts as possible, with the BEST possible chance to hit. I wasted it when i needed 7s to hit in my first battle and that was silly.

Thanks for reading.

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Sun Jul 18, 2010 8:10 am
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Warrior
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Interesting reading, thanks for going to the effort. Do you think having one big unit with they eye is better than running several smaller units?

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Sun Jul 18, 2010 9:37 am
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Noble
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My thoughts on this unit have been roughly along these lines, but it's nice to see some quantification of what I've been learning. Great article.

Edit: @Tsunami: I think it depends upon personal playing style. A 30-man unit will be more susceptible to focus fire and uber-spells, but will be able to similarly deal more damage to enemy units, and be more likely to survive or even win a combat with the enemy.

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Sun Jul 18, 2010 9:37 am
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Noble
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Good Article!


I would definatly always start the crossbowmen in 15x2 if space allows. First of all because against more killy enemies you would need to reform to 5x6 anyway to get stubborn. Secondly because you never know what happens - the enemy can switch focus and choose not to engage the crossbowmen, in which case continually having 60 shots is the best deal.


Sun Jul 18, 2010 10:08 am
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Malekith's Best Friend
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i didnt include the possibility of reforming to 5x6. the reason is pretty simple, very few units that can beat the RXB in combat (so not goblins) will reach them and have more than the 3 ranks a 10x3 horde has, thus it probably has stubborn OR will beat the enemy in close combat :)

yes, a big unit can be targeted with über spells, but i prefer to let a few mini spells go through and save my DD for such big nasties. smaller units are susceptible to small spells instead, and ofc the guiding eye is better in a big unit.

mileage will vary, but my bet is that one or even two of these big units will be very competitive. not sure how much i like that though, since ive always preferred to outmanoeuvre my enemy to just kill him with mindless dice rolling... but i guess those days are sorta over...

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Sun Jul 18, 2010 11:56 am
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I plan on running two, but unfortunately, only one gets guiding eye. I need another 30 Crossbowmen now...


Sun Jul 18, 2010 1:33 pm
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Malekith's Best Friend

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How about;

5) I deploy in a line and get the first turn. I can then do the following:

¤ Move + shoot at long range (60)
¤ Shoot at long range (60)
¤ Shoot at short range (60)
¤ Stand and shoot (60)

6) I deploy in a line but don't get the first turn. I can then do the following:

¤ Shoot at long range (60)
¤ Shoot at short range (60)
¤ Stand and shoot (60)

So the difference here is no reforming. You're trading up to 10 attacks in close combat and an extra rank for another 40 short range shots (where 20 are -1 for stand and shoot).

Unless this affects the timing for Guiding Eye (which is probably does), it means another 16.6 hits in both cases.


Sun Jul 18, 2010 2:07 pm
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Malekith's Best Friend
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ofc that makes for better shooting, but i would not want to risk such an expensive unit in close combat formed in only 2 ranks tbh. you wont win the combat, and you wont be steadfast. ofc, if you can kill so many enemies that you think your 2 lines of elves can handle them, go ahead, but i wouldnt risk that.

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Sun Jul 18, 2010 8:00 pm
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Noble
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Lord Tsunami wrote:
ofc that makes for better shooting, but i would not want to risk such an expensive unit in close combat formed in only 2 ranks tbh. you wont win the combat, and you wont be steadfast. ofc, if you can kill so many enemies that you think your 2 lines of elves can handle them, go ahead, but i wouldnt risk that.

Well, one point in favor of it, is that apparently even if you lose combat, you can reform with a leadership test.

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Sun Jul 18, 2010 8:53 pm
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I have a question those 30 man RXB, are you runing them with a full command, Standard/Muso, or without a command? I plan on running two blocks of them and was wondering are the benifits of having them with command worth the pts to pay for them?

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Wed Jul 21, 2010 1:00 am
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If you invest in 30 Xbows, I think you need the Full Command. They are going to get stuck in combat and are working for the Horde rule, why not give them the +1 Combat Res, and a Champion to maybe protect a Sorc you hid in the unit?


Wed Jul 21, 2010 2:51 am
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Dragon Lord
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Champion isn't really useful in a unit of crossbows, but standard and musician (especially musician for swift reforms) are a must.

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Wed Jul 21, 2010 3:50 am
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Yeah Dalamar, thats what I have been thinking too and running the RXB so big i think its safe to keep my sorceress outside of the unit maybe on a peggy for mobility.

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Wed Jul 21, 2010 4:06 am
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Even if you keep her in the unit, champion might keep her safe from challanges (really? if you refuse your opponent will only have choice of sorceress to send to back ranks) but not from regular rank and file attacks which are just as deadly to our T3 sorceresses.

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Wed Jul 21, 2010 4:46 am
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A Sorceress should be deployed on the corner of the front rank anyway, to minimize damage in case of a miscast. It's quite possible to reform the unit to make it so the crossbowmen are wider than what they're fighting, allowing only 2 enemy models to allocate against the Sorc (one in corner-to-corner, one supporting from the 2nd rank.)

Of course, I personally like the Black Dragon Egg. Either jam up the enemy as they're about to charge, killing a lot of their unit and possibly preventing them from charging due to Noxious Breath, or else providing a nasty 2D6 breath weapon and make the Sorc durable to rank-and-file hits with Toughness 6.

Sorry, that was off-topic, since it eliminates the possibility of taking the Guiding Eye.

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Wed Jul 21, 2010 6:51 pm
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Slave (off the Altar)

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Thanks for your analysis of the rxb unit it is really useful and as you already stated correct.

But there is one point I want to address.

Quote:
The Guiding Eye should in short be used when you can fire as many bolts as possible, with the BEST possible chance to hit. I wasted it when I needed 7s to hit in my first battle and that was silly.


I agree that the more shots you have the more you get out of your eye (unless you ad very few extra shots). But I think it might be useful if people are aware that the best chance to hit is not always the best moment to use the eye. I know you know seeing your advise on the +1 to hit spell. So I'd like to add a bit about the mechanics of rerolls before people extrapolate your advise to other reroll situations.

With a low chance to hit, you'll on average have lots of shots that miss and thus benefit from the eye, but these shots will still have a low hit chance.
At a high chance to hit a lot of shots will hit initially thus there are less shots that will benefit from the eye.

Words are all nice but maths is better:
hit roll chance w reroll benefit of reroll
6+ 0.17 0.31 0.14
5+ 0.33 0.56 0.22
4+ 0.50 0.75 0.25
3+ 0.67 0.89 0.22
2+ 0.83 0.97 0.14

Multiple shot decreases the chance to hit by 1 but doubles the number of shots so it will be better to use multiple shots in all* cases. For example going from 5 to hit single shot to 6 to hit double shot with reroll
5 singe w reroll = 0.22
6 double w rerool = 2*0.14= 0.28


In short the best chance to hit is not always the best moment to use the eye. The sweet spot is at 4+.
Though I must admit that this point is mostly irrelevant for crossbow men as with -1 to hit for multiple shots their best to hit chance will often be 4+. And Lord Tsunami advice on when best to use the eye is of course still correct.


Now the next part of the discussion, the FAQ:

The faq states that you can use it after rolling to hit:

Q. When is The Guiding Eye used? (p100)
A. Declare that you will use it after the character and any unit
he has joined rolls to hit, but before rolling to wound.

Therefore I'd like to expand on what Lord Tsunami already calculated, with some examples that can influence your decision of when to use the eye, be warned there is more math ahead. ;)

Ideally now you want to use the eye (and yes this may seem contrary to what I explained earlier) with the best possible chance to hit, but only after you roll the worst number of success. Of course this is so unlikely that waiting for such an event will surely mean we wont use the eye often.

Therefore I calculated if waiting past the ideal moment to use the eye in the hopes of using it on a bad roll after this ideal moment would pay of. Apparently not, because we have so many shots, chances of really bad rolls are actually quite low (chance to roll equal to or less than half what you'd expect with 80 shots and a 4+ to hit are 4.3e-6 (p=0.5, n=80, x<=20).


Therefore I'd say it is still best to use the guiding eye at the moments proposed by Lord Tsunami except under two situations.


1 :At the ideal moment to use the eye the roll to hit is far above average and using the eye now would yield less hits than using the eye later (probably the next turn during stand and shoot)

For example at the ideal moment 4+ to hit with 80 shots you initially hit 60 times if, you rerol you only get an average extra hits of 20*0.5 =10
The next turn (stand and shoot so -1 to hits) you hit at 5+ rerolling would yield and average extra 17.6 hits. Or there is a 0.94 chance that using the eye on the 5+ roll one turn later yields 10 or more extra hits. (p=0.556, n=80 x=>37(26.7+10)


2: You have a really bad roll before you'd otherwise use the eye and the extra hits you get from rerolling now are higher than the extra hits you generally get by rerolling at the ideal time.

For example 80 shots at 6+ to hit (moving extra arrow over half range) on this shot you hit with 0 attacks if you use the eye now you will on average get 13.3 extra hits.
Its only worth it if these 13.3 extra hits are more than the extra hits you generality get at the ideal moment.
If the ideal moment to use the eye would be a 5+ then its better to wait for this ideal moment to use the eye because a 5+ to hit has a reroll benefit of 0.22. 0.22*80 = 17.6 extra hits. Or there is a 0.81 chance you get 13.3 extra hits or more when using it on the 5+ roll (p=0.556, n=80 x=>40(26.7+13.3)

In case of 0 hits on a 5+ roll with 4+ as ideal reroll moment it would be better to use the reroll on the zero 5+ hits.
5+ = 0.33 chance of a hit thus the reroll would net you on average 80*1/3= 26.67 hits
While the reroll benefit of 4+ is 0.25 which is lower than the 0.33. and would only net you 0.25*80=20 extra hits . Or there is a 0.02 chance you get 27 extra hits or more when using it on the 4+ roll (p=0.75, n=80 x=>67(40+27)

Final example 5+ to hit and only 20 hits
The eye would yield and extra (80-20)*1/3= 20 hits when used now.
Using the eye on an ideal 4+ to hit would yield and extra 80*25 =20 hits.
Or there is a 0.56 chance you get 20 extra hits or more when using it on the 4+ roll (p=0.75, n=80 x=>60(40+20).In this case it wouldn't matter a whole lot when to use it

Of course other factors play a roll as well, maybe you have a decent chance now that if you use the eye you can expose a wizard by killing its unit, or maybe you expect a lot of casualties in this unit during the coming turn.


Thu Jul 22, 2010 12:06 pm
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Cold One Knight
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In short:

Use the eye's reroll if any of your rolls is TERRIBLE.

If your rolls aren't terrible, use the eye when you need 4+ to hit (unless those rolls are abnormally good.)

If abnormally good, then save eye for stand-and-shoot or next turn.


Thu Jul 22, 2010 6:34 pm
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Timz wrote:
In short:

Use the eye's reroll if any of your rolls is TERRIBLE.

If your rolls aren't terrible, use the eye when you need 4+ to hit (unless those rolls are abnormally good.)

If abnormally good, then save eye for stand-and-shoot or next turn.


This is a very good one :D

People use The Guiding Eye in some games?


Thu Jul 22, 2010 8:01 pm
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Malekith's Best Friend
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oh yes. RXB are truly deadly with it :)

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Thu Jul 22, 2010 8:42 pm
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Timz wrote:
In short:

Use the eye's reroll if any of your rolls is TERRIBLE.

If your rolls aren't terrible, use the eye when you need 4+ to hit (unless those rolls are abnormally good.)

If abnormally good, then save eye for stand-and-shoot or next turn.


:roll: Not entirely as you can see, with a terrible roll on 6+ to hit it almost always pays of NOT to use the rerol then.


Fri Jul 23, 2010 7:47 am
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Capricious wrote:
:roll: Not entirely as you can see, with a terrible roll on 6+ to hit it almost always pays of NOT to use the rerol then.


Depends on your definition of "terrible" really. If the target is at long range and facing the other way and not a direct threat to any of your units and, oh no! you didn't roll any 6s on 40 dice, then, yeah, so what... in that case, "zero hits" doesn't count as terrible.

OTOH, if the target is a Wizard on his own with a Power Scroll and the Purple Sun of Xereus and about to launch the powered-up version down your battle line and wipe out a third of your entire army in one fell swoop, then, not rolling any 6s on 40 dice? That could lose you the game, use the Eye, for God's sake use the Eye!

I personally think use of the Eye is much more situational than most are suggesting. Yes, when you need 4s to hit will statistically yield the most "extra" hits from the Eye - but if you're only shooting at a unit of Fast Cavalry because there are no other targets available this turn, there's not much point. Using it when you need 6s might not statistically be that sensible, but as described above there are times when that's OK. And if you use it against, say, a horde of Gnoblars (2 points each) then to get the points back you'd need to ensure it killed an extra 13 models, so an extra 26 hits (they are T3 right?), so you must be in a VERY large unit of RXBs for that to be likely...

About the only thing that approaches being a "rule" is that if you've not used it by the time you get charged, you might as well use it on your stand-and-shoot, unless your first stand-and-shoot rolls yield enough hits to critically weaken the unit charging you. Otherwise there's no point "saving it for later" as the chances are there won't be a "later".


Fri Jul 23, 2010 8:34 am
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Slave (off the Altar)

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Ok I should have put the disclaimer I put under the initial post under that one as well.

Quote:
Of course other factors play a roll as well, maybe you have a decent chance now that if you use the eye you can expose a wizard by killing its unit, or maybe you expect a lot of casualties in this unit during the coming turn.


If I'm not mistaken that is in the same line as your storey.

I agree fully with you that using the eye in the situation you described is a good move, killing wizards is very high on my priority list . But that wasn't what this analysis was about, it was about infantry rushing to your line, and closely linked to that, the statistical most beneficial moment to use the eye in such a scenario. Some might find that so situational that they can't really be bothered with it, others might use that info so now and then.

I get the idea you propose to 'save' the eye for special opportunities and if none arise use it at the last reasonable possible moment aka the stand and shoot.
Which depending on the army you face is indeed a good proposition, especially if it involves killing an enemy wizard which will often far outweigh killing some extra rank and file.


Fri Jul 23, 2010 10:30 am
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