Slitherine

Ok - calculators out (Hammy - I think you're the statistics nazi right? )

What's the chances in this match up?

BG of Superior Heavily Armoured Cataphracts vs BG of Average Heavily Armoured Knights... lets assume BG of 4 vs BG of 4. Be interested in the 'with General/without General' modifiers too.

I think it's something like this, but I'm not good at this level of statistics:

Impact Phase:
Knights have a 50% chance of a hit with each dice
Cataphracts have a 33% chance of a hit with each dice, but a 17% chance of a re-roll.

Melee Phase:
All is even except for re-rolls, but the knights get twice as many dice.

Who's going to win? I think the Knights win by a small edge, but it can swing dramatically one way or another based on the impact phase.

How are the knights formed up? Are there units to either side?

If you assume they are either 1 rank of 4, or front rank of 3 and rear rank of 1, and that this is one BG fighting another out in open space, the knights will get 4 dice vs. 4 in impact, 6 dice vs. 4 in the first melee phase (can't expand or move non-fighting bases to other end in opponents turn except to match an exisitng overlap), and then (assuming no bases are lost) you get to the 8 dice vs.4 in the melee next turn.

So the cats really need to get on top early or things are likely to go from bad to worse quite rapidly!

In impact, I reckon the expected number of hits is 2 inflicted by knights, 1.55 inflicted by cats. (33% chance of hit per dice, plus 33% of 17%, = just under 39 % hit ration overall.

In first melee round, knights 3 hits vs. cats 1.55 hits.

In subsequent melee rounds, knights 4 hits vs. cats 1.55 hits.

So in terms of hits, it starts off with a significant edge to the knights and moves to a huge edge for the knights. The chances are that the knights are not going to be taking many cohesion tests or needing to make death rolls.

Being superior obviously helps the cats on their cohesion tests, but considering they are quite likely to lose by 2 hits or more, and they are going to struggle to avoid losing bases, I really wouldn't fancy their chances

Adding generals to both BGs doesn't alter the outlook much, but the expected hit ratios move a little bit further in the knights favour. Knights get 17% re-roll which succeeds 50% so expected hits rate 58.5%, i.e. 2.34 impact, 3.51 first melee, 4.68 subsequent melee. Cats get an additional 17% re-roll with 33% chance of success, so overal hit % increases to 33.3 + (2 x 16.7/3) = 44.4%, so expected hits = 1.78 in each phase.

Why Knights against Cataphracts its not a great match up and one thats not seen much on table 2 dice knights 1 dice Cats, Lance knights none for Cats.

Knights plus in impact
Knights double dice in melee

Knights win.

Of course its a game of skill till you roll the dice.

A better question would be av armoured knights vs superior ha cats. Then the cats are up in melee.

Assuming they don't drop at impact, they are then

4@4 Sup vs 6@5 Av

2+0.5*2/3 = 2.33
against
2
(assumes the spare K can't get involved).

I can crunch the numbers if you want but it is not a good matchup for the cataphracts. Fortunately there are not many historical instances of cataphracts fighting heavily armoured knights so it is really only an anachronistic issue.

If you want to work out some neat probability stuff there is a really nice website called anydice.com

Martin Stephenson has written some veru interesting articles on his blog about anydice.
http://blog.vexillia.me.uk/2010/09/dice ... -sums.html
http://blog.vexillia.me.uk/2010/09/fiel ... ments.html

Hope that is of interest.

hammy wrote:Fortunately there are not many historical instances of cataphracts fighting heavily armoured knights so it is really only an anachronistic issue.

Well, there is the rather famous battle where the Palmyrans defeated the Duke of Burgundy on 23rd May, 2011!

Most FoG commentary does not speak favorably of average knights, yet average undrilled knights cost the same as superior undrilled cataphracts. I think in most circumstances I would prefer to have the knights, especially those that dismount as superior foot.

Most FoG commentary does not speak well of average anything

ShrubMiK wrote:Most FoG commentary does not speak well of average anything

Really? What about LH skirmishers, Dom Rom and similar swarms, Eastern MF armies...

Delbruck wrote:Most FoG commentary does not speak favorably of average knights, yet average undrilled knights cost the same as superior undrilled cataphracts. I think in most circumstances I would prefer to have the knights, especially those that dismount as superior foot.

Indeed, there are plenty of situations where I would rather have superior cataphracts compared to average knights but in an isolated one on one fight the edge is very much with the knights.

There are many many situations where a contest between two troop types of the same cost would not end up in an even fight. That is the way of ancients wargaming.

countadam wrote:

ShrubMiK wrote:Most FoG commentary does not speak well of average anything

Really? What about LH skirmishers, Dom Rom and similar swarms, Eastern MF armies...

I think you miss my point...which was about the typical comments on this forum rather than saying that there are no armies out there that have any average troops.

Typical comments are indeed that average troop are poor and poor troops are worse. But if used well they can be very effective. I don't think I've seen KMS use any superior troops in competition for more than a year and he's always in the top 25% of comps and ranked 5th in BHGS FoG.