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Thread: Unit size = unbalanced??

  1. #1

    Default Unit size = unbalanced??

    I want to know, if i'm using a 1.02 patch, and then changed, as an example, heavy cavalry 60 to 40 unit in troop stats, will this cause them to become weaker or it just for a cosmetic reason in-game.

  2. #2

    Default Re: Unit size = unbalanced??

    Yes, they will be 2/3 as strong. You could increase their attack and defend to compensate.

  3. #3

    Default Re: Unit size = unbalanced??

    ok. thanks. i thought their strength will be the same. now i know it is the unit quantity that determine their strength.

  4. #4
    Camel Lord Senior Member Capture The Flag Champion Martok's Avatar
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    Default Re: Unit size = unbalanced??

    Welcome to the Org, ghobot21!


    Quote Originally Posted by ghobot21 View Post
    now i know it is the unit quantity that determine their strength.
    Well quantity is only part of the equation, albeit probably the largest part. As Sasaki pointed out, however, a unit's attack & defense stats are a major factor as well.
    "MTW is not a game, it's a way of life." -- drone

  5. #5

    Default Re: Unit size = unbalanced??

    Quote Originally Posted by Sasaki Kojiro View Post
    Yes, they will be 2/3 as strong. You could increase their attack and defend to compensate.
    Unit strength isn't linearly related to unit size because each man can only strike once within a combat cycle, but he can be attacked multiple times. So, a 40 man unit is something less than 2/3 as strong relative to a 60 man unit.

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  6. #6
    Senior Member Senior Member econ21's Avatar
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    Default Re: Unit size = unbalanced??

    Quote Originally Posted by Puzz3D View Post
    Unit strength isn't linearly related to unit size because each man can only strike once within a combat cycle, but he can be attacked multiple times. So, a 40 man unit is something less than 2/3 as strong relative to a 60 man unit.
    Doesn't that assume that all men get a chance to strike? So it may be valid for missile combat, but with melee, unit frontages may restrict the ability of the larger unit to bring its numbers to bear. For example, in a fight between a 40 man and a 60 man unit, suppose you form up the two units in 4 ranks:

    Code:
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
           S  S  S  S  S  S  S  S  S  S
           S  S  S  S  S  S  S  S  S  S
           S  S  S  S  S  S  S  S  S  S
           S  S  S  S  S  S  S  S  S  S
    On impact, the larger unit only gets 2 more men to fight - the two closest to the flanks of the smaller unit. So, it has a 20% more men in combat rather than the 50% superiority it has in total numbers. Over time, so long as it does not hold ranks, the larger unit will bring more men to bear, but so will the defenders:

    Code:
                      L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
        L  S  S  S  S  S  S  S  S  S  S  L
        L  S  S  S  S  S  S  S  S  S  S  L
        L  S  S  S  S  S  S  S  S  S  S  L
        L  S  S  S  S  S  S  S  S  S  S  L
        L                                L
    Here, we have 22 L soldiers in combat against 16 S - a 37.5% advantage in numbers. If completely surrounded, the numerical advantage actually worsens - 32 L vs 24 S, a 28% advantage.

    What I am saying is that a smaller unit may be able to punch above its weight by restricting the ability of the larger formation to bring all its numbers to bear. Think the Spartans at Thermoplyae. If terrain does not allow this, a square or ideally circular defensive formation seems best for minimising the enemy advantage of numbers. This is the lesson of fortifications throughout history and those "circle your wagons" type encounters we read about with the Boers and Zulus. A singleline formation is worst if the enemy can get behind you and so bring all his numbers to bear (as well as get a lot of unopposed rear strikes).

    Now it is still true that replacing the smaller unit with a larger one will lead to a big rise in its killing power, as they will get a lot more strikes in the front row:

    Code:
    L  L   L  L  L  L  L  L  L  L  L  L  L  L  L  
    S  S  S  S  S  S  S  S  S  S  S  S  S  S
    Compared to the situation on the front row in the first diagram, they have gained 5 more strikes on impact. But this is somewhat diminished by the cost of exposing themselves to a further 3 strikes back.

    I understand what Puzz3D is saying - and there is a mathematics behind it. But in practice, with TW games, it often seems to me that unit size matters less than one might think.

    Another point is that in the case of cavalry, a lot of their overall combat effectiveness may not be so related to their "strikes" in combat. Specifically, the morale collapse they can engender by making charges into the enemy rear and the ability to turn tactical victories into strategic ones by sweeping up routers are both probably largely unaffected by whether the unit is size 60 or size 40. These points may apply more against the AI in campaigns rather than to MP battles. But the value of the bodyguard units in TW campaigns bring home the benefits of even small numbers of heavy cavalry.

  7. #7

    Default Re: Unit size = unbalanced??

    I've always found the differing unit sizes in MTW to be a big factor. For example many novice players mistakenly believe Byzantine Infantry to be a great unit, but are then surprised to learn that they are inferior to FMAA (I think they have the same stats but less morale - but I don't have the stats handy at the moment so don't quote me).

    What makes Byzantine Infantry so effective is the larger unit size than other sword units. The "wrap around" effect has always been a big factor in MTW due to the differing units sizes - as opposed to the unit sizes in STW which were all the same (apart from Kensai and Battlefield Ninja).

    As far as this game goes, I've never tried changing unit sizes so I'm not sure of the effects it would have. Taking an MTW'esque approach and reducing the size of sword units in relation to yari units may not be worthwhile, as yari are not as disadvantaged against swords in STW.

    Last edited by caravel; 10-02-2009 at 16:55.

  8. #8

    Default Re: Unit size = unbalanced??

    40 man units of cavalry are better than 60 man in shogun. I never combine them when I get some that size. They are easier to manuever around and strike an enemy unit from behind.

  9. #9

    Default Re: Unit size = unbalanced??

    Quote Originally Posted by econ21 View Post
    Doesn't that assume that all men get a chance to strike? So it may be valid for missile combat, but with melee, unit frontages may restrict the ability of the larger unit to bring its numbers to bear. For example, in a fight between a 40 man and a 60 man unit, suppose you form up the two units in 4 ranks:
    It doesn't assume that. The larger unit will always have more men engaged than the smaller unit. The smaller unit will loose men at a faster rate than the larger unit. The 60 man unit will not loose 2/3 of it's strength in beating the 40 man unit. Strikes at a flank or rear of a man get a substantial combat bonus which further increases the advantage of the larger unit.
    Last edited by Puzz3D; 10-22-2009 at 03:53.

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  10. #10
    Senior Member Senior Member econ21's Avatar
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    Default Re: Unit size = unbalanced??

    Quote Originally Posted by Puzz3D View Post
    It doesn't assume that. The larger unit will always have more men engaged than the smaller unit. The smaller unit will loose men at a faster rate than the larger unit. The 60 man unit will not loose 2/3 of it's strength in beating the 40 man unit.
    That's all true, but it's just quantifying the advantage of the larger unit that is tricky. I think all of what you have said above could be true and the 40 man unit be say, 70% as strong as the 60 man unit rather than less than 2/3 as strong as you stated. I don't see how it overturns my point that the larger unit typically cannot bring all its numbers to bear meaning that the combat strength of the smaller unit may be more rather than its numerical size.

    To take the issue further, I think we need a mathematical measure of a units' combat strength. But I confess I don't know how to construct that. I can see how you could quantify a unit's offensive strength (e.g. expected casualities inflicted) and even its defensive strength (expected casualities suffered versus a benchmark attacker). But how do you put them together to measure overall combat strength? If it was just casualities inflicted minus casualities suffered, it would not be very useful for solving this argument as it might average around zero, so it would be hard to say if a unit is more or less than 2/3 as strong as another.

    Strikes at a flank or rear of a man get a substantial combat bonus which further increases the advantage of the larger unit.
    That's a good point - I am not sure if outweighs my point about inability to bring numbers to bear, but it certainly needs to be weighed against it.

  11. #11

    Default Re: Unit size = unbalanced??

    Quote Originally Posted by econ21 View Post
    That's all true, but it's just quantifying the advantage of the larger unit that is tricky. I think all of what you have said above could be true and the 40 man unit be say, 70% as strong as the 60 man unit rather than less than 2/3 as strong as you stated. I don't see how it overturns my point that the larger unit typically cannot bring all its numbers to bear meaning that the combat strength of the smaller unit may be more rather than its numerical size.
    Assuming equal combat stats, if you put the two units on hold formation, the combat will always be one-on-one. In this case, the 40 man unit will be exactly 2/3 as strong as the 60 man unit. On average, the 40 man unit would kill 1 man for every 1 that it looses. If the 40 man unit fights until it looses all 40 men, the larger unit will also loose 40 men and have 20 men remaining. This is the definition of 2/3 as strong, i.e. the stronger unit loosing 2/3 of it's strength.

    If you put the two units on engage-at-will formation, the 60 man unit will not loose 2/3 of its strength in beating the 40 man unit. Men in the larger unit will wrap around the smaller unit and strike at the flanks of enemy men. Even if it's only 2 men extra of 10 men engaged head-to-head, those 2 represent much more than a 20% advantage. I don't remember my test results, but as I recall the 60 man unit can win with as many as 40 men remaining.


    Quote Originally Posted by econ21 View Post
    To take the issue further, I think we need a mathematical measure of a units' combat strength. But I confess I don't know how to construct that. I can see how you could quantify a unit's offensive strength (e.g. expected casualities inflicted) and even its defensive strength (expected casualities suffered versus a benchmark attacker). But how do you put them together to measure overall combat strength? If it was just casualities inflicted minus casualities suffered, it would not be very useful for solving this argument as it might average around zero, so it would be hard to say if a unit is more or less than 2/3 as strong as another.
    I don't think you can develop an algorithm to measure this because you don't know the correlation coefficient that binds the men together. Each man in a unit does not move independently (Poisson distribution) as you've pointed out, so not all the men are randomly engaged. Even so, the smaller unit has no advantages as far as I can see, so the rate of losses in the smaller unit will always be greater than in the larger unit, and it will always be less effective than the ratio of the starting strength of the two units.

    You could develop a table of losses vs size difference with empirical tests. Based on my testing in the past the effect is very strong, but i can't remember the results. One thing I do remember is that with two 60 man units a win is almost guaranteed if one unit can gain a 15 man (25%) advantage in men with say a very good charge. The other thing I clearly remember is that, with 60 man units fighting head-to-head and with equal combat stats and charge bonus, a 1 point (20%) combat advantage produces a win 6 times out of 10, and a 2 point (44%) advantage produces a win 9 times out of 10.
    Last edited by Puzz3D; 10-26-2009 at 13:41.

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