ScrapYard Armory

A BattleTech weblog

May-14-2011

A Time of War Initiative Analysis

One of our projects here at The ScrapYardArmory is to create a system to calculate a Battle Value for RPG characters for use in tactical infantry games.  This only takes into account skills, abilities, and attributes that are directly or semi-related to what happens in combat situations.  For starters, Initiative is an important factor and in order to better understand what affect modifying a character’s initiative has, a fancy pants graph was made to visualize it.

First a little about how we do personal initiative… The standard initiative is 2d6.  Combat Sense makes it 3d6 and ignore the MINimum (or lowest) roll.  Combat Paralysis makes it 3d6 and ignore the MAXimum (or highest) roll.  (Max and Min is sort of habit from working in LibreOffice’s Calc and Excel.)  Furthermore the Tactics/Infantry skill is added to the roll up to a maximum of +6.  The resulting number is displayed using two 6 sided dice adjacent to the character on the map.  The highest initiative a character can have is 12.  The Reflex Attribute breaks ties and where Reflex is the same, the characters act simultaneously (appropriately conducted by the GM).

To see what affect Combat Sense, Combat Paralysis, and the Tactics/Infantry skill have, an analysis was conducted.  The average roll for each was calculated and represented by a bar on the graph below.  The  Combat Sense, Combat Paralysis, and standard initiatives are colored differently so you can see their relationship.  Ignore Max is Combat Paralysis while Ignore Min is Combat Sense.  Then every individual roll’s winning percentage against other rolls was calculated and averaged together to get an average Win % vs 2d6 OR Win % vs All.  Win %’s are the blueish shapes and labeled on the right side of the graph.  The +0 to +6 mods are from the Tactics/Infantry skill bonus to initiative.  The rolls were then ordered by their Average Roll where you can see the standard initiative 2d6+0 averages to 7 as expected.

 

What I didn’t expect was that only 2 of the Combat Paralysis rolls were lower than 2d6+0, and not really a whole lot lower.  But, the Win % drops off swiftly at the low end.  (Note that 2d6 only wins against itself 44.4% because ties don’t count.)

If you look closely, you will notice that while the Average Roll increases from left to right, the Win % doesn’t always increase.  Ignore Max+3 has an Average Roll a only few hundredths more than Ignore Min+0, but has a slightly lower Win %.  I believe this is due to an increased number of ties (Remember that only wins were counted and a tie is not a win).  You can see this happens again closer to the right, but really neither matters a whole lot since the numbers are still so very close.

You may also have noticed that the colors of the bars are symmetric left to right with Combat Paralysis tending to the left and Combat Sense to the right.

Not too many characters probably end up too far on the right side with high Tactics/Infantry skills, but you can see how they are much more likely to get a high initiative hitting the maximum of 12 more and more often.  With Combat Sense they’ll tend to the right pretty quickly though.  How does this affect our Battle Value?  We’re still not sure as we try to estimate the value of initiative vs other things like weapons, health, etc.

This post is really just meant to share our findings with you so you have a better understanding of the effect your character creation has on Initiative.

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  1. EastwoodDC Said,

    I’m not understanding something here. The first bar “Ignore Max +0” averages about 5.7, and wins against 2d6 a bit more than 10% of the time. The third bar “2d6 +0” average about 7 and wins against 2d6 about 20% of the time? Shouldn’t 2d6 versus 2d6 win 50% of he time?

    How did you generate your numbers?

  2. Saxywolf Said,

    Win % isn’t vs 2d6. It is against all the different rolls and then averaged together. Although, showing each of their win% vs straight 2d6 would be interesting…

  3. EastwoodDC Said,

    OK, that helps. What you have as % win is essentially your chance of winning the initiative against an opponent randomly selected from all those possibilities. That’s a useful way of considering how good a particular skill level is in general.

  4. Saxywolf Said,

    It would be if the enemies have an even distribution of initiative roll types, but I think they would tend toward the 2d6. So, having a win % against 2d6 would be useful as well… added.

  5. EastwoodDC Said,

    Enemies won’t have an even distribution, but you might make an educated guess about what that distribution is, and make a comparison against that. For instance, if you think 40% will be “2d6+0”, 30% “Ignore max 2d6+2”, and 30% “Ignore min 2d6+1”, You could take that weighted average of the corresponding probabilities.

    I’m not suggesting you *should* do this, as it might be a lot of work for not much more usefulness, but that’s how you might get around the enemy having an even distribution.

  6. Saxywolf Said,

    Oh, I thought about something like that… but I think the two Win %’s I show give you a good enough idea of how the rolls compare. Plus, the enemy force could vary greatly depending on their experience level.

  7. EastwoodDC Said,

    What you have is more than enough. What I really wanted to point out is that you are touching on a method of making calculations under uncertain assumptions, which can be really useful sometimes. You might not know exactly what the enemy distribution will be, but if you can make a good guess, then you can still calculate useful probabilities.