Topic: For The People Material
That was a good post and worth an answer. There are many situations in the world which are not monotonic. Something happens in the ACW casualty statistics that is not a linear progression, but has a step function in it. It has something to do with the density of targets, but more defenders does not always equate to better results. This is why I did not go for a straight odds CRT, 2-1 at one size battle behaved differently than 2-1 in a medium battle. In fact this was an earlier controversy with the CRT, the results were insensitive to force ratios until they got near 3-1. Some thought that was highly incorrect and illogical, but the numbers are what they are.
Something that I have learned about designing games is some things are true, but not entirely explanable, and counter intuitive. I can either ignore it and let logic apply or I can actually be an historian and try to make sure it doesn't get left on the cutting room floor because it is inconvenient. So, you can sit back and go, that doesn't make any sense, but at the macro level some things are true even if they are counter intuitive, which is why they are called counter intuitive. All of my data comes directly out of a wealth of Operations Research papers that proliferated during the mid-60s, which were and remain the major sources for my ACW combat research.
FTP has three basic defensive situations, unfortified, forts, and fortified lines (resource and capital spaces). So this example is a fort/ fortified lines situation. I should note that if there is no fort in Richmond then the Union can win a small battle, but this is a fort/fortified lines example which makes a difference. There were seventeen instances of assaults on fortified lines during the Civil War (based on Livermore's calculations). In all small battle equivalent situations on fortified lines there were no successes. At the medium battle level there were three successes. A great question is why? I have some theories, but it appears that less is more in this particular case, at least based on the historical record. The statistics are what they are... so in this example you do pick up a 1 in 18 (as close as I could get it) chance of winning a medium battle in a fortified line situation.
Again this phenomena is again what it is...in very small battles and very large battles there is little variation in losses for both sides, in essence more or less equal. However, in medium density battles there is a slight bias whereby the defender lost a bit more than the attacker. I believe that this was based on a number of factors such as some magic density of targets to maneuver room relationships and historically it was due to the CSAs ability in the aggregate of being able to create local advantage even though they were outnumbered, but the Union had a few successes when they pulled this off. Again that is what the numbers show, so this is how I captured it. It should be noted that the probability of the 1SP in a small battle being eliminated is 84% vice 100% in a medium battle, so there is an attacker disadvantage when going from a small to a medium battle (without modifiers).
This situation is taking advantage of historical hindsight to some degree as I pointed out in the earlier example concerning the medium battle bias. However, in FTP terms this example has other costs that are not being evaluated. First off, the ability for the Union to roll a 10 prior to Grant with a 15 SP army is in itself very small. You need to have McClellan or Meade with Pleasanton in a fort, or Lee has to be OOS for this to occur. I would also note that leaving the leader casualty rules aside, the Union in a medium battle is very likely to give as good as it gets due to the lopsided nature of the force ratio giving the Union a +2, since its an army the lowest drm for the Union is probably a +2, giving the Union a 50% chance to kill 3 CSA SPs, which was my statistical point that the larger the fight the smaller the variability in losses. I should also note that the Union doesn't have to roll a 10 to eliminate a 5SP army in a large battle, so the bigger message is small armies may get the edge in one transaction (battle), but payback is hell (when the 10 SP army counterattacks against 1 or 2 surviving SPs).
There is no question that there are a few arbitrage situations where players can gain some benefit from the numberical relationships of a medium battle over either a small or large battle. However, that is the point, historically that bias was there. You cannot win a game working the seams of this historical bias, but as an historian I try to make the system as faithful to the reality as I can. Hence the way things are...as I said the CRT is not flawed unless my interpretation is flawed and I have looked at this in great detail, so it is what it is for a reason, not a mistake or something I had to fudge to make it work as a game.
Great discussion,
Mark
Something that I have learned about designing games is some things are true, but not entirely explanable, and counter intuitive. I can either ignore it and let logic apply or I can actually be an historian and try to make sure it doesn't get left on the cutting room floor because it is inconvenient. So, you can sit back and go, that doesn't make any sense, but at the macro level some things are true even if they are counter intuitive, which is why they are called counter intuitive. All of my data comes directly out of a wealth of Operations Research papers that proliferated during the mid-60s, which were and remain the major sources for my ACW combat research.
1. Example #1: the Union attacks Richmond with 4 SP, the CSA defends with a fort and 1 SP. There is 0% chance of victory. Add a second CSA SP and the Union can win if they kill 2 CSA SP to 1 Union loss. Twice the defense = worse defense. The results of going from a small battle to a medium battle.
FTP has three basic defensive situations, unfortified, forts, and fortified lines (resource and capital spaces). So this example is a fort/ fortified lines situation. I should note that if there is no fort in Richmond then the Union can win a small battle, but this is a fort/fortified lines example which makes a difference. There were seventeen instances of assaults on fortified lines during the Civil War (based on Livermore's calculations). In all small battle equivalent situations on fortified lines there were no successes. At the medium battle level there were three successes. A great question is why? I have some theories, but it appears that less is more in this particular case, at least based on the historical record. The statistics are what they are... so in this example you do pick up a 1 in 18 (as close as I could get it) chance of winning a medium battle in a fortified line situation.
2. Example #2: The much discussed 1SP attack of a large force(5SP) or more. This force will always cause a 1SP loss and if can roll a 6 will cause 2 SP loss. Only risking 1SP. If you can get modifiers by leaders or defender OOS this can be lucartive killing 2 SP 50% of the time. But look at what happens if you are only attacking 4 SP. Suddenly you can only kill 1 SP 50% of the time with no chance to kill 2SP even with DRMs. Is this is not gamey, or unrealistic? A small force attacks a weaker force and has less than 50% chance of matching the results if they had attacked a larger force? News FLASH! : This is a game. Do we really want more rules?
Again this phenomena is again what it is...in very small battles and very large battles there is little variation in losses for both sides, in essence more or less equal. However, in medium density battles there is a slight bias whereby the defender lost a bit more than the attacker. I believe that this was based on a number of factors such as some magic density of targets to maneuver room relationships and historically it was due to the CSAs ability in the aggregate of being able to create local advantage even though they were outnumbered, but the Union had a few successes when they pulled this off. Again that is what the numbers show, so this is how I captured it. It should be noted that the probability of the 1SP in a small battle being eliminated is 84% vice 100% in a medium battle, so there is an attacker disadvantage when going from a small to a medium battle (without modifiers).
3, Example #3 The CSA has a dream team with an Army with DRMs of +9. If they make a medium attack against 15 Yankee SP they can not lose unless attacking a resource space. This would require them to attack with 4 SP. However if they attack with a stronger force say 5 SP they could lose if the Union can roll a 10. They would also lose their Army and 10 SW. All for making the attacking force stronger.
This situation is taking advantage of historical hindsight to some degree as I pointed out in the earlier example concerning the medium battle bias. However, in FTP terms this example has other costs that are not being evaluated. First off, the ability for the Union to roll a 10 prior to Grant with a 15 SP army is in itself very small. You need to have McClellan or Meade with Pleasanton in a fort, or Lee has to be OOS for this to occur. I would also note that leaving the leader casualty rules aside, the Union in a medium battle is very likely to give as good as it gets due to the lopsided nature of the force ratio giving the Union a +2, since its an army the lowest drm for the Union is probably a +2, giving the Union a 50% chance to kill 3 CSA SPs, which was my statistical point that the larger the fight the smaller the variability in losses. I should also note that the Union doesn't have to roll a 10 to eliminate a 5SP army in a large battle, so the bigger message is small armies may get the edge in one transaction (battle), but payback is hell (when the 10 SP army counterattacks against 1 or 2 surviving SPs).
There is no question that there are a few arbitrage situations where players can gain some benefit from the numberical relationships of a medium battle over either a small or large battle. However, that is the point, historically that bias was there. You cannot win a game working the seams of this historical bias, but as an historian I try to make the system as faithful to the reality as I can. Hence the way things are...as I said the CRT is not flawed unless my interpretation is flawed and I have looked at this in great detail, so it is what it is for a reason, not a mistake or something I had to fudge to make it work as a game.
Great discussion,
Mark
Posted by markherman
at 4:38 PM EDT
Updated: Monday, 31 March 2008 5:08 PM EDT
