Deconstructing the RTW Battle Engine: A Tool for Determining Chance to Hit

[NobleNick]

To the moderators: This is a post concerned with the internal workings of the RTW battle engine. If you think there is a better place for this post to be, please put it there (because I would like to find that place, if it exists).

Summary: Below you will find a chart that can be used to extract the actual overall average chance of each soldier in a unit to hit a soldier in another unit. Many conditions must be met in order to extract reasonably accurate data, and even more must be met in order to draw reasonable and acurate conclusions. All of this is detailed below. In addition, I've also posted a simpler chart. The purpose of the simpler chart is to help folks understand the workings of the full chart, however, the simple chart is a bonafide tool in and of itself.

Chart including partial unit rout. Here is the full chart. Explanation of use may be found below.

Chart including partial unit rout.

Simple chart: Here is the simple chart. It is the same as the full chart, except it is missing 10 of the 12 curves. Explanation of its use may be found below.

Simple chart

Background: At the time of this writing, I have only played Vanilla 1.5 RTW. I have been curious as to the intenral workings of the battle engine. I want to know the answers to questions like: EXACTLY how much more effective is a gold shield Legionary Cohort than a silver shield? EXACTLY how much of an advantage is it to be 10, 20 or 30 feet higher than your opponent when trading arrow volleys? EXACTLY how much more effective is a flank or rear attack than a frontal attack?

I have posted in this forum and searched other forums for the answers to these questions; but have found very little quantitative data. The bulk of what I have found have been vague qualitative comparisons, and comments like, "It's very complicated." I'm sure it is. But I refuse to believe that a little work and patience won't reveal some usable data; and that is what I intend to do: Extract enough data so that I will **KNOW** whether or not the statements like, "Cretan Archers are better than Roman Archer Auxilia," are true.

Justification: I have run literally a hundred or so controlled tests in the Custom Battle "sand box," to try to extract some meaningful relationships. Among the many dismaying things I noticed, I realized that there is not a constant linear relationship between how good a soldier is at hitting his target and how well his unit fares. I am not talking about battle-to-battle variability (statistics); but, rather, the fact that a small increase in average combat effectiveness results in a large sway of the end result.

For instance: If each soldier in unit A has a 1.1% chance to hit with each try (turn), and each soldier in unit B has only about 90% of that (a 1% chance), what is the expected outcome? Obviously Unit A should win, but by how much? No credit if you gave the intuitive answer: that Unit A should have about 10% of their men left. Unit A performs 10% better as a unit only for the first volley. After that, even though each man continues to perform 10% better than those in Unit B, Unit A also has more men. This leads to the mathematically correct (but unintuitive) answer that if Unit B fights to the bitter end (no rout) Unit A will, on average, have about 30% of their men left (not 10%).

So that is the reason for the charts: To convert end of battle results into a relative turn-by-turn effectiveness. A happy discovery for me was that if one also keeps track of the number of turns a battle takes, one can extract actual (instead of just relative) turn-by-turn effectiveness.

Chart Limitations: To use the chart you need a battle result for a battle between two similar units (e.g., archer versus archer) that had EXACTLY the same number of starting combatants.

The chart gives you back one or two pieces of data: If you have only the starting and ending unit numbers, then you get a RELATIVE (normalized)average turn-by-turn effectiveness for each combatant in each unit in that battle. If you also know how many turns the battle lasted, then you also denormalize your result to get an ACTUAL average turn-by-turn effectiveness for each combatant. You must collect and save many of these results in order to get a "per man" effectiveness that is useful for comparing different units.

Also realize that terrain, weather, difficulty setting, handicaps, the infernal desire of some archers to reform before re-firing, special hidden bonuses, intentionally built-in variability, unit orientation and formation, changes in unit stance (e.g. running), allowing one unit to consistently get off the first volley, the way the eagle flew, the general's speech, the color of the rabbit's liver, and other things that I am sure I've missed will skew your results and/or conculsions if you are not careful. The charts will almost certainly lead you to draw the erroneous conclusions if you do not practice good experimental hygiene. Drawing conclusions based on runs of less than 20 individual battles (for the most simple experiments) is risky.

Explanation of simple chart: The simple chart has 2 curves; and is good only for interpreting battles that resulted in 100% of the enemy killed, with no routs.

The curve sloping up towards the right uses the axis numbered 0 through 100. This curve gives you relative turn-by-turn effectiveness. What I mean by that is that the chart tells you how much better the average soldier in the winning unit was than the loser. The number is given as the average percent chance EACH soldier in the winning unit had of killing an opponent, EACH turn, ASSUMING that each enemy soldier in the losing unit had an average of 1% chance of killing an opponent on each turn.

The curve sloping down towards the right uses the axis numbered 0 through 300, and is useful only if you also know the battle length in turns. (For instance, archer units fire in volleys. Each volley is a turn.) The chart gives you the number of turns the battle would have lasted *IF* the relative effectiveness you determined on the chart was also the actual effectiveness.

How to use the chart: See the simple chart, below. Let's say, for this example that you and the opponent had a simple battle that involved 160 of your archers against 160 of his archers. Let's assume you win: The enemy archers get wiped out by your unit. None of the enemy routed. you have 104 men left. The battle lasted 39 turns.

You enter the chart with 104/160 = 64% and go straight across to the "% remaining" curve (red line). Then drop straight down to the "Per Turn Effectiveness" (Still on the red line). The number is "0.017" which is a RELATIVE number. Since the chart is normalized to an enemy that has a 1% chance per turn, per soldier, to hit, you could read this number as (1.7) x (1%) = 1.7% . This does NOT necessarily mean that each of your guys had a 1.7% chance to hit each turn. This is a NORMALIZED number. It means that, on average, each one of your guys hit 1.7 times as often as the opponent's average man. This is valuable information, in and of itself; and we could stop right here and be happy. But wait, there's more...

DENORMALIZATION: Since you have the battle length, you decide to do the next step: Starting from the "0.017" that you found in the first step, you go back up to the "Turns" curve (green line) and then over to the axis on the right. The middle gray line between the 60 and the 90 is 75; so this looks like about 78 turns. This is how long the battle would have lasted if, indeed, the enemy had a rating of 1% effectiveness and yours had 1.7%. BUT this battle only lasted 39 turns, which means that these guys killed themselves off 78/39 = 2 times faster. Happily, linear relationships do hold for this DENORM-alization factor. Here, DENORM = 78/39 = 2. The enemy's actual effectiveness is 1% x DENORM = 1% x 2 = 2%, and your guys performed at 1.7% x DENORM = 3.4%. There you have it: this is (for this example) the actual average turn-by-turn effectiveness of each of your guys in the unit. Each soldier had an average 3.4% chance of killing an opponent, each turn; whereas each enemy soldier had a 2% chance of killing one of your men.

Tutoring chart

So, this is great, if you can get a unit to hold together until it is destroyed, but most units rout before then. You could pump up the experience on the units to get them to hold together; but I have information the leads me to believe that this also affects attack and defense factors. I don't need this skewing my results.

That is the reason for the full chart. The Full chart works exactly like the simple chart. The only difference is that the simple chart had only one pair of curves, that were good for "0% enemy remaining" when the enemy unit routs (in other words, it did not rout). Now you have curves for "10% enemy remaining" when the enemy unit routs. Or 20%, 30%, 40%, or 50%. If, for instance, the enemy had 30% of its men left when the rout occured, ignore the existence of all other curves and just use the pair of 30% curves in exactly the same manner as was shown for the 0% curves in the simple chart (the 0% were the ONLY curves in the simple chart).

Remember, you enter the axis on the left with the percentage of the WINNING unit's men remaining at the time the losing unit routed. You go over to the curve that slopes UP to the right and represents the percentage of the LOSING unit's men that were left at the time the rout started. Then you drop down to find the turn-by-turn average relative effectiveness of each man in the winning unit (losing unit's men are always assumed to have a normalized effectiveness of 1%).

To Denormalize, you then go straight up from the normalized effectiveness that you just found, unitl you hit the curve that that slopes DOWN to the right and that represents the percentage of the LOSING unit's men that were left at the time the rout started. Then you go straight to the right (the axis lnumbered 0 through 300) and read off the number of turns a normalized battle would have taken to get to that point. Divide this number by the number of turns it actually took toget to the start of the rout to get DENORM. The losing units actual effectiveness is 1% x DENORM. The winning unit's actual effectiveness is its normalized effectiveness, that you found in the first step, times DENORM.

When you enter the chart on, let's say, the 30% curves; you will find a normalized effectiveness. This effectiveness is the same as if the battle had continued. So, if you are curious, you can follow this line up and down to where it intersects the 0% curve, to find out how many of the winning unit's men would have been left if their enemy hadn't routed.

When collecting battle data to use in the chart, you must be ready and pause the battle INSTANTLY when a unit routs. Then record the results at this instant as your "end of battle" results. Otherwise your data will be in error when you use the chart, and the results will be worthless.

Miscellaneous Ramblings: I developed the charts to help me with examining archer units. I picked archer units because they offer the least unknowns: I can put them out on a level field on a calm clear day, and it is relatively easy to count the volleys. I am trying to use this controlled situation to break down just one or two pieces of the puzzle. I am hoping that after I eliminate a few unknowns, most of the rest will be much easier.

The reason I have posted these charts is to see if anyone else out there is interested in exploring this subject, and may have been held back by lack of tools.

[John Wayne]

Shouldn't this be in the Mod Workshop?

Anywho, what is this supposed to show?