Double-Breaks Far too Frequent

[melm]

Thanks Pete for the sample.

There can be two separate questions.
Q1: Does the sample win-draw-loss ratio comply with tooltip figure? In warband(close order) case, the ratio is around 15-70-15.

So we can do such test.
H0: win ratio = 15%, H1: win ratio != 15%
Then we need to collect win ratio sample from Pete's experiment.
Since Pete has done 25 sets, we can get 25 win-ratios for our sample. Quite small sample size I'm afraid. We may still use t-test to do it.

If we look at the aggregate number,

OK, if I stop now I have done 750 impact combats.
70 led to a fragmented unit (9.3%)
96 led to a disrupted unit (12.8%)
584 led to no cohesion loss (77.9%)

There are 225 red results

Because win or loss can be either side, I expect 15%x2 = 30% win or loss result. So the number will not be far away from 30%. Pete says there are 225 red results. 225/750 = 30%. The same as I expect.

Q2: Does double-drop happen too frequently? The better statement is that do we have evidence that double-drop happens more often than that designed?

Once a warband lost the impact, -3 modifier will be applied, which is A)significant casualty B) lost badly C) additional modifier (Honestly, I don't know what it is). So total is -3.
And we still need 6 to pass the test. Thus we need 9 or above to pass. Thus the probability to pass is 10/36 = 27%.

here were 59 passed cohesion tests out of 225 "red results" (70+96+59) which represents 26.2% of the total

26.2% is quite close with my expect from calculation, which is 27%.

166 cases failed the test. Among them, double drop cases are 70. According to Mike_C' s post, double drop happens when dice roll sum is 2 or below 2. So when our roll sum is 5 or below 5, double drop happens. Thus, the probability I expect is 10/36= 27%. Since there are 70 frag cases, the sample proportion is 70/225= 31%. I can say it's close if we consider the variation of the sample since there is only ONE number here to compare.

[Geffalrus]

Seems like we're all restating things, so I guess I'll do that as well. My view on this is that a crucial aspect of this RNG discussion is unit and army design. We've talked a lot about the example of the massive warband army vs. another. We've discussed elsewhere about the possibility of increasing battle size to allow larger armies. We've all talked about zealots. The linkage between all these is that our perception of luck is heavily influenced by the number of rolls happening. The impact foot trait has a massive effect on unit survival because it both involves a large POA - AND - a penalty to cohesion tests. The more impact rolls you have, the more likely you are to see extreme results. However, the fewer rolls you have within one battle (because you have fewer impact units) the more likely you are to be surprised by extreme cases, because when those extremes occur, they will occupy a larger percentage of the results that you are witnessing.

Unit and army design can exacerbate this. When you have a cheap impact foot unit like the zealot that has an extra +50 POA from Superior but still only costs 51 points, you have an increased opportunity for extreme cases because there are more zealots rolling and they have a very high chance of winning the impact (depending on their foe). The inverse happens with pike units where in general they have very good rolls due to pike and deep pike. However, because they are expensive and few in number, they are vulnerable to bad rolls that will naturally occur over the course of many games.

Luck has an important, but relatively unpredictable, effect on games between roughly equal players. This luck can be further enhanced or mitigated through army choice (as well as terrain, strategy, and the fact that equally skilled does NOT mean skilled at the same aspects of this game).

[Cunningcairn]

I see Pete has already provided some samples but for what it's worth the following combat results are from impact between 31 pairs of average, close order warband in good going. As mentioned above this is checking fragmentation from impact combat and not the CT test after loss. I did not record every RED combat CT test but from feel only about a third fragged after a RED loss.

#1 Blue attacks Yellow from the left – 3 frags on charge 1 Frag on defence 12.9%
#2 Blue attacks Yellow from the left – 1 Frag on charge 1 Frag on defence – 6.5%
#3 Blue attacks Yellow from the left – 4 Frag on charge 1 Frag on defence – 16.1%
#4 Blue attacks Yellow from the left – 3 Frag on charge 2 Frag on defence – 16.1%
16 Frags out of 124 combats - 12.9%
11 Frags on attack
5 Frags on defence

[76mm]

hmmm, now up to 12 double-breaks vs none for my opponent. Every single warband on the left half of my line has double-broken. Most of these have been straight-up, one-on-one fights in open terrain. Extraordinary.

Pete, could you send me the scenario you've been using for testing?

[stockwellpete]

Pete, could you send me the scenario you've been using for testing?

If you can tell me how to, I will. I am not sure myself.

Edit: I have put it in Dropbox and I have tried to create a link . . .

https://www.dropbox.com/sh/eaj9oed9ookw ... R_-Ja?dl=0

Does this work?

[76mm]

Does this work?

I found and downloaded a Test.BAM file, is that it? If so, now I just need to figure out how to load it, I haven't played a single-player game in ages.

[stockwellpete]

Does this work?

I found and downloaded a Test.BAM file, is that it? If so, now I just need to figure out how to load it, I haven't played a single-player game in ages.

If you put it in your My Documents area - My Games - FOG2 - Campaigns folder. And then in the game itself go to Battles - Epic Battles. That is how I am set up anyway. Then I set it to Hotseat mode.

[jomni]

Seems like we're all restating things, so I guess I'll do that as well. My view on this is that a crucial aspect of this RNG discussion is unit and army design. We've talked a lot about the example of the massive warband army vs. another. We've discussed elsewhere about the possibility of increasing battle size to allow larger armies. We've all talked about zealots. The linkage between all these is that our perception of luck is heavily influenced by the number of rolls happening. The impact foot trait has a massive effect on unit survival because it both involves a large POA - AND - a penalty to cohesion tests. The more impact rolls you have, the more likely you are to see extreme results. However, the fewer rolls you have within one battle (because you have fewer impact units) the more likely you are to be surprised by extreme cases, because when those extremes occur, they will occupy a larger percentage of the results that you are witnessing.

Unit and army design can exacerbate this. When you have a cheap impact foot unit like the zealot that has an extra +50 POA from Superior but still only costs 51 points, you have an increased opportunity for extreme cases because there are more zealots rolling and they have a very high chance of winning the impact (depending on their foe). The inverse happens with pike units where in general they have very good rolls due to pike and deep pike. However, because they are expensive and few in number, they are vulnerable to bad rolls that will naturally occur over the course of many games.

Luck has an important, but relatively unpredictable, effect on games between roughly equal players. This luck can be further enhanced or mitigated through army choice (as well as terrain, strategy, and the fact that equally skilled does NOT mean skilled at the same aspects of this game).

You got that right. Against a human, luck, tactics are secondary. What I found crucial to victory happens before the battle. Terrain, army building to counter anticipated enemy army composition. Sadly, I lack in these aspects and lose a lot of head-to-head games.

[MikeC_81]

First of all, thanks to Pete and other who ran the tests. I am just going to recap the mechanics of combat, the basic math behind it and predicted results vs actual data before going onto more discussion. Melm already had a good post on this but I'll make sure everything is visible.

What I expected

From my time doing tests a year ago for the Beginner's guide, I knew that the odds of 2 units fighting each other in combat with the same PoA results in approximately each side losing 14% of the time and draws happening around 72% of the time. Every time a unit loses in close combat, it has to take a Cohesion Test and this mathematical function is public information. Simply roll two dice and a score of 6 or more passes and a score of 2 or less means you get the dreaded "double drop" where you not only fail the test but lose 2 ranks of cohesion from it. When bad things happen, you subtract the dice roll for various factors. The relevant factors for this test are Losing to Impact Foot, Suffering more than 5% combat damage, Total combat damage suffered this turn exceeds total damage inflicted by a large margin. The last two are kind of nebulous and I never could get a good answer as to what those meant from RBS other than "Its complicated" but the relevant fact at hand here is that I have never seen two steady, non-light foot units fight each other, produce a loser, and not have those two penalties apply. There is no such thing as a "bad loss" vs a "not bad loss" between these units as far as empirical data shows.

The test set up by Pete involved smashing 2 warbands units together repeatedly to see if double drops occurred more than they were supposed to as was charged by 76mm. The expected result is therefore easy to calculate. Each Warband has the same PoA and thus the odds of either of them losing are 14% + 14% = 28%. This gives us the odds in any given Warband vs Warband Impact round, the % chance someone has to take a CT test. We also know all the factors involved in such a test which rolling two dice and subtracting the result by 3. One needs to roll 3 or higher on those two dice after modifiers are applied to avoid the dreaded double drop. So in effect if you roll 5 or lower in this scenario, a double drop will happen (5-3=2). The odds of you rolling a 5 or lower on two dice is 27.78%. You can either just believe me on this one or you can work it out yourself, I am not going to proof that here.

So to find out how often we get double drops per Impact combat round between two Warbands, we simply multiply the odds of either Warband losing and thus having to take a test with the odds of them rolling a 5 or lower on that test. 28% x 27.78% = 7.7784%. Since Pete smashed 30 warbands vs 30 warbands twenty-five times, we would expect each test to yield an average of 2.33 Double Drops (frags) out of 8.4 CT tests per run.

Here is Pete's Data condensed (cut and paste into a spreadsheet for easier viewing or just skip it and read after) :

frag disrupted CT Passed CT Total
3 4 1 8
3 6 1 10
6 3 2 11
2 5 5 12
3 3 0 6
5 0 3 8
2 5 2 9
1 2 3 6
1 2 3 6
2 4 1 7
3 6 4 13
2 2 3 7
2 6 2 10
0 3 3 6
2 3 1 6
5 7 3 15
2 5 0 7
3 4 3 10
2 6 2 10
2 7 5 14
2 3 3 8
3 1 5 9
2 1 4 7
7 4 0 11
5 3 0 8

2.8 3.8 2.36 8.96

Last line is Averages for the 25 runs.

Gee Mike, is 2.8 a lot higher than 2.33?

No, it is actually well within reason. On average on each run, 8.96 Warbands were forced to take a CT test rather than the 8.4 we expected. The reason why that may be the case is because the 14% chance to win may not be accurate. The exact interaction between units in combat remains an overly complex calculation that even RBS can't fully explain to me. The numbers for the win/draw/loss table I posted on page 2 of this thread was obtained by empirical trial and error right clicking the attack tooltip and coming up with a "close number". It could be that the odds of winning and losing are closer to 15%. Or this is just a case of variance.

In any case, the percentage of Warbands that actually double dropped in Pete's scenario is 2.8/8.96 = 31.25% when we are expecting 27.78%. This would mean a mean of 2.48 double drops per run. The difference here is negligible over a sample size of 224 events (total number of CTs taken over the whole test). A layman's way of looking a it is to suppose for example RBS's code was wrong and required an unmodified roll of 7 instead of 6 somehow. This would mean the expected percentage of failing would shoot up 41.6% and the tests do not come close to that.

As an aside, the theoretical numbers for hold firms is 2.48 vs 2.36. Disrupts was 3.9 vs 3.8.

Once can also look at the distribution of double drops. In 25 runs only 5 entries recorded show significant deviation from the expected norm of 2.33 double drops. I am not going to do a standard deviation analysis on this but it is not in any way abnormal to the point where you can say something unintended is happening.

But it appears one side favoured another over the 15 battles?

This is difficult to say. We are not given all the data unfortunately on exactly who won, how many times, in each run. We merely got a lot of ''RNG neutral situations". Since each Warband vs Warband encounter is independent, we would need to know exactly how many holds, disrupted, and fragmented results for each combat loss each side had to do a real number crunch here. Besides, chopping the 750 combats in to 25 battle runs is entirely an arbitrary affair, you can't say whether one side was favoured or not from this alone, it could be that Side A had the lion's share of small advantageous runs but suffered the majority of the unfortunate ones where large numbers of double drops happened. In other words, if we sliced the results differently into say segments of 5, it could turn out that Side A was the beneficiary of being favoured. Suffice to say that MVP7's comment that it is exceedingly unlikely for there to be balanced luck is correct.

So what does this mean?

It means that arguments that Cunningcairn, 76mm and others are advancing about them getting far more double drops than what the numbers predict is as evidence that something is broken is almost certainly unfounded. Extreme events like the ones described by 76mm at the start of this thread remain exceptionally rare events. They are either victims of the extreme cases of variance (which can happen, otherwise people will never win the lottery for example or their playstyle involves them frequently subjecting their troops to additional factors cause morale drops by the addition of more negative CT die roll modifiers that they may not be aware of.

Also the sample sizes are not small as some have claimed. While they are small in that they are not large enough to drive the overall data towards to the exact theoretical numbers if we were to run the tests towards infinity, they are large enough to show that there is no systemic issue in the background which would lead us to believe the number crunching in the back is in any way shape or form. The Win/draw/loss numbers remain very close to my previously observed estimates (within 1% of overall outcomes) and the CT test are producing results consistent with our understanding of how CT tests work, especially when examining the disrupts and hold firm numbers. If the back end formulas were not as advertised, it is unlikely we would get such close conformity in the frag, disrupt, and hold firm numbers to what we were expecting.

Players should, and be expected to, plan for occasional unexpected events to the best of their abilities. Truly outrageous events that torpedo a game beyond any control of a player is, as shown, exceedingly rare. Players may simply not be aware of the risks or potential domino effects they put themselves in.

Ok fine, but I still think there is too much RNG

I have yet to see a a logically coherent argument that RNG is overriding skill on a consistent basis. Several arguments to that effect have presented here have already been debunked. Those include:

1) Lopsided game scores - can be explained by the snowball nature of the game

2) Games between evenly skilled players are determined by RNG - true if both players are Skynet and play to the theoretical skill and execution cap. No one is at this cap so one can always improve skill to mitigate RNG.

3) Games within an FoG2DL are between evenly skilled players and RNG effects those games negatively - even if true, low skilled players are unlikely to play anywhere close to the execution cap meaning they are introducing RNG into their own games by lack of skill. That is a player driven problem, not a game driven problem. The answer is to tell players to improve their play if they don't like RNG screwing them over.

I would like to know how RNG can be reduced even if you think it isn't a problem

Several possibilities exist, most create problems while at the same time don't actually solve anything. Or worse, they introduce a whole slew of new problems or phenomenon which then need to be looked at or combated or fundamentally change the way the game plays.

For example lets say we simply reduce the scores required to pass CT tests by 1. This would mean that troops all around hold their battle lines longer. The logical strategy adjustment would be to reduce reserves to compensate as troops in the back have less chance to plug a hole or exploit one that forms. This would only mean that battle lines would be pushed out longer and the player that does suffer the catastrophic event now has been incentivized to have fewer options to deal with it - effectively re-magnifying that effect to one of a lower occurrence but more catastrophic than before. This is a perfect example of a change made to accommodate more skill that has the potential to actually strip skill from the game , in the form of accurately judging how much to spend on which units to form said reserve, and accentuate luck instead by pushing out longer, narrower battle lines where any breakthrough due to luck leaves fewer reserves to deal with them and most likely a longer distance to travel to reach the point of crisis.

[jomni]

Mike, you deserve a PhD!

[rbodleyscott]

Mike, you deserve a PhD!

I imagine he probably already has one.

[stockwellpete]

But it appears one side favoured another over the 15 battles?

This is difficult to say. We are not given all the data unfortunately on exactly who won, how many times, in each run. We merely got a lot of ''RNG neutral situations". Since each Warband vs Warband encounter is independent, we would need to know exactly how many holds, disrupted, and fragmented results for each combat loss each side had to do a real number crunch here. Besides, chopping the 750 combats in to 25 battle runs is entirely an arbitrary affair, you can't say whether one side was favoured or not from this alone, it could be that Side A had the lion's share of small advantageous runs but suffered the majority of the unfortunate ones where large numbers of double drops happened. In other words, if we sliced the results differently into say segments of 5, it could turn out that Side A was the beneficiary of being favoured. Suffice to say that MVP7's comment that it is exceedingly unlikely for there to be balanced luck is correct.

I can see what you are saying but it was quite strange how the RNG seemed to be favouring Side B decisively at certain points in the test. So out of the 25 sets Side A was moderately disadvantaged 5 times and severely disadvantaged 3 times, while Side B was moderately disadvantaged just once and severely disadvantaged 2 times. This is obviously not a very scientific measure of mine, but I would say that if one of these particularly one-sided sequences happened in a game then the player on the receiving end would be in big trouble. It is quite possible that Side A was getting compensation from smaller advantages elsewhere in the test, but the point is that these would not be game-changing advantages and would be more easily mitigated by player contingency plans. The other thing to say is that these combat sequences where there were decidedly more double and single drops than the overall average might suggest were quite common and were happening roughly once in every second set of 25 combats.

Just to give one sequence in the test (the dots represent combats where no cohesion drop occurred) . . .

D . . F . D F . D D . . F F . . F . F F

So in 20 consecutive combats there were 7 double drops and 4 single drops with Side A suffering 5 and 2 and Side B getting 2 and 2. So that was designated a "severe disadvantage" for Side A just to give a rough indication of how that sequence might have impacted on a game. You have to remember that the double drops almost inevitably lead to routed units in the next turn and adjacent friendly units having to take morale cohesion tests as well. So the impact of this sequence is likely to be massive.

[stockwellpete]

Truly outrageous events that torpedo a game beyond any control of a player is, as shown, exceedingly rare.

Not as rare as you might think. In the 25 sets (think of them as separate games if you like) one side or the other was severely disadvantaged in 5 of them (20% of the total).

[stockwellpete]

Ok fine, but I still think there is too much RNG

I have yet to see a a logically coherent argument that RNG is overriding skill on a consistent basis. Several arguments to that effect have presented here have already been debunked. Those include:

1) Lopsided game scores - can be explained by the snowball nature of the game

Sometimes they can be, but sometimes they can be explained by the impact of the RNG.

2) Games between evenly skilled players are determined by RNG - true if both players are Skynet and play to the theoretical skill and execution cap. No one is at this cap so one can always improve skill to mitigate RNG.

No one has argued this. My point was that RNG is likely to be more of a factor the more equal the two players are in terms of their skill and their form on the day.

3) Games within an FoG2DL are between evenly skilled players and RNG effects those games negatively - even if true, low skilled players are unlikely to play anywhere close to the execution cap meaning they are introducing RNG into their own games by lack of skill. That is a player driven problem, not a game driven problem. The answer is to tell players to improve their play if they don't like RNG screwing them over.

My point was that matches in the FOG2DL tend to be between more evenly matched players than, say, the average pick-up game or matches in the earlier rounds of the automated tournament. So, just as I have answered to your point 2, RNG is likely to be more of a factor in FOG2DL matches than these other categories of matches.

So these arguments have not been "debunked" as you suggest. You may have debunked particularly crude approximations of what has been argued by some of us, but our actual arguments have a lot more nuance than you are allowing for.

[stockwellpete]

I would like to know how RNG can be reduced even if you think it isn't a problem

Several possibilities exist, most create problems while at the same time don't actually solve anything. Or worse, they introduce a whole slew of new problems or phenomenon which then need to be looked at or combated or fundamentally change the way the game plays.

Which problems would this idea introduce?

" . . . imagine two players sitting at a table playing a game of TT FOG. Instead of rolling a die each time for combat or rallying etc, they would reach down into a bag that contained 60 discs (10 of them numbered 6, 10 of them numbered 5 and so on, all the way down to 10 of them numbered 1). When the score on the disc was fed into the game the disc would not be returned to the bag. So, if the player pulled out a 6, then there would only be nine 6's left in the bag and so the chance of getting another one for that player would be reduced a bit, and the other player would now have a slightly better chance than his opponent of getting the next 6. And so on. In this way the relative "luck element" between the two players would be moderated, but not removed altogether. Once a player had used 30 discs, the bag would be filled up again . . ."

What are the other possibilities for RNG adjustment please?

For example lets say we simply reduce the scores required to pass CT tests by 1. This would mean that troops all around hold their battle lines longer. The logical strategy adjustment would be to reduce reserves to compensate as troops in the back have less chance to plug a hole or exploit one that forms. This would only mean that battle lines would be pushed out longer and the player that does suffer the catastrophic event now has been incentivized to have fewer options to deal with it - effectively re-magnifying that effect to one of a lower occurrence but more catastrophic than before. This is a perfect example of a change made to accommodate more skill that has the potential to actually strip skill from the game , in the form of accurately judging how much to spend on which units to form said reserve, and accentuate luck instead by pushing out longer, narrower battle lines where any breakthrough due to luck leaves fewer reserves to deal with them and most likely a longer distance to travel to reach the point of crisis.

My idea here was that the -1 penalty might be removed from CT tests only in situations where shock troops fought each other. So their ferocity was, in effect, mutually nullified. If both sides were ferocious, it wouldn't be a factor really, would it?The shock units would still have the same attributes when fighting other types of units. It would certainly need testing but it doesn't seem to be particularly unrealistic. Battle lines where shock troops meet would hold together a bit longer, but I don't think that many players would be abandoning the idea of having a reserve because of it.

[rbodleyscott]

For example lets say we simply reduce the scores required to pass CT tests by 1. This would mean that troops all around hold their battle lines longer. The logical strategy adjustment would be to reduce reserves to compensate as troops in the back have less chance to plug a hole or exploit one that forms. This would only mean that battle lines would be pushed out longer and the player that does suffer the catastrophic event now has been incentivized to have fewer options to deal with it - effectively re-magnifying that effect to one of a lower occurrence but more catastrophic than before. This is a perfect example of a change made to accommodate more skill that has the potential to actually strip skill from the game , in the form of accurately judging how much to spend on which units to form said reserve, and accentuate luck instead by pushing out longer, narrower battle lines where any breakthrough due to luck leaves fewer reserves to deal with them and most likely a longer distance to travel to reach the point of crisis.

My idea here was that the -1 penalty might be removed from CT tests only in situations where shock troops fought each other. So their ferocity was, in effect, mutually nullified. If both sides were ferocious, it wouldn't be a factor really, would it?The shock units would still have the same attributes when fighting other types of units. It would certainly need testing but it doesn't seem to be particularly unrealistic. Battle lines where shock troops meet would hold together a bit longer, but I don't think that many players would be abandoning the idea of having a reserve because of it.

Firstly, this can't simply be "Shock Troops" vs Impact Foot without seriously impacting game balance, because Shock Troops include Offensive Spearmen and Pikemen. Though some people might want to change the balance between those and Impact Foot, the design policy is that we do not.

It could be "Impact Foot" vs "Impact Foot", though this would of course affect legionary vs legionary battles as well as warband vs warband battles. Legionaries vs legionaries will already have a significantly lower rate of double drops, because they get +1 for heavy foot AND are usually of Superior or at least Above Average quality. (Noting that statistically re-rolls have a higher damping effect on double drops than they do on single-drops, as the random roll for a double-drop is more likely to include a 1 on one of the "dice"). Also there is the issue of Warbands vs Legionaries, as the proposed change would make warbands significantly more resilient against legions than they are now. I submit that this would not be realistic and hence not a good thing.

Then logically, there is the case of Lancers vs Lancers, and I would submit that we don't want to make cavalry battles less volatile than they are now. Arguably they are already significantly less volatile than they were historically.

Everything that changes has ramifications which usually go beyond what was envisaged when the change was proposed.

[stockwellpete]

Pete, when you have completed doing that set of samples, it would be worth comparing a set for 30 Heavy Infantry Offensive Spearmen vs 30 Heavy Infantry Offensive Spearmen.

I have done just 5 sets for this as requested by Richard . . .

Set 1 - 1 fragmented, 0 disrupted, 5 cohesion tests passed, RNG neutral
Set 2 - 1 fragmented, 2 disrupted, 3 cohesion tests passed, RNG neutral
Set 3 - 1 fragmented, 3 disrupted, 3 cohesion tests passed, RNG neutral
Set 4 - 0 fragmented, 5 disrupted, 2 cohesion tests passed, RNG favoured Side B (0 disrupts) Side A severely disadvantaged (5 disrupts)
Set 5 - 0 fragmented, 1 disrupted, 4 cohesion tests passed, RNG neutral

So in 150 combats, there were 31 "red results" which resulted in 3 frags, 11 disrupts and 17 cohesion tests passed.

[rbodleyscott]

Pete, when you have completed doing that set of samples, it would be worth comparing a set for 30 Heavy Infantry Offensive Spearmen vs 30 Heavy Infantry Offensive Spearmen.

I have done just 5 sets for this as requested by Richard . . .

Set 1 - 1 fragmented, 0 disrupted, 5 cohesion tests passed, RNG neutral
Set 2 - 1 fragmented, 2 disrupted, 3 cohesion tests passed, RNG neutral
Set 3 - 1 fragmented, 3 disrupted, 3 cohesion tests passed, RNG neutral
Set 4 - 0 fragmented, 5 disrupted, 2 cohesion tests passed, RNG favoured Side B (0 disrupts) Side A severely disadvantaged (5 disrupts)
Set 5 - 0 fragmented, 1 disrupted, 4 cohesion tests passed, RNG neutral

So in 150 combats, there were 31 "red results" which resulted in 3 frags, 11 disrupts and 17 cohesion tests passed.

This is a rate of 0.6 frags per set, compared with 2.8 for warbands vs warbands in your tests. The warband vs warband combats have more than 4 times as many double drops as the Offensive Spearmen vs Offensive Spearmen combats do.

Taken in conjunction with my previous post above, I think that what this suggests is not that the game rules need changing, but that monolithic warband vs warband battles are unsuitable for tournament play.

[stockwellpete]

Firstly, this can't simply be "Shock Troops" vs Impact Foot without seriously impacting game balance, because Shock Troops include Offensive Spearmen and Pikemen. Though some people might want to change the balance between those and Impact Foot, the design policy is that we do not.

It could be "Impact Foot" vs "Impact Foot", though this would of course affect legionary vs legionary battles as well as warband vs warband battles. Legionaries vs legionaries will already have a significantly lower rate of double drops, because they get +1 for heavy foot AND are usually of Superior or at least Above Average quality. (Noting that statistically re-rolls have a higher damping effect on double drops than they do on single-drops, as the random roll for a double-drop is more likely to include a 1 on one of the "dice"). Also there is the issue of Warbands vs Legionaries, as the proposed change would make warbands significantly more resilient against legions than they are now. I submit that this would not be realistic and hence not a good thing.

Then logically, there is the case of Lancers vs Lancers, and I would submit that we don't want to make cavalry battles less volatile than they are now. Arguably they are already significantly less volatile than they were historically.

Everything that changes has ramifications which usually go beyond what was envisaged when the change was proposed.

So the only option left is shock units of the same type fighting each other? Is that a possibility?

[rbodleyscott]

Firstly, this can't simply be "Shock Troops" vs Impact Foot without seriously impacting game balance, because Shock Troops include Offensive Spearmen and Pikemen. Though some people might want to change the balance between those and Impact Foot, the design policy is that we do not.

It could be "Impact Foot" vs "Impact Foot", though this would of course affect legionary vs legionary battles as well as warband vs warband battles. Legionaries vs legionaries will already have a significantly lower rate of double drops, because they get +1 for heavy foot AND are usually of Superior or at least Above Average quality. (Noting that statistically re-rolls have a higher damping effect on double drops than they do on single-drops, as the random roll for a double-drop is more likely to include a 1 on one of the "dice"). Also there is the issue of Warbands vs Legionaries, as the proposed change would make warbands significantly more resilient against legions than they are now. I submit that this would not be realistic and hence not a good thing.

Then logically, there is the case of Lancers vs Lancers, and I would submit that we don't want to make cavalry battles less volatile than they are now. Arguably they are already significantly less volatile than they were historically.

Everything that changes has ramifications which usually go beyond what was envisaged when the change was proposed.

So the only option left is shock units of the same type fighting each other? Is that a possibility?

It is a possibility, but I don't want to introduce it for lancers vs lancers or even for warbands vs legionaries, for the reasons stated above.

As I say, the real (and very simple) solution is not to set up tournament scenarios with massed warbands vs massed warbands!