Camel archers and Numidian cavalry

[elitetroops]

I agree that knowing the distribution is important. As I said earlier, the median is not very useful, but knowing how many units you need for 90% success rate is. Problem is that those tests are specific for only one scenario. I sometimes do them, for example when warrior rushing on immortal (did I mention you can start wars earlier on marathon? ) it is very much required to figure out how many I need to kill one or two archers. Since it can't be tested for every situation, going with the mean plus a few extra is usually a good estimate. How many extra is situational, it's something you develop a sense for over time (and something you sometimes miscalculate and regret).

In this case when testing the efficiency of a promotion I think the mean did tell enough. As mean increased by 25% when adding flanking into the mix, I am also certain that fewer units are needed for 90% success rate when going full combat.

Glad you are now convinced about flanking. Maybe you already did it this way, but it's quick to set up tests with hundreds of units by editing in one with correct promotions, then open worldbuilder save in text editor and copy paste. You should also be able to copy entire cities complete with defenders this way.

Interesting that so few of the retreating HAs dealt damage. I used stack attack and didn't track retreating HAs specifically. Only noted that after the initial attack by 100 flanking HAs, on average slightly over 10% of defenders were left at full health, meaning almost 90% of the attackers managed to deal damage. This number varied quite a bit in different tests. Maybe non-retreating are more likely to deal damage as they stay and fight to the end?

 

[dankok8]

I agree that knowing the distribution is important. As I said earlier, the median is not very useful, but knowing how many units you need for 90% success rate is. Problem is that those tests are specific for only one scenario. I sometimes do them, for example when warrior rushing on immortal (did I mention you can start wars earlier on marathon? ) it is very much required to figure out how many I need to kill one or two archers. Since it can't be tested for every situation, going with the mean plus a few extra is usually a good estimate. How many extra is situational, it's something you develop a sense for over time (and something you sometimes miscalculate and regret).

In this case when testing the efficiency of a promotion I think the mean did tell enough. As mean increased by 25% when adding flanking into the mix, I am also certain that fewer units are needed for 90% success rate when going full combat.

Glad you are now convinced about flanking. Maybe you already did it this way, but it's quick to set up tests with hundreds of units by editing in one with correct promotions, then open worldbuilder save in text editor and copy paste. You should also be able to copy entire cities complete with defenders this way.

Interesting that so few of the retreating HAs dealt damage. I used stack attack and didn't track retreating HAs specifically. Only noted that after the initial attack by 100 flanking HAs, on average slightly over 10% of defenders were left at full health, meaning almost 90% of the attackers managed to deal damage. This number varied quite a bit in different tests. Maybe non-retreating are more likely to deal damage as they stay and fight to the end?

The median is useful because it tells you where the middle of the distribution is so you can gauge how skewed the data is along with the mean.

The tests are scenario specific indeed. The combat units being stronger are significantly more likely to damage and heavily damage the Spear compared to flankers or unpromoted HA's. The combat engine is such that when a unit has a higher A/D ratio it is more likely to do damage and will do more damage on average.

I'm pretty sure dying and retreating HA's should be equally likely to deal no damage because the roll for retreat is done after the attacking unit is already at 0 HP and if the retreat is successful then the HP lost in the last combat round is given back to the retreating unit. And the retreat roll is done every time an attacker is at 0 HP as long as the unit has a withdrawal chance.

 

[elitetroops]

Otherwise I'm very familiar with how combat rolls are calculated, just never looked into retreating mechanics at all.

Something is off here. You attacked at 3.81% odds and reported over 50% ratio of withdrawing HAs not dealing any damage to the defender. I'm using higher tile defense and attacking at 1.03% odds, yet mostly only 10-20% of flanking HAs fail to deal damage. Tested also with unpromoted, same results. It shouldn't be possible that you are less likely to deal damage when you are attacking with better odds. From your results I can also tell that the same 55.6% ratio cannot have been true for all first attackers.

 

[dankok8]

Otherwise I'm very familiar with how combat rolls are calculated, just never looked into retreating mechanics at all.

Something is off here. You attacked at 3.81% odds and reported over 50% ratio of withdrawing HAs not dealing any damage to the defender. I'm using higher tile defense and attacking at 1.03% odds, yet mostly only 10-20% of flanking HAs fail to deal damage. Tested also with unpromoted, same results. It shouldn't be possible that you are less likely to deal damage when you are attacking with better odds. From your results I can also tell that the same 55.6% ratio cannot have been true for all first attackers.

I just checked the odds of the Spear going undamaged and it's 15% in any given battle round. Take away the possibility of an outright win and it's maybe 16-17% for all the death or withdrawal outcomes. Hmm... that does seem like a crazy streak. With just 18 withdrawals on the first attack we would expect maybe 3 not do any damage but I got 10! Hmm... small sample size my only explanation. It didn't occur to me how insane it was in the moment!