Morien
05-19-2009, 10:10 PM
I have been spouting some probabilities of the Pendragon Combat System in previous threads. In one of them, Two Equal Knights, I was starting to muse how long is the average Pendragon combat? Best way to see would be to simulate two knights and their rolls and see what happens. So I got stupid and wrote the program (in python). I was going to just edit the previous thread, but then I figured that this might something deserving its own thread, while the old one is pretty limited in scope.
At the moment, the program does the following:
1) Takes into account +5/-5 for rearming and/or being on the ground
2) Takes into account (non-/modified) skill being 20 or over.
3) Checks if the roll is Fumble (no shield, +5/-5 next round), Miss (no shield), Success or Critical.
4) Compares to see if the roll is a draw, a partial success or a hit.
5) Rolls damage, deducts hit points (if penetrated armor), checks for Major Would (checking HP roll and valorous, a fail in either leads to a loss of match) and Knockdown (including +5/-5 for next round, if DEX fails)
6) Checks if HP <= unconsciousness, at which point it declares a winner
It doesn't allow for different weapons than a sword, yet, but allows to set different skills, damages, hit points, armor... to the knights.
Here are some results, from 1000 combat simulations (each, takes like 3 seconds to run):
Skills: [ 29. 29.]
Shortest fight: 1.0 Longest fight: 16.0
Average duration: 3.069 Median duration: 2.0
Shorter than median: 0.274 Exactly median: 0.228 Longer than median: 0.498
Average HP of A in win: 25.5795918367 Median HP of A in win: 28.0
Average HP of B in win: 25.7274509804 Median HP of B in win: 28.0
Skills: [ 24. 24.]
Shortest fight: 1.0 Longest fight: 19.0
Average duration: 3.895 Median duration: 3.0
Shorter than median: 0.376 Exactly median: 0.166 Longer than median: 0.458
Average HP of A in win: 25.0117878193 Median HP of A in win: 28.0
Average HP of B in win: 25.0488798371 Median HP of B in win: 28.0
Skills: [ 19. 19.]
Shortest fight: 1.0 Longest fight: 21.0
Average duration: 5.74 Median duration: 5.0
Shorter than median: 0.445 Exactly median: 0.115 Longer than median: 0.44
Average HP of A in win: 24.4724857685 Median HP of A in win: 28.0
Average HP of B in win: 24.5665961945 Median HP of B in win: 28.0
Skills: [ 15. 15.]
Shortest fight: 1.0 Longest fight: 15.0
Average duration: 4.458 Median duration: 4.0
Shorter than median: 0.385 Exactly median: 0.181 Longer than median: 0.434
Average HP of A in win: 23.7443762781 Median HP of A in win: 28.0
Average HP of B in win: 23.8473581213 Median HP of B in win: 28.0
The shortest and longest fight tell little, since we already knew that it is possible to crit a guy on a draw and end the fight there, and there are always outliers where they keep hacking at one another without effect (especially since damage is 5d6 and armor 12+6). Median duration is more interesting, since it shows how long the battles tend to last (if you have 1001 battles and arrange the duration from shortest to longest, the median duration is the 501st duration on that sorted list). As you can see, the mean duration (the regular average) is pretty similar, albeit slightly higher due to those outliers.
I found it very surprising how short Pendragon combat really is! I mean, I knew to expect the 20+ crowd being tink-BOOM, but that skill 15 gave an average duration of just 4.5 rounds... That was a surprise. Also, it was a small surprise that many (50% or more) of all the fights, regardless of skill, end in that one critical, leaving the winner unscathed (median HP in win). Well, this is probably due to the fact that most of the hits do no damage... But when running the test with 10+6 armor, skill 19, the results were almost identical. Still most of the fights leave the victor unscathed. I suspect that what we are seeing here is the +5/-5 on the ground effect. The guy who connects first knocks the other over and then keeps hammering him, knocking the opponent over again and again, until there is a critical or he wears the opponent down. In fact, let me test that hypothesis with DEX 19... Yep, that was it. Now the victor gets some (minor) scratches, too, and the fights last a round or two longer, due to that +5/-5 being so rare.
Anyway, I hope you found this interesting. If there are match-ups that you'd be curious to see, let me know and I can run it.
At the moment, the program does the following:
1) Takes into account +5/-5 for rearming and/or being on the ground
2) Takes into account (non-/modified) skill being 20 or over.
3) Checks if the roll is Fumble (no shield, +5/-5 next round), Miss (no shield), Success or Critical.
4) Compares to see if the roll is a draw, a partial success or a hit.
5) Rolls damage, deducts hit points (if penetrated armor), checks for Major Would (checking HP roll and valorous, a fail in either leads to a loss of match) and Knockdown (including +5/-5 for next round, if DEX fails)
6) Checks if HP <= unconsciousness, at which point it declares a winner
It doesn't allow for different weapons than a sword, yet, but allows to set different skills, damages, hit points, armor... to the knights.
Here are some results, from 1000 combat simulations (each, takes like 3 seconds to run):
Skills: [ 29. 29.]
Shortest fight: 1.0 Longest fight: 16.0
Average duration: 3.069 Median duration: 2.0
Shorter than median: 0.274 Exactly median: 0.228 Longer than median: 0.498
Average HP of A in win: 25.5795918367 Median HP of A in win: 28.0
Average HP of B in win: 25.7274509804 Median HP of B in win: 28.0
Skills: [ 24. 24.]
Shortest fight: 1.0 Longest fight: 19.0
Average duration: 3.895 Median duration: 3.0
Shorter than median: 0.376 Exactly median: 0.166 Longer than median: 0.458
Average HP of A in win: 25.0117878193 Median HP of A in win: 28.0
Average HP of B in win: 25.0488798371 Median HP of B in win: 28.0
Skills: [ 19. 19.]
Shortest fight: 1.0 Longest fight: 21.0
Average duration: 5.74 Median duration: 5.0
Shorter than median: 0.445 Exactly median: 0.115 Longer than median: 0.44
Average HP of A in win: 24.4724857685 Median HP of A in win: 28.0
Average HP of B in win: 24.5665961945 Median HP of B in win: 28.0
Skills: [ 15. 15.]
Shortest fight: 1.0 Longest fight: 15.0
Average duration: 4.458 Median duration: 4.0
Shorter than median: 0.385 Exactly median: 0.181 Longer than median: 0.434
Average HP of A in win: 23.7443762781 Median HP of A in win: 28.0
Average HP of B in win: 23.8473581213 Median HP of B in win: 28.0
The shortest and longest fight tell little, since we already knew that it is possible to crit a guy on a draw and end the fight there, and there are always outliers where they keep hacking at one another without effect (especially since damage is 5d6 and armor 12+6). Median duration is more interesting, since it shows how long the battles tend to last (if you have 1001 battles and arrange the duration from shortest to longest, the median duration is the 501st duration on that sorted list). As you can see, the mean duration (the regular average) is pretty similar, albeit slightly higher due to those outliers.
I found it very surprising how short Pendragon combat really is! I mean, I knew to expect the 20+ crowd being tink-BOOM, but that skill 15 gave an average duration of just 4.5 rounds... That was a surprise. Also, it was a small surprise that many (50% or more) of all the fights, regardless of skill, end in that one critical, leaving the winner unscathed (median HP in win). Well, this is probably due to the fact that most of the hits do no damage... But when running the test with 10+6 armor, skill 19, the results were almost identical. Still most of the fights leave the victor unscathed. I suspect that what we are seeing here is the +5/-5 on the ground effect. The guy who connects first knocks the other over and then keeps hammering him, knocking the opponent over again and again, until there is a critical or he wears the opponent down. In fact, let me test that hypothesis with DEX 19... Yep, that was it. Now the victor gets some (minor) scratches, too, and the fights last a round or two longer, due to that +5/-5 being so rare.
Anyway, I hope you found this interesting. If there are match-ups that you'd be curious to see, let me know and I can run it.