Post by hodsopa on Feb 25, 2017 12:42:36 GMT
For 16 recent games, I've noted down each side's movement PIPs, each side's kill chances (eg Sp vs Sp, if one rolls a 1 the other kills on a 6, so each has 1/36 of a kill chance) and the kills actually obtained. Since I'm not so cruel as to make my opponent wait while I do this, they are all solo games, mostly with armies for the recent Mercian DBA and the upcoming Northern Cup.
I decided to count all kills equally (not double for a general, not 0 for a Hd).
The number of kills obtained by each side can be expressed as the sum of (a) the number of kill chances obtained and (b) the difference between the number of kills they 'ought' to have obtained and the number they actually obtained. For example, last night I fought the Later Sargonid Assyrians against the Medes. The Medes had 30/36 kill chances (which I call "0.8 kill chances" and converted none of them ("combat luck of -0.8"). The Assyrians, rather lucky, had 45/36 kill chances ("1.3 kill chances") and obtained 3 kills, including the Median general (3-1.3 = "combat luck of 1.7".)
In this particular case the difference in kills obtained was 3. This was accounted for by a difference of 0.5 in kill chances (1.3 minus 0.8) and a difference of 2.5 in combat luck (1.7 minus (minus 0.8)).
My hypothesis is that the number of "kill chances" that an army obtains is a reflection of the skill of the player in choosing and using it. If so, the comparison between the role of kill chances and of combat luck can be used as an index of the relative role of skill and luck in the game.
Skill is relevant in solo games because some armies are better than others (=more skilful choices, in tournaments where you choose what you bring) and because I think I play some armies ("medium" in weight) more skilfully than others ("heavy" and/or shooters). But the result will still probably be an underestimate of the relative role of skill that would appear in competitive games (there are some players against whom I nearly always lose; I think they are more skilful than me across a range of army types).
However, two other factors might influence the number of kill chances obtained - invader vs defender, and PIP dice obtained ("movement luck").
Among these 16 battles, the invader won 10 (63%). However, in a larger dataset that I have kept (85 battles), the invader won only 38 (45%). At least at the moment, this makes me feel comfortable in discarding this as a factor.
Among the 16 battles, the winner's PIP dice averaged 0.1 more than the loser's, a rather small difference. A larger dataset of 29 battles gives the same result. In the 16 battles, the correlation between the difference in PIP dice in any particular battle and the difference in kill chances in that battle was only 0.05, implying that "movement luck" explained only 5% of the difference in kill chances. Again, this seems small enough to set aside in this small sample.
So let's cut to the chase. Across the 16 battles, the winner killed on average 3.1 more elements than the loser. Differences in "kill chances" (calculated as above) accounted on average for 1.45 elements of this differential; differences in "combat luck" accounted on average for 1.65 elements.
Conclusion: based on this small sample, it seems that luck and skill play roughly equal roles in DBA 3.0.
But: it would be interesting to have a larger sample and to use competitive games rather than sole games.
(Maybe if I make a table with all the kill chances, rather than working them out for each combat, it will slow things down less.)
Comments welcome!
Paul H
PS later today I plan to mail some more slightly obsessive statistics, about differences between troop types
I decided to count all kills equally (not double for a general, not 0 for a Hd).
The number of kills obtained by each side can be expressed as the sum of (a) the number of kill chances obtained and (b) the difference between the number of kills they 'ought' to have obtained and the number they actually obtained. For example, last night I fought the Later Sargonid Assyrians against the Medes. The Medes had 30/36 kill chances (which I call "0.8 kill chances" and converted none of them ("combat luck of -0.8"). The Assyrians, rather lucky, had 45/36 kill chances ("1.3 kill chances") and obtained 3 kills, including the Median general (3-1.3 = "combat luck of 1.7".)
In this particular case the difference in kills obtained was 3. This was accounted for by a difference of 0.5 in kill chances (1.3 minus 0.8) and a difference of 2.5 in combat luck (1.7 minus (minus 0.8)).
My hypothesis is that the number of "kill chances" that an army obtains is a reflection of the skill of the player in choosing and using it. If so, the comparison between the role of kill chances and of combat luck can be used as an index of the relative role of skill and luck in the game.
Skill is relevant in solo games because some armies are better than others (=more skilful choices, in tournaments where you choose what you bring) and because I think I play some armies ("medium" in weight) more skilfully than others ("heavy" and/or shooters). But the result will still probably be an underestimate of the relative role of skill that would appear in competitive games (there are some players against whom I nearly always lose; I think they are more skilful than me across a range of army types).
However, two other factors might influence the number of kill chances obtained - invader vs defender, and PIP dice obtained ("movement luck").
Among these 16 battles, the invader won 10 (63%). However, in a larger dataset that I have kept (85 battles), the invader won only 38 (45%). At least at the moment, this makes me feel comfortable in discarding this as a factor.
Among the 16 battles, the winner's PIP dice averaged 0.1 more than the loser's, a rather small difference. A larger dataset of 29 battles gives the same result. In the 16 battles, the correlation between the difference in PIP dice in any particular battle and the difference in kill chances in that battle was only 0.05, implying that "movement luck" explained only 5% of the difference in kill chances. Again, this seems small enough to set aside in this small sample.
So let's cut to the chase. Across the 16 battles, the winner killed on average 3.1 more elements than the loser. Differences in "kill chances" (calculated as above) accounted on average for 1.45 elements of this differential; differences in "combat luck" accounted on average for 1.65 elements.
Conclusion: based on this small sample, it seems that luck and skill play roughly equal roles in DBA 3.0.
But: it would be interesting to have a larger sample and to use competitive games rather than sole games.
(Maybe if I make a table with all the kill chances, rather than working them out for each combat, it will slow things down less.)
Comments welcome!
Paul H
PS later today I plan to mail some more slightly obsessive statistics, about differences between troop types
