Topic: Balancing Tyrell
Posted: 2014-Dec-09 16:10
I think the discussion of balancing Tyrell went 'off-topic' with the Greyjoy bashing in a theoretical 2nd ed card scenario (theoretical and not hypothetical because we'll see 2nd edition cards at some point).
Let me just sum up a few opinions on Tyrell here, relevant to our current situation and dealing solely with the 6 player set-up (because 5-player is a rather rare occurrence as far as I know?):
1. Tyrell is more dependent on entirely contingent events (i.e. the human factor in people making sub-optimal moves, the situation being different already on turn 2-3, what - primarily - Baratheon and Martell does).
2. Tyrell is the weakest faction in a 6-player, especially with 2nd edition rules implemented (again, only those currently available on the web site).
3. Tyrell is, statistically, the faction doing 'worst'. (i.e., objectively, the hardest to play).
4. Tyrell does way better with preceding mustering
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So, let us stop for a moment and review these three opinions. First of all, we can - I believe - easily synthesize 2. and 3. into one hypothesis (The win rate of Tyrell, compared to the 5 other factions, is lower in 6-player games - and much lower in games with 2nd ed rules implemented) and then empirically test it. We can, also, test 4., in the process and compare 2+3 and 4 for that matter.
I of course don't have access to the raw data on the site, but I have access to a number of options in regards to dependent/independent variables (the independent variable always being the win rate of Tyrell, naturally) and a N (total sample size) in the thousands.
First of all, at face value, Tyrell and Lannister are tied for the lowest mean win rate (6 player games) on Thronemaster, at 11,6%. With 314 and 315 wins, there is objectively 0% statistical difference between Lannister and Tyrell in terms of overall wins. HOWEVER, Martell is responsible for 11,7% of the wins, i.e. also objectively 0% statistical difference between the win rate of Tyrell, Martell and Lannister! Again, this was for ALL 6-playe wins on the server (N=2707). What does this tell us? Well. We can consistently (again, no access to raw data - but a high N in our mean rate means we have a rather solid foundation to claim our parameters are a good representation of the population) say that if a player controls Tyrell, Martell or Lannister - they are playing one of the factions with the lowest mean win rate.
Applying 2nd ed settings (both with and without garrisons, since choosing only one lowers N horribly), we end up at 85 and 87 wins respectively (with N=737). We're still at a very meager win rate and we still see no difference between Martell and Tyrell that we can call statistically significant (we have Lannister at 84 wins - also not statistical difference here).
We could also ask if Martell, Lannister and Tyrell are even significantly under the average win rate (at 11,6% mean win rate, when the average ought to be 1/6 = 16,66%) which isn't completely off. Using a simple binomial calculation test, we see that the probability of a faction achieving 85 wins (or less) out of 737 games is just MARGINALLY above the critical value (0.05, or 5% in a one-tailed test). Meaning that even at 11,6% - it isn't even, per standard quantitative method and good practice, a freak number for Tyrell to be at a 11,6% win rate.
So, while we can conclude that Tyrell, Martell and Lannister are all equally CONSISTENTLY placing below the average win rate, we do not a) have information on placings outside the win (which is, to be honest, rather problematic in a raking system where it matters as much whether you consistently place high - rather than your win rate alone), b) have a solid statistical foundation on which to claim that Tyrell, Martell and Lannister are underperforming significantly and - most importantly - c) there is NO evidence for Tyrell being worse off than Martell or Lannister. ON AVERAGE. Again, we're only speaking means here.
Furthermore, we should remember that this is correlation - and to a degree predictive - not causality. We can not say why this is so - it might be due to player skill, people choosing other factions, what games end up finishing etc. - rather than Tyrell being structurally less well off. We do not have the numbers to test this - although - at face value, it seems obvious that most game settings don't really change a thing for Martell/Tyrell, while a couple of game settings really change the win rate of Lannister. At the same time,although it seems unlikely that any consistent 'faction bias' is in place - we just can't know for sure.
The Stark (and dependent on settings, Greyjoy) win rate is statistically SIGNIFICANTLY above average though. Like. Freakishly so. So;
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Don't buff Tyrell, nerf Stark - would be my statistically founded advise.
