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Subject: New analyzed data from Keldon's server on rftgstats.com, includes Brink of War! rss

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rain
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frunkee wrote:
Biggest prestige lead for a winner: 21 (http://www.keldon.net/rftg/showgame.cgi?gid=95826)
It looks like a joke game.


For the record, boom and chuckle are the same bloke (a member of our local crew).

Also, just in case it matters for stats, I have a few games recorded under the monicker XrainX as well as my regular handle rain.
 
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Alex Brown
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Tom Lehmann wrote:

If I'm understanding you accurately (and please correct me if I'm wrong), you're arguing that evaluation is easier in BoW, which I tend to interpret in terms of combos, not Prestige: "Oh, here, I've drawn a combo -- then I'll play those cards (reduced evaluation) and, hey, no one else hit their combos, so I win. Yawn."


Yes and no. I think effective decisions more often consider the evaluative angles than than the interactive angles than earlier formats. Where I could have been clearer would have been to present each decision as being on a spectrum between evaluative and interactive concerns. In BoW, I think winning play ends up closer to the evaluative end than before. The better combos are the reason.

I don't think decisions are easier. I still think deep knowledge of the deck is paramount. It's just that I think opponent play doesn't matter as much as before.


Tom Lehmann wrote:
I don't see what this has to do with Prestige per se (other than the fact that there are some Prestige combos). Could you explain why you believe this is a Prestige -- as opposed to a general combo -- effect?


To be honest I think you could be right. I just assumed Prestige was inseparable because nearly all of the new prominent cards tend to give some amount of Prestige. I overlooked that pretty much six-cost developments in general got a lot better (My favourite cards are probably still the Imperium six-cost developments).

To that end I have likely done you a disservice saying Prestige was the problem rather than the prominence of expensive cards. I'm still not sure either way, but I think you are right that I haven't really shown Prestige as the real difference.



Tom Lehmann wrote:
I do agree that the combos stand out more in BoW, so the evaluation part of the game for me is no longer "how do I combine these cards to make something t vbhat can work", but "how can I advance in several directions at once", so I can jump on a combo if one shows.

So, for me -- and here I'm just talking about my own personal play experience, not my thinking as a designer -- the evaluation portion of the game is still holding up; it's just changed to really emphasize flexibility over finding combos.


I can agree with this.

Tom Lehmann wrote:
With regard to interaction, vis a vis just the AIs, the format I find most enjoyable is 3P. With two opponents, often going in very different directions, and the higher interaction and lower control, I still find both the interaction and evaluation aspects of the game compelling.

(I personally find 2PA BoW TOs Goals too easy generally -- it's trivial for me, with all my play experience, to win 2/3 of the time -- and the time and effort involved in bringing that win % up to ~75% by much slower and more careful play just isn't worth it. I'd rather play 2 AIs 3P.)


I think this is probably something I can get behind strongly. With Prestige, goals and 2PA, there seems to be a 'perfect storm' leading to an emphasis on extreme play. While combos are the eye of the tornado, Prestige is still relevant because it adds another layer of advantage that can be difficult for an opponent to recoup. As the overall strategy lends more to 'first to' combo, goals tends to enhance the aggressor. Finally, the ability to Dev/Dev, Settle/Settle, Build/Trade, Trade/Produce and Consume/Trade are all big departures from the slower, more interactive pace of 3er.

I like 3er the most too, and still enjoy 4er. I like takeovers all the time, and enjoy Prestige in multiplayer games. Goals I'm not so sure on, but my default is to play them.

Overall I think you could be right that it's more about combos than Prestige, though I don't particularly like the Prestige powers either. I could have been clearer, but my argument is mainly that the BoW format creates such powerful card combinations that the subtler mode of advantage through canny role selection is dwarfed. In some respects, it's just moved from being a 'Spike' game to being more of a 'Johnny' game--to bastardize MaRo's Magic player personalities. I can enjoy both, though I'm a Spike at heart.

I agree with your example. I tend to beat the AI about 2/3 but have never been able to really move that beyond 3/4 in stretches. About 1/5 of the time I feel like I had no chance because my hand just couldn't compete with the early combo from the AI.

I couldn't have played 760 games without enjoying them, but the evaluative angle can only go so far so I find myself craving interactivity again to give the game eternal life
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Mark Delano
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rrenaud wrote:
Are you counting games like

http://www.keldon.net/rftg/showgame.cgi?gid=118290 ?

in the data file, prestige is 0 and the cards are empty, but it still has the scores.

Edit: also, you probably want to correct for number of players.

52% in all 2p games is unimpressive, 52% in 4 player games is much better.


I'm not counting games that have empty cards. That's 52% across all games. Here it is broken out by number of players:

EDIT: I thought I wasn't counting games that had empty cards. I found a hole, so I'll have revised numbers soon.
 
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Mark Delano
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The numbers broken out by number of players:

Two Player Advanced -
Games: 33393
Prestige Lead Winners: 21872 (65.5%)
Prestige Tie Winners: 3077 (9.2%)
Ave. Winner Prestige lead: 2.10

Two Player -
Games: 2576
Prestige Lead Winners: 1747 (67.8%)
Prestige Tie Winners: 254 (9.9%)
Ave. Winner Prestige Lead: 2.39

Three Player -
Games: 6060
Prestige Lead Winners: 3537 (58.4%)
Prestige Tie Winners: 69 (1.1%)
Ave. Winner Prestige Lead: 2.66

Four Player -
Games: 1360
Prestige Lead Winners: 715 (52.6%)
Prestige Tie Winners: 1 (0.1%)
Ave. Winner Prestige Lead: 2.79

Five Player -
Games: 218
Prestige Lead Winners: 97 (44.5%)
Prestige Tie Winners: 0 (0%)
Ave. Winner Prestige Lead: 2.71

Six Player -
Games: 49
Prestige Lead Winners: 20 (40.8%)
Prestige Tie Winners: 0 (0%)
Ave. Winner Prestige Lead: 2.44

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John Riston
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mrkeldon wrote:
I have updated the showgame script on the webserver to handle game logs from version 0.8.0 and version 0.8.1 games. Hopefully most of the games that had no log will now be shown correctly -- let me know of any that don't.


Keldon,

This one doesn't have a log.

http://keldon.net/rftg/showgame.cgi?gid=119691
 
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Serge
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ristonj wrote:
Keldon,

This one doesn't have a log.

http://keldon.net/rftg/showgame.cgi?gid=119691

It shows a log for me, tho maybe it was fixed that quickly...
 
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Keldon Jones
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entranced wrote:
It shows a log for me, tho maybe it was fixed that quickly...


Yeah just fixed it (and any others that may suffer from that bug).
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Rob Neuhaus
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It could be interesting to see how the prestige numbers compare to say, player with most vp chips, or player with most points from goals, or player with the most military, or most points from 6 devs, etc.
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Serge
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I couldn't help myself checking the impact of first prestige lead, and ending prestige in the series of expert 2pa BoW pbfs. FWIW:

PBF Opponent First PL Ending PL Winner
17 onigame forum forum forum
18 rrenaud rrenaud forum forum
19 Stunna forum forum forum
20 onigame onigame forum onigame
21 Kesterer forum Kesterer forum
22 TomL TomL forum TomL
23 DogOfJustice forum forum forum
24 entranced tied forum forum
25 3amigos forum 3amigos forum

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Michael Link
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WOW...in 8 of 9 games the side which got outright or tied for 1st prestige leader won the game. Wow. Still a small sample size, but definitely high-level games.
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mar hawkman
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Yes, but in 5/9 of them the ending prestige leader was not the same as the starting prestige leader
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Edward
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How does it feel, rrenaud, to be the only person thus far to squander the first Prestige Lead?

(To be fair, if only you had drawn a better final 6-dev than a 3VP Galactic Exchange ...)
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Rob Neuhaus
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Heh .

I think if I hadn't "squandered" the prestige lead, I might have gotten doubled!
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Michael Link
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marhawkman wrote:
Yes, but in 5/9 of them the ending prestige leader was not the same as the starting prestige leader


That's the interesting part...it's the fact that the first, but not the final, prestige leader is so tightly correlated with winning. If most or all of those are with a single prestige, it says something about the opportunity gained by having the first one. This may be extra card/VPC throughout the game, or by tempo gained by being able to spend the Prestige Action, etc.

Again, its a small sample size, but an interesting signal nonetheless.
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Rus
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Entranced, I think you are trying to say that there may be correlation between prestige and winning at a high level. Even if there is, correlation does not imply causation. How do we know that prestige lead isn't a consequence of a player doing well rather than the cause? Your data (by itself) doesn't show causality, only correlation.

I just discovered another interesting fact (though I think somebody mentioned it before). Let's look at PGA's "skill normalized winning rate" (SNWR) metric introduced by rrenaud. (Numbers below are my estimates from reading the graphs and rrenaud, I assume the error bars are 1-sigma?)

The 71543 BoW games: 1.47 (+/- 0.01)

Top 10 ranked players on Keldon:

Kesterer: 1.33 (+/- 0.15)
rain: 1.2 (+/- 0.2)
GuySrivinasan: 1.5 (+/- 0.25)
Meddler: 1.3 (+/- 0.2)
ttor68: 1.5 (+/- 0.2)
takusto_II: 1.1 (+/- 0.2)
UlyZed: 1.15 (+/- 0.2)
rbelikov: 1.2 (+/- 0.2)
pirouli: not on the graph at all?
MsiwM: 1.9 (+/- 0.6)

Excluding pirouli and MsiwM because of high variance as compared to others, the mean for the top 8 players is 1.28 (+/- 0.15). We can therefore say with about 70% confidence that there is less correlation between PGA and winning for the top 8 players. So there may be something to Tom's claims that PGA isn't as overpowered at the top level. (I would caution though that the data still says nothing about causation, however: i.e. it doesn't by itself tell us whether PGA is the engine of a winner or merely a trophy.) 70% confidence isn't much to claim anything, but at least now we have a number and we're not just shooting words.

It's interesting also to see whether SNWR differs from player to player at the top. In other words, are some top players better at winning with PGA than others? Although some players seem to have a very high measured SNWR (MsiwM is 1.9) and some players seem to have a much lower SNWR (takusto_II has 1.1), if we take variance into account the data is actually consistent with everyone's SNWR being the same. There's just not enough samples to answer that question.

That said, my (rbelikov) lower than average PGA SNWR mean of 1.2 does seem consistent with my perception that PGA isn't as overpowered for me as others seem to claim. Perhaps different top players at the top prefer different strategies and some top players are better at winning with prestige whereas some top players are better at winning with other strategies. Once again, data does not support (nor reject) this claim, but perhaps this can explain why there is disagreement about the value of PGA amongst the top players.

(By the way, the SNWR of PGA is only 1.3 at the top... I wouldn't call that unbalanced even if this is a causal relationship!)
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Rob Neuhaus
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On the graph, it draws two standard devs.

If you view source, you can see the raw stats.

Here it is for kesterer, for example.


"Pan-Galactic Affluence": {
"prob_per_card_ssd": 0.012247448713915891,
"win_points": 1.95,
"prob_per_card": 0.1,
"norm_win_points_ssd": 0.09036756198234304,
"norm_win_points": 1.3326989540849719
},


Note that the maximum possible norm win points is going to be lower than the maximum possible unnormed win points for a high rated player, because the skill normalization is going to discount the wins. If Kesterer, based on his skill advantage over his opponents, was expected to get 150 win points in 100 2p games, the max possible win points is 200/150 ~= 1.33. This discounting might explain the push towards 1 vs the population. If you look at other high performing cards for the population vs individuals, you'll probably also observe that behavior.
 
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Rus
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rrenaud wrote:
On the graph, it draws two standard devs.


Ah, ok, that means that the 70% confidence that PGA is less correlated with wins at top level as compared to all games is actually more like 95% confidence (70% did seem kind of low given the number of samples). Of course, this assumes that both sample sets are free of bias, and you mention a possible bias here:

rrenaud wrote:
Note that the maximum possible norm win points is going to be lower than the maximum possible unnormed win points for a high rated player, because the skill normalization is going to discount the wins. This discounting might explain the lower absolute numbers.

But, if I understand correctly, your normalization is precisely what removes this kind of bias, rather than introduces it.

In any case, I hope others follow my example and attach numerical confidence levels to their claims from now on. (Otherwise the claims are not much above personal beliefs in my view.)
 
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Tom Lehmann
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theright555J wrote:
it's the fact that the first, but not the final, prestige leader is so tightly correlated with winning. If most or all of those are with a single prestige, it says something about the opportunity gained by having the first one. This may be extra card/VPC throughout the game, or by tempo gained by being able to spend the Prestige Action, etc.

In my pbf game, I took the PL on round 2; we tied for it on rounds 3 & 4 (both sides gaining prestige during these rounds); I retook the lead on round 5; and the forum took it on round 6 as the game ended.

Overall, I got 2 cards/4 VPs from PL, the forum got 2 VPs. The forum searched early (and immediately placed what they searched for, additional Military (Space Mercs)); I spent a prestige action on round 4 to get out two 6-devs when the forum was short on cards. So, our use of the Search/Prestige cards was worth useful early card selection (forum) and a 2 cost/-1 VP discount (me).

Yeah, the Prestige lead was useful, though it initially came at a cost (-1 VP for the 2 cost Ravaged Uplift world as opposed to, say, +1 VP for the 2 cost Pre-Sentient Race). However, this was compensated later on when I drew and played Uplift Code (as RUW has a chromosome while PSR does not). It also made two of my choice selections easily predictable (Produce), but the forum wasn't able to effectively leech off of them.

Obviously, Prestige affected play, but playing fast and aggressive, combined with drawing very good 6-devs had a lot more to do with my ~20 VP win, imo.
 
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rbelikov wrote:
Entranced, I think you are trying to say that there may be correlation between prestige and winning at a high level.

Nah, wasn't trying to say anything, just providing possibly relevant data from a sample of high level play. I hadn't even noticed the pattern that theright555J pointed out.
 
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Rob Neuhaus
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tl: dr; The skill normalization that I do is a kind of linearization that breaks down in the extremes.

Imagine that there is a guy so good, he wins 90% of his games.

But he likes PGA just like everyone else, it makes him 20% less likely to lose.

For ordinary players under this model, the skill normalized win rate of PGA is 1.2.

For our hypothetical great player, the max win rate possible (card wins every time he plays it), the win rate will be = 10 / 9 ~= 1.11. Since PGA helps him, it's win rate is > 1, it's probably somewhere around 1.02.

You'd see 1.02 < < 1.2, and conclude PGA helps him less than it helps others. You'd reach the same conclusion even if he won every game that he played with PGA and it had a win rate of 1.11.
 
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John Riston
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Found another one, Keldon.

http://keldon.net/rftg/showgame.cgi?gid=9093

Edit: Looks like it's fixed. Thanks!
 
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rrenaud wrote:
You'd see 1.02 < < 1.2, and conclude PGA helps him less than it helps others. You'd reach the same conclusion even if he won every game that he played with PGA and it had a win rate of 1.11.
Indeed I would. That's what in my mind "PGA helping him less than it helps others" means. I think that we are using different definitions here. I think in a statement like "PGA makes him 20% less likely to lose", you view 20% as a percentage (multiplicative), whereas I view it as percentage points (additive). By my definition, yes, for somebody who has a 90% chance of winning, a given card can only help 10% (percentage points) at most. Yes, I would say that in that case PGA helps him less than others for whom it increases their winning chances by 20% (percentage points). This is similar to saynig that a powerful sword helps a weak fighter a lot more than a strong fighter (who doesn't really need a sword and might as well just use his fists).

You see how this is a question of semantics and highlights the need for precise definitions. I suspect that most people here would agree with each other's views if they only precisely defined their claims!
 
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Eric Brosius
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You could use a logistic model or something similar to eliminate this issue. That would make going from a 98% win rate to a 99% win rate much more of a change than going from 57% to 58% (as it should be.)
 
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Sean McCarthy
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Eric Brosius wrote:
You could use a logistic model or something similar to eliminate this issue. That would make going from a 98% win rate to a 99% win rate much more of a change than going from 57% to 58% (as it should be.)


I read the entire thread to see if anyone had said this yet and it's the last post. As I remember from the flex stats, the "winning rate" boosts of cards are not produced through a sensible process. My suggestion last time was to calculate the effective Elo boost a card gives you in games when you play it, as this is at least theoretically comparable between players of different base skill levels. However IIRC I though even this had some problems. I think it's an interesting thing to ponder, and worthy of some logical analysis rather than just picking some formula.
 
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Mark Delano
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The prestige lead at the end seems tied to the leader ~65% most of the ways I could think to cut the data. The strongest change is definitely related to number of players, but that's to be expected. The next best I could find was difference in ELO ratings. For every 50 ELO difference between the winner and loser there was roughly a 1% increase in likelihood the winner had the prestige lead.

From this it looks like as players get better they learn to win with and without prestige in sync, but do get better at leveraging prestige to beat less experienced players.
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