EPTBalance Discussion Math(Best of N format analysis) - Page 2
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BobMcJohnson
France2916 Posts
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Skwid1g
United States953 Posts
On August 21 2012 23:31 imallinson wrote: It's fascinating just how small the OPness can be to create a large skew in tournament results. It highlights just how volatile balance is even in a two race setup. It's also funny that having more games in a series actually increases the effect of OPness when I think most people's assumption would be that it decreases the effect. No, it's pretty obvious that if you have a better chance to win it'll be amplified over a boX (where X is 3 or greater) rather than a single game. It's because of this that bo5/bo7s are preferred; the player who has a better shot at winning (usually through being a better player, sometimes through imbalance though) has a better shot of advancing as he's more likely to win games than his opponent. | ||
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VGhost
United States3613 Posts
Logically, this also ought to apply to player win probability - to pick a couple players at random, Grubby is far more likely to manage to win one game against MVP than a Bo3 series, and more likely to squeak out a Bo3 than string 3 wins together to take a Bo5, etc. But - this is completely tangential to your point - this suggests there's a point at which the entertainment value of a tournament is better served by shorter series (higher probability of upsets), while "accuracy" of results (the "best player" wins) demands longer series. | ||
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Orek
1665 Posts
On August 22 2012 22:52 Setev wrote: First of all, very very detailed work by OP, and marvelous job done. But I keep getting confused by all those colours and graphs. IMO drawing all those colourful tables will confuse people instead of clarifying. Why not use probability trees instead? IMO I think they are much better diagrams than tables. Just my 2 cents =D + Show Spoiler + Anyway, a simpler way to explain will be to use the Binomial Theorem. Let P(A) = Probability that OP race wins a best of n series, P(B) = Probability that UP race wins a best of n series p = probability that OP race will win the match q = 1 -p = probability UP race will win the match n = total number of games played rp = number of games won by OP race rq = number of games won by UP race P(A) = nCrp * (p)^rp * (q)^(n-rp) for rp = 1,2,3,..,n P(B) = nCrq * (p)^rq * (q)^(n-rq) for rq = 1,2,3,...,n We'll notice that P(A) - P(B) will get more apparent the higher the value of n. You are absolutely right. Thanks for your input. It's just that what is easy to do on my notebook is not necessarily what is easy to upload on TL.  I probably need to use scanner for my next math project to fully deliver the work.As you pointed out, yes, Binomial Theorem plays an important role here. From Best of 5 onward, it is so much easier to calculate win rate that way. General win rate of OP race is: ![[image loading]](http://i.imgur.com/NY3hn.png) Using this equation, it is possible to calculate something like Best of 15 win rate. Knowing this, I still thought using the excel table image was more intuitive at relatively small best of 5 or less. | ||
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nn42
Sweden18 Posts
However, I don't see how this could add to the balance discussion as it is currently. Blizzard provides the community with win-rates on ladder. TLDP brings win rates from tournaments. We get the actual win rates from there. Seeing as there's no mathematical way of separating player skill from racial imbalances these calculations quickly becomes irrelevant to the debate. ie MKP would probably beat any mid master player as off race in an open bracket MLG. (and I saw Welmu (normally P but off raced as T) 2-0 Grubby on ladder). BoN series stats would be interesting overall, because I believe the mental state of each player in the series accounts for most win rates, not the balance of the game itself. At least not in this state where the game is currently. I'd like to discover if there's varying results in terms of win orders in comparison to race in a series. e.g. Zerg has a higher probability to come back from a 2-1 deficit in a Bo5 against Terran. Combine that with various game stats like time data, etc, for each game and I'd find that much more valuable to the discussion, more in depth stats. I think most sports fans have accepted the idea of a extended BoN beyond Bo1 favors the "better" player/s. What you concluded here, atleast to me, is that a player with >50% win rate will increase his/hers win rate exponentially if the games played increases. As a math fan it might seem intriguing, as part of a balance discussion it just confirms what most people already figured out without the exact math to support it. You might have targeted the math people on TL though, so don't get me wrong here  You bring up a great point though in all of this and that's peoples perception of imbalance is mostly based on the wrong data. | ||
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Kasu
United Kingdom345 Posts
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S:klogW
Austria657 Posts
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Phanekim
United States777 Posts
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Gyro_SC2
Canada540 Posts
For exemple: next TSL no terran = underpowered this thread informe me that is the TSL qualification would have a BO5 instead of BO3, there will be less terran. | ||
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Cheerio
Ukraine3178 Posts
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gondolin
France332 Posts
As you said, a BOX is an amplificator of probability (that is if player A has p chance to win against player B, with p>0.5, then the player A has q chance to win against player B in a BOX with q>p). This is what we want in a tourmanent, that the best player win. Now of course the higher X is, the higher the amplification of probability will be, but more game will be played on average. One can aks if there are better system than a BOX in term of amplification by number of games? For instance, one could look on X More Wins (XMW), where a player win if he has X more wins than the other. If each player are of equal strength, it will take on average X^2 games to designate a winner. This blog post is pretty interesting in this regard http://www.madore.org/~david/weblog/2012-06.html#d.2012-06-02.2051 unfortunately it is in French, but you can look at the graph which give in order: BO1, BO3, BO5, 2MW, BO7, BO3 of BO3, BO9, 3MW In particular, one case see that 2MW is a bit better than a BO5 as amplificator of probability. Moreover, if the player are of equal strength, it will require 4 games in average against 33/8 for BO5 (and more generally it will always require less games on average). The drawback of course is that in a BO5 there is a maximum of 5 games while in a 2MW there is no such limit, but I find the idea interesting. | ||
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