Brainstorm
Force of Will
Lion's Eye Diamond
Counterbalance
Sensei's Divining Top
Tarmogoyf
Phyrexian Dreadnaught
Goblin Lackey
Standstill
Natural Order
Seriously, this is pretty dumb.
On one hand, replacing W & L numbers by the best mle estimator of the winrate %age (pmle=W/(W+L)) + a second value to represent uncertainty (like width of the 95% confidence interval for pmle, or the quasi-std sqrt(pmle*(1-pmle)/n) (*)) doesn't reduce the available information, as from those two values, you can reconstruct both W & L.
On the other hand, you don't need to assume anything to establish those. There is no hypothesis to make or test against. It's simple mle.
(*) I'm saying quasi-std as this is improper ; the only actual std is sqrt(p*(1-p)/n) where p is the actual value of the parameter. But :
- this doesn't change the fact that this allows the reconstruction of original W & L numbers if one so desires,
- this still does quite adequately match expectations / will properly represent what the standard deviation of the process is, a) given that real matchups never go outside 0.2-0.8 for p, and b) as long as you don't go out of your way to use it wrong, ie if you have like only 5 matches.
Representing data is as far as a close field as it gets. There are many valid options, that might be considered.
It also depends of what you want to get out of the data. Win rate for a specific MU is one thing, but a logical use could also be to evaluate which deck to take between the few available to someone. In which case you don't necessarily care about whether a given MU has x% win rate or a lot of data points, you could just sum up all win and losses irrespective of against which deck those were collected.
That calculation is less logical than it seems. It assumes you will face the same meta represented in the data (the data are implicitly weighted in that sum). That makes strong model assumptions even though it seems like such a simple calculation of adding up Ws. Given the MU win rates you're free to adjust to any meta you expect for an event.
For example: Someone will 5-0 and 4-1 a couple MTGO Leagues, think they've broken the meta, perform poorly in a Legacy Challenge, and wonder why. Why didn't it win as much as expected? They're facing a different metagame. Leagues are full of combo and random brews. Big events are full of tier 1 fair blue. Their deck may do better against the League meta than the Challenge meta.
Edit: In simpler language, it's the whole "apples and oranges" thing. Summing wins mixes apples and oranges. If win rates vary by matchup (like most do), it depends on the meta. 20-2 vs Belcher and 0-5 vs Delver is a strong record of 20-7, but is bad for an event full of Delver. It's far more logical to start with the matchup win rates and weight them by the expected metagame (much more Delver than Belcher).
Last edited by FTW; 11-26-2021 at 06:47 PM.
This. Leagues are a mixed bag, if you try enough of them with any viable deck, you will get a 5-0, quite a few 4-1 and a crap-load of 3-2s, just based on the games you go against random junk someone is trying the viability of. The key here is to try enough of them, which means you may lose money to get that elusive 5-0, but you will get one of them.
Looking at any recent legacy data all I can say is that I remember the days when cards were banned in modern because they affected 'diversity', ie, Splinter Twin and the construction of URx decks. These days, as long as it sells, who cares.
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