I so far have a over 2000 game sample size from Limited, Standard and Modern. Before the London mulligan depending on matchups, formats and play skill going first ranged from less than 5% increat in win percentages to over 10%; since the onclusion of the London mulligan this number has shot up and nearly doubled. Now my sample sizes are small and diverse, I hope others can review a larger sample set from mine to refute this but it seems both anecdotally and statistically to have drastically increased win percentages for going first.
If you had 2000 games of one deck vs another deck piloted by the same people that would be an good start but 2000 games across three formats means essentially nothing. Then we have how did you measure this advantage. Do you have records of your previous matchups, formats and skill level?
A quick looks shows that old percentages were between 10% and 16% advantaged by being on the play. This was only for the first game as the second and third game have significantly more factors in play that skew numbers making it harder to say going first was the advantage. I'm sure someone is going to run some real numbers and find that some decks benefit more from this mulligan but that overall it doesn't change significantly for tournament magic because game 2 and 3 involve a lot of other factors that mess with the slight advantage of going first.
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A quick looks shows that old percentages were between 10% and 16% advantaged by being on the play. This was only for the first game as the second and third game have significantly more factors in play that skew numbers making it harder to say going first was the advantage. I'm sure someone is going to run some real numbers and find that some decks benefit more from this mulligan but that overall it doesn't change significantly for tournament magic because game 2 and 3 involve a lot of other factors that mess with the slight advantage of going first.