cEDH Tournaments and First Player Advantage: Data from Silicon Dynasty
Hello everyone! Spielrahoo (Shaun) here. I’ve posted in the cEDH Reddit several times regarding turn order win rates from Eminence’s publicly available data, most recently Silicon Dynasty. This article serves as an update to these posts, which are linked here:
- After Punt City
- After Playing with Power Mox Masters October 2022
- After Playing with Power Mox Masters December 2022
To quickly summarize, in all of these posts, I analyzed win rate by seat position in the Swiss rounds of each of these tournaments, ignoring byes and matches that ended in draws. All of these data are publicly available on the Eminence Events and Mox Masters websites.
From Silicon Dynasty, win rates by seat position were as follows across 199 pods of Swiss:
- Seat 1 won 54 pods for a win rate of 27.1%. In previous events, it ranged from 30.6% to 39.2%.
- Seat 2 won 60 pods for a win rate of 30.2%. In previous events, it ranged from 18.9% to 21.6%.
- Seat 3 won 42 pods for a win rate of 21.1%. In previous events, it ranged from 21.6% to 30.6%.
- Seat 4 won 43 pods for a win rate of 21.6%. In previous events, it ranged from 17.1% to 18.2%.
Cumulatively, here are the win rates across 648 pods of tournament EDH with 95% confidence intervals calculated using the variance of binomial distribution:
- Seat 1: 31.5% with a 95% confidence interval of 27.8% to 35.1%.
- Seat 2: 24.2% with a 95% confidence interval of 20.9% to 27.6%.
- Seat 3: 24.1% with a 95% confidence interval of 20.7% to 27.4%.
- Seat 4: 20.2% with a 95% confidence interval of 17.1% to 23.4%.
What does this all mean?
Statistically speaking, because the expected win rate of 25% falls outside the lower end of the 95% confidence interval for seat 1, this seat’s win rate advantage is real.
Statistically speaking, because the expected win rate of 25% falls outside the upper end of the 95% confidence interval for seat 4, this seat’s win rate disadvantage is real.
Because the expected win rate of 25% falls within the 95% confidence interval for both seats 2 and 3, we cannot be sure if there is a win rate advantage or disadvantage for either seat. In addition, because of their large overlap in confidence intervals, we cannot be sure if either seat has a win rate advantage over the other.
In a 4 player game of commander, each seat would have an expected win rate of 25% against players of relatively equal skill if seat position/turn order didn’t matter. However, as these data very strongly suggest, turn order does have an influence. These win rate discrepancies may not matter much in pickup games, but tournament games with prizes on the line are another matter. Seating and thus turn order in the Swiss rounds of tournaments is randomized; players who are seated in early positions more frequently have a statistical advantage over others.
The million-dollar question remains: Is this a problem worth solving? That is a loaded question that has been discussed extensively in the past. The biggest concern is that any proposed solution would be worse than just living with this issue.
A common talking point is that player skill should overcome seat position. Put another way, good players should be able to find ways to win despite their seat position. I present the following data, which are new to this series. These are the Swiss win-loss-draw records of the top 16 competitors of Punt City, MM October ‘22, MM December ‘22, and Silicon Dynasty.
While the sample sizes are likely too small to be statistically significant, even with these win rates well above 25%, these data suggest that the competitors doing well in tournaments still win more when in seat 1 and less in seat 4, suggesting that even competitors doing well are not immune to the effects of seating position.
If this problem is worth tackling, barring any format level rules changes the most practical solution I can see is placing a higher emphasis on a “fairer” distribution of seating during Swiss rounds of tournaments rather than truly random seating. This would require tournament software to take prior seating positions into account when assigning future seating, but it could be done. I don’t know what unintended consequences this would cause.
That’s all I have for this time. I’ll be back with another update after we have more tournament results! At the pace that we are having new events early this year, it might be worth it to wait until we have a few more tournaments under our belts rather than giving an update after each Eminence or PWP event.
Shaun aka spielrahoo on the Playing with Power and Spike Feeders discords