What is the Astros Tournament Ranking?
The Astros Tournament Ranking (ATR) is a tournament adjustment to a player's ELO. My hope is that it will provide tournament organizers with a foundation to allocate players in their events and to develop a robust ranking of tournament performances for the Stratego community.
How does it work?
The ATR is like the ELO method for 40-piece matches on Stratego.com. ATR is comprised of two components: Unadjusted ELO and Net ELO.
A player's Undjusted ELO is their highest ELO at the start of any tournament, starting with the Pro Perfect in April 2018. If a player has never played in an ATR-ranked tournament, then their ELO at the start of their first ATR-tournament is their initial rating.
During the tournament, the results of every match are recorded, but a player's rating does not change until the end of the tournament. Net ELO is the summation of how much ELO would change after each match based on the relative ATR ratings of each player. The change from each match is calculated with the same ELO formula that Stratego.com uses and is described in detail here:
Calculating Net ELO at the end of the tournament allows all games to be consider simultaneously. This is preferable because the order of opponents does not matter.
The only difference between ELO calculations in the ATR and Stratego.com is that the ATR uses a K value of 40 instead of 25. The ATR assigns a higher weight to tournament matches versus regular ranked games because players tend to take tournament games more seriously and there are significantly fewer cheating players.
A player's post-tournament ATR rating is equal to their Unadjusted ELO plus their time-weighted Net ELO from each tournament that they have played.
How do ratings change over time?
Unadjusted ELO uses the highest ELO that each player had at the start of a tournament. ATR ratings will trend upwards over time because a player’s Unadjusted ELO can only increase. The system is designed this way because players are assumed to play at their peak ability during tournaments. While this does not hold true for every player, I again assume that players are more focused and compete at a higher level during events.
Additionally, a player's Net ELO from each tournaments trend towards zero using the exponential decay formula with a half-life of 365 days, decay starts from the date that a tournament ends. This ensures that outlier performances do not significantly affect a player's rating.
Why is the ATR better than other rating systems?
Other rating systems only consider a player's tournament performance. Even the most frequent tournament participants rarely play more than 30 such games a year and they frequently face opponents with significantly fewer games. The goal of a good rating system is to estimate the relative abilities of competitors. Therefore, it is not possible to generate good estimates of ability with such limited data.
On the other hand, the ATR considers hundreds, or thousands, of games for each player because it uses 40-piece ELO ratings. The ATR assumes that such ELO ratings are approximate and adjusts them based on meaningful, controlled tournament games.
The ATR also has the advantage of being intuitive because it uses a similar methodology to Stratego.com.
Player A has never played in an ATR event and has an ELO of 800 at the start of Tournament 1.
Player A plays 5 matches in Tournament 1, winning 3. Her calculated ELO from each match are: +17, -8, +4, +13, -6 for a net ELO of 20.
After Tournament 1, Player A’s ATR rating is 800 + 20 = 820
Tournament 2 (Starts 243 days after Tournament 1 and ends 365 after Tournament 1)
Player A has a rating of 780. However, their ELO at the start of Tournament 1 was 800, so Player A's Unadjusted ELO is 800.
Since Tournament 2 is 243 days after Tournament 1, only 63.05 percent of her Net ELO from Tournament 1 is counted.
Player A's initial ATR is 800 + 20 * 0.6305 = 812.6
Player A plays 3 matches in Tournament 2 with results of: +5, +17, -12 and has a net ELO of +10.
Player A's ATR at the end of Tournament 2 is: 800 + 0.5 * 20 + 10 = 820
Edited by astros, 6 days ago.