Introduction & Addenda
As of December 1st, 2015, DestinyTracker collects information from every Crucible match to generate and maintain an Elo score for all players. Elo is a competitive index originally conceived for Chess that has caught on in the world of video games, appearing in games with large eSport scenes such as League of Legends. This thread will detail how DestinyTracker calculates Elo scores and the modifications made to better suit Destiny's matchmaking system.
Each player begins with a set Elo score (DestinyTracker starts each player off at 1000) which then moves up or down solely on whether you win or lose a match. The number of points awarded or lost depends on the estimated probability that you have of winning that match. This probability is calculated by comparing the Elo ratings of members of both teams (or all players in Rumble) to determine the chance of winning a match.
Because Elo is intended for one on one competitions, Elo had to undergo a few adjustments in order to be compatible with the way Destiny and its players compete in the Crucible. These changes account for:
- Join In Progress
- Fireteam Size
Elo is a zero-sum formula. That is, points that are lost by one party are awarded to another. In order to punish players for quitting matches, DestinyTracker Elo is not zero-sum. Our justification for this can be found below, and we encourage those with a statistics background (or otherwise!) to weigh in on this issue. That said, the average Elo will lower over-time, but is easily remedied by appending the difference between the average and 1000 to return the average to normal levels.
To establish how a player's Elo rating changes, a probability is drawn to determine the likelihood of a player winning their match. DestinyTracker uses the average of two probabilities to cater to team-based matches. Probability is determined by using the following formulae:
Player Probability = 1 / (1 + 10 ^ ((EnemyTeamAverageElo – PlayerElo) / 400)
Team Probability = 1 / (1 + 10 ^ ((EnemyTeamAverageElo – PlayerTeamAverageElo) / 400)
Final Probability = (PlayerProbability + TeamProbability) / 2
When calculating the averages of both teams, all players who have a hand in the match are used (including those who quit and join in progress). Everyone who has a hand in the game's outcome are considered for these purposes. As a baseline, a player who is 200 points over the opposition has a 75% chance of winning their match.
An average of both a player and his/her respective team is used to better balance the distribution of points among members of the team. Players much higher suffer greater losses and fewer gains due to their increased pull on the game's outcome.
Using the probability calculated in the previous step, a player's Elo change becomes the difference of their standing in the match minute that calculated probability:
NewPlayerElo = PlayerElo + 32 * (Standing – Probability)
When determining standing, a 1 is used for a win while a 0 is used for a loss. This determines whether or not a player gains or loses Elo, and the probability determines exactly how much their Elo is expected to change. For Rumble placements, standing is reduced by 0.2 for each position below the first place finish. This means that a fourth place finish will use a 0.4 as their standing (rather than treat it as a loss).
Fireteams and Join in Progress are two large hurdles that test validity when dealing with values that estimate player skill. To counter these issues, DestinyTracker adjusts a player's Elo change based on largest Fireteam size and Join In Progress to avoid punishing those who prefer to fare the Crucible alone and grants lesser gains to those who win matches by stacking teams against random opposition. These modifications are applied to the previous formula in the following way:
NewPlayerElo = PlayerElo + ((32 * (Standing - Probability)) * FireteamChange) * JoinInProgressPercent
For those already knowledgeable on the Elo rating system, we employ a K-factor of 32 across all ranges of players; this is done because Destiny does not employ skill-based matchmaking. In the event that a significant 2100 range does develop, DestinyTracker will revisit and explore the possibility of adding a second, lower value.
DestinyTracker has added precautions to prevent stacked teams from procuring an unfair advantage over solo searching players. Because Destiny does not inherently match based on team size or skill, the largest size fireteams from both teams are used to modify the calculated Elo changes prior to being applied.
The difference between both sides' largest fireteams adds a change of 10% for each additional member on the largest of the two fireteams. For example, a fireteam of six against a group of four will modify Elos by 20%. For the larger fireteam, this value reduces the Elo awarded for a win and increases the Elo taken away for a loss (by 20% in this example). For the smaller fireteam, a win will award more points (20% more) while a loss will take away fewer points. This accounts for the change in probability associated when teams have vastly different fireteam set ups. The chart below illustrates provides two examples of how fireteam size affects the change in Elo.
Players present in fireteams that aren't members of the largest for that team are currently not considered. A fireteam of four and two is treated similar to a fireteam of four with two random, solo searching players. We are still exploring percentages to determine what would be most appropriate without being unfair. We encourage feedback, particularly on this issue.
Join In Progress
Join in progress is a major issue, particularly for players who prefer to play solo (or Rumble). To prevent players from taking heavy losses due to Join In Progress matches that are already decided for them, a threshold protects the Elo rating of late joining players. Players who join a match more than a quarter of the way through will have his/her Elo be unaffected by a loss (for the purposes of the formula listed above, joining past the threshold returns a 0 for JoinInProgressPercent). Due to the nature of Rumble, there is no quit threshold for join in progress matches. Instead, no points will be deducted if a player joins a match in progress where they would lose Elo for their standing.
For late joining players that win their match, Elo points are awarded proportionately to the time that was spent in the match. A player who joins during the last quarter of the game, who would have normally received 10 points to Elo, will only receive 2.5 as they were not present for the entire match. This encourages played to stick out their matches, even if they join a match in progress. Partial points are not awarded in Rumble matches. Guardians who earn Elo in a Join In Progress match will earn full credit for their placement.
Any matches that are joined prior to the quarter threshold are considered fair play, Elo will rise and fall like a regular match.
Quitting is unfortunately a common occurrence in Destiny. While disconnects from matches are inevitable for some, penalties are required to encourage sticking matches to the end. A player who quits their match will automatically receive a loss, regardless if the team goes on to win that match. Players who quit their match beyond the quarter threshold as used in the Join In Progress calculations will not be affected by a quit penalty.
Handling quits by penalizing players eliminates the ability for DestinyTracker Elo to not be zero-sum. During testing, we found that trying to redistribute points from quits skewed the numbers to an unfair point. A team of +12 Elo combined with a quitter who took a loss of -16 points to Elo causes the opposing team to lose significantly less Elo. With more quitters, the focus of Elo turns to where and how many quitters were in a match rather than the Elo ratings of the players who remained in the game.
Elo ratings of players who quit still contribute to the averages of their respective teams, as do players who join in mid-match.
Elo Rank Placement
Every Guardian is assigned a rank based on their position on the Elo leaderboards. There are a total of nineteen ranks spread across seven tiers. Ranks are broken down by percentile, which dynamically change as player Elo ratings fluctuate from day to day. This means that both active and inactive players may see ranks change overnight, which consistently encourages improvement. The final tier, Legionnaire, consists of the 200 highest rated players for that playlist.
The cutoffs for each rank are redrawn every night, though your ranks will update as our collector scans your games. Be forewarned, a freshly earned rank can be lost overnight when the boundaries for each rank are reevaluated. Keep that in mind when you reach that shiny new rank!
Tiers & Percentiles
How is my Elo rating calculated?
Elo rating is a win/loss based formula that estimates your skill level against your competition. The exact formula we use to calculate a player's Elo rating can be found above.
What factors influence my Elo rating?
Whether you win or lose a match determines whether your Elo goes up or down. To what degree your Elo moves is dependent on the Elo ratings of other players in the game. If you win against higher rated opposition, your Elo will increase more than if you had won a match against opposition lower than your current Elo.
When is Elo adjusted?
As of December 1st, 2015, DestinyTracker gathers data from every Crucible match played and evaluates the Elo rating for all players in it, even those who have never visited the site. Once you have finished a match, it enters the queue to be scanned. Once the scanner reaches that match, your Elo will be adjusted. Please note that this is not immediate and can not be forced by collecting your stats.
Where can I find my own personal Elo ratings?
You can find your Elo ratings under your playlist statistics. Assuming you have your account linked, select 'My Stats' in the navigation bar at the top of the page and select 'Playlist Stats' under the PvP Group. If you don't currently have an account, or are trying to find another player, you can select 'Playlists' from a user's player page to get there as well.
Is my leaderboard position for Elo based on members of DestinyTracker or the whole Destiny community?
Since we track the Elo ratings of all players, your leaderboard position indicates your location out of all players who have played a game of Crucible after December 1st, 2015.
What is the average Elo rating? What is the starting value for each player?
If a player appears in a scanned game and has not received an Elo rating, their starting Elo will begin at 1000. If this is your first time visiting, your Elo may have already adjusted from games that were collected in the past. The average Elo will be slightly less than 1000; this is because we punish players with loss when they disconnect from a match.
Where is Elo used?
DestinyTracker calculates your Elo for each Crucible playlist. Your game history from all characters will apply to these ratings.
Can my Elo decrease?
Yes, losing games in Crucible will cause your Elo to drop, regardless of how well you do. However, if the probability of winning your match is low, your points will decrease at a lower rate.
Is there a limit to how high an Elo rating can go?
Theoretically, no. But players with higher Elo ratings gain less for wins and lose more for losses when they play, simply because the competition they match with will be close to the average (because there is no skill matching). Your best bet is to the use the top ten players in Elo to determine what the upper bound is. It may be beneficial to add that a difference of +200 Elo indicates a 75% chance of winning a match.
Why do I have a lower Elo rating than someone who has worse stats that mine?
Elo adjusts based on wins and losses and the degree at which Elo moves is dependent on the Elo ratings of everyone else in the match. If you haven't played a lot of Crucible (less than fifty games), you may want to give it more time to see how it will adjust afterwards. The other player could also be on a solid winning streak, which might inflate their score.
Will my Elo drop when I delete a character?
No, Elo ratings are modified using post-game carnage reports and do not use totals from characters in any way.
Why does my Elo rank drop even though I haven't played any games?
Elo ranks are percentile-based and change as other Guardian Elo ratings fluctuate. If your Elo falls into a new percentile, your rank will change, despite possibly not playing any games.
My question hasn't been answered, how do I get in touch?
Any questions or feedback regarding Elo ratings can be freely asked in this thread, or can be directed to Darkened Night.