Rankings

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HoV.png
All-time and Tournament Rankings.

Each player's prowess in The Banner Saga: Factions is recorded in the Hall of Valor in Strand. There, you can review your overall performance and that of the top players of the game. There is a different listing for all-time and current-tournament performance, accessible by clicking on the appropriate banners.

The most important performance statistic is the player's rating/ranking [1]; this is measured by means of an Elo-ranking system [2], similarly to chess. The Elo-ranking of each player is used by the game's Matchmaker in order to arrange matches between equivalently ranked players. This helps make every battle equally challenging regardless of your ranking!

Ranking vs. Match type

Your Elo-ranking is affected differently, depending on the match type selected in the Great Hall.

  • Quick matches do not affect your Elo-ranking. Play freely, experiment with tactics and earn Renown!
  • Ranked matches normally affect your all-time Elo-ranking. For the change in your ranking, refer to the formula section. Ranked match may be against opponents from the Quick match queue; this case results in only a small fixed change in Elo-ranking.
  • Tournament matches affect both your all-time and your current-tournament Elo-ranking. These are the matches to give your best show!
  • Friendly matches do not affect your Elo-ranking.

Finally, note that Ranked & Tournament matches are open only to specific team-powers, e.g. 6 and/or 12.

Elo ranking

Upon first arrival in Strand — or upon registering in a new Tournament — each new player is assigned an Elo-ranking of 1000. Then, for each battle won or lost, his Elo-ranking is increased or decreased, respectively. The amount of change in the Elo-ranking depends on the ranking-difference of the two combatants. As a rule of thumb, a win/loss against a higher (or lower) ranked player results in a bigger (or lower) +/- change in your ranking. The maximum allowable change in Elo-ranking is governed by a constant called $K$-factor.

Formulas

The algorithm of calculating the change in Elo-ranking after a match, is the following. Firstly, the K-factor is calculated independently for each player, $K_i$ where $i={1,2}$, according to their Elo-ranking, $R_i$.

(1)
\begin{align} {K_i} = \left\{ \begin{array}{l l} 32 & \text{when ${R_i} < 2100$} \\ 32-{16\times (R_i - 2100)/300} & \text{when ${R_i} \in [2100,2400]$ } \\ 16 & \text{when $R_i > 2400$} \end{array} \right. \end{align}

The above formula means that for entry- and mid-level players a $K = 32$ is typically used, while $K = 16$ is reserved for high-level players. Subsequently, given the outcome (or score) of the match for each player, $S_i$, the change in the Elo-ranking $\Delta {R_i}$ is calculated for each player separately:

(2)
\begin{align} \Delta {R_i} = {K_i} \times \left({ S_i - S_i^{e}}\right), \end{align}

where $S_i^{e}$ is the expected/estimated score for the $i$-player, given by

(3)
\begin{align} S_i^{e} = \frac{10^{R_i/400}}{10^{R_1/400}+10^{R_2/400}}. \end{align}

A score of $S=0$ denotes a defeat and $S=1$ a victory. A tie (currently unavailable in Factions) would correspond to $S=0.5$, for both players. Evidently, the player scores must satisfy $S_1 + S_2 = 1$.

TBSF_ELO_Change_Kfactor32.png
Graph: Change in Elo-ranking after a battle.

Remarks

  • This ranking concept can be explained by the wagering analogy of the pot [3]. Before the match, each player places some if his $R_i$ in the pot, with the favorite to win (i.e. the one with the higher $R$) having to put in more. At the end of the match, the winner takes all the pot.
  • The Elo-ranking is designed so that when a player reaches his/her true ranking, he/she cannot expect big deviations from it, regardless of the opponents' rankings [4]. In this respect, the estimated score $S_i^{e}$ represents the probability of winning and, statistically speaking, the expected Elo-ranking change is $E[~\Delta R_i~|~R_1,R_2~]=0$.
  • The formula for $\Delta {R_i}$ means that when the players are equally matched, $R_1 = R_2$, the Elo-ranking change is $\pm~K/2$ for the winner/loser, respectively. Viewed in terms of the pot analogy (with $K=32$), firstly both players remove $16$ from their $R_i$ contributing to a total of $K=32$ in the pot. The winner takes all, so $\Delta R_{\text{winer}} = +16$, while the loser takes nothing, i.e. $\Delta R_{\text{loser}} = -16$.
  • When you are playing a Ranked match but your opponent is from the Quick match queue, you can only get a fixed ranking-change of $\Delta R = \pm2$.

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