Step-by-Step Guide
- Set your War Banners to match the game: the Emblem Stat, Emblem Quality and Emblem Trait of each of the nine Emblems.
- Open the War Banner Optimiser tab and set the three Roll Operations the game is offering you.
- Read the recommendation and the table beneath it. The
recommendation names the single best move. The table gives the outcome of
every action open to you: each Roll Operation on each War Banner it applies
to, and rerolling for a new set.
Note: a Roll Operation can leave a War Banner worse than it was, and the Chance Worse column gives the odds of that happening. The Expected column still decides a single roll: it is the average change across every outcome, weighted by how likely each one is, so a Roll Operation can be worth taking even when the Chance Worse column is high, as long as its rare good outcomes are big enough. Click a row in the table to see all the outcomes behind it.
- Pick a Roll Operation, or none at all if nothing is
expected to gain.
Note: each recommendation looks one move ahead only, so the Expected column alone may not be the best guide across a run of rolls. Weigh the Worst and Best columns too. With Roll Tokens to spare you can absorb a bad outcome and fix it later, so the Best column is what to chase; on your last one the Worst column is what to protect.
- Update your War Banners after each Roll Token you spend, then repeat from step 2.
- Open the Roster & Titles Optimiser tab once your
War Banners are settled.
Note: Rosters and Titles are free to change and War Banners are not, so there is nothing to gain from doing this earlier.
- Read the recommendation and the table beneath it. The
recommendation names the best Roster-Title combination. The table gives
every Roster you could field, ranked, with the best Titles to run
alongside each one.
Note: the Roster and the Titles have to be decided together. One Prefix and one Suffix cover all five players, so what a Title is worth depends on which Teams you pick, and which Teams are best depends on the Titles. That is why every row comes with its own pair rather than letting you choose them separately. Click any row to see what every other Title pairing would score for that Roster.
- Pick a Roster-Title combination.
Note: the recommendation and tables assume every Team plays the median number of series in the Period, since how far a Team actually goes is the one thing this cannot predict. That judgement is left to you, so favour Rosters you expect to play the most series. Toggle Show expected points for every possible number of series to see what a Roster scores at each.
Set your Roll Operations
Pick a Roll Operation
Note: each recommendation looks one move ahead only, so the Expected column alone may not be the best guide across a run of rolls. Weigh the Worst and Best columns too. With Roll Tokens to spare you can absorb a bad outcome and fix it later, so the Best column is what to chase; on your last one the Worst column is what to protect.
Roll Operation outcome summary
Pick a Roster-Title combination
Note: the recommendation and tables assume every Team plays the median number of series in the Period, since how far a Team actually goes is the one thing this cannot predict. That judgement is left to you, so favour Rosters you expect to play the most series. Toggle Show expected points for every possible number of series to see what a Roster scores at each.
Best Roster-Title combinations
Click a row to see the score contribution of all Title combinations.
This is for anyone who wants to see the numbers underneath. They are the same calculation the optimisers run — the whole Period, at the median number of series, with no Emblem multipliers. One exception: each Emblem Stat below is measured in isolation, so these figures do not capture how Emblem Stats move together. Each picks its own best games, while a real War Banner has to pick one set for all three, so adding three of them overstates what that banner would score. The optimisers themselves do account for this.
Matches per Team and Role
How many matches stand behind every figure on this tab, for each Team and Role.
Expected points per Emblem Stat and Role
Total points each Emblem Stat is expected to score over the Period for a Role, averaged across all Teams, before any multiplier. Emblem Stats this Period's War Banner cannot hold are dimmed.
Expected points per Emblem Stat, Team and Role
Total points each Emblem Stat is expected to score over the Period, for a given Team and Role, before any multiplier. Emblem Stats this Period's War Banner cannot hold for that Role are dimmed.
Expected multiplier per Title and Role
What each Title is expected to add over the Period for a Role, averaged across all Teams, as a percentage of the same War Banner without it. All Roles weights each Role by what it scores.
Expected multiplier per Title, Team and Role
What each Title is expected to add over the Period, for a given Team and Role, as a percentage of the same War Banner without it. Judged on every Emblem Stat the Role can hold, so it does not depend on which three a War Banner happens to carry.
Data
- The data is taken from professional matches played on patch or later, covering all 16 Teams at the tournament.
- The data comes from both OpenDota and the match replays themselves, read using a custom parser built for this.
- Matches are exponentially weighted, so recent ones count for more.
- Coverage is uneven, between and matches for a given Team and Role. A Role is two players for Core, one for Mid and two for Support, and a match only counts for it when all of them played it on the same side, so the same Team can have far more matches for one Role than for another.
- Much of the data is Bo1 and Bo2, where nearly every game is trivially the last possible match of its series. That makes the recorded trigger for the Clutch far more common than it will be at the tournament, so it cannot be read from the data at all.
- The data needed for is not available yet. We are working on acquiring it.
Assumptions
- How far a Team goes is not predicted. A Team plays , and the tables assume the median of each — series respectively.
- The grand final is a Bo5 but is modelled as a Bo3. Only the best two matches of a series count either way, and it is a single series, so the difference is minimal.
- Roll odds are not published. Emblem Traits and Emblem Stats, and which three Roll Operations are offered, are taken as equally likely. For Emblem Quality, Valve states only that a larger boost is rarer, so the odds were estimated from a few hundred recorded rolls: for tiers I to V.
- Randomly increase one Quality and Randomly increase two Qualities and reduce one both prioritise Emblems below tier V when increasing, and above tier I when reducing. Where that is not possible, the Emblem is picked anyway and rerolls to a random tier instead, which is how a Roll Operation promising an increase can hand back a lower one.
Calculation
- A Role scores the average of its players, counting only the Emblem Stats on their War Banner. The best two matches of a series count, then the best series of the Period — two maxima in sequence, which rewards a high ceiling over consistency.
- The result is therefore not a mean but the expected value of that maximum. Every pair of games a series can produce, and every best-of-several a Period can produce, is enumerated and weighted by its probability. A series runs two or three games in the proportion observed in the data, where of Bo3s go to three. Nothing is simulated.
- Those games are drawn to match how a Bo3 actually plays out. Two games means one side swept, so both are wins or both are losses; three games means the first two were split, which is what took it to a third, and the decider goes to whoever takes the series. Drawing freely would invent 3-0 series and split two-game ones, neither of which can happen.
- Prefixes and Suffixes are applied to each player in each match, before either maximum is taken, because which matches they fall in determines their value. They can be changed freely, so Roll Operation evaluation excludes them.
- The exception is the Clutch. It pays out in the last possible match of a series, which is a position rather than a property of the match, so it is applied to the third game of a series that runs to three and to nothing at all in a series that ends 2-0. That game is drawn like any other, and deciding games tend to score a little above average, so its worth is slightly understated.
- Since the Team is chosen later, a War Banner is valued as the mean of what it is worth to each of the 16 Teams in that Role. Valuing it against only the strongest Team was tested and made very little difference to which Roll Operations come out ahead, so the simpler measure is used.
- Taking a Roll Operation and rerolling both cost one Roll Token and both replace all three on offer, so the only difference between them is whether the operation is applied. A reroll therefore carries an expected change of zero, and a Roll Operation is worth taking only if it exceeds zero. Where none exceeds zero on any War Banner, a new set cannot contain one either.
- Every outcome of a Roll Operation is enumerated and weighted by its probability, and a reroll cannot return the value an Emblem already holds. The expected change is the deciding figure: a Roll Operation with a positive expectation may still be more likely to lower a War Banner than to raise it, where the gain in its rare favourable outcomes is large enough.