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Warband Objective Card Analysis: A Random Walk Down Beastgrave

Updated: Jun 8

Hello!


This is a guest article by Khel, an Underworlds player from Barcelona. Khel was interested in the glory flow of common objectives and decided to do some very cool analysis on the topic.


As with all data, this isn't a complete picture of the game, and there are likely always things that could be done to improve the numbers to get closer to reality, but I think this is a great glimpse into how objectives work in the game and why some things tend to work better than others. I personally find it endlessly interesting, and am very happy Khel reached out to share this article.


--WiggleFish

1. Introduction


Khel here!


Long ago I read an article called Understanding Base Glory on the End Phase blog which I found quite insightful. It basically dealt with the concept of passive glory: objective cards which are basically free to score and do not require interaction with the opponent.


In this article I want to expand on that idea. In particular, the question I try to address is "What does the glory distribution of every competitive warband look like?"

For the time being, the scope of this experiment are just warbands which according to Beastgrave Q3 Data Final Results post of Well of Power blog form the meta, plus Hrothgorn's Mantrappers. This is:

  • The Grymwatch

  • Lady Harrow's Mournflight

  • Rippa's Snarlfangs

  • Stormsire's Cursebreakers

  • Skaeth's Wild Hunt

  • Thundrik's Profiteers

  • Thorns of the Briar Queen

  • Hrothgorn's Mantrappers

All the data gathered for this experiment comes from Underworlds Deckers, and was extracted on May 1st, 2020.


2. Data


A collection of objective cards has been built for each warband in the scope of this exercise. This collection is formed by all cards used in a 10% or more of the glory decks which can be found in Underworlds Deckers for the warband.

For each card in a collection, the following information was registered:

  • Glory – Glory it scores.

  • Surge – If it is a Surge.

  • Requires Obj – If it requires any amount of surges scored that round (relevant for Combination Strike and Opening Gambit)

  • Requires Glory – If it requires any amount of glory scored that round (relevant for Solid and Great Gains).

  • Deck Frequency – How frequently, according to Underworlds Deckers, the card appears in the Glory Decks of the warband.

  • Field Odds – Roughly speaking, the probability of scoring the card along a round. This is where things go tricky, as I have assigned these odds according to my insight of the game. Although I have thought of the figures I have used and consider them fair, I am sure that some of them could be more accurate, and some could even be completely off-base. The different odds I used can be found in the annex, and I am open to rerun this experiment with sharper data if the community steps in to refine my numbers.

  • Restricted – If the card is restricted.

Field Odds assumes that the warband has won the boards roll-off and taken 3 objectives. This clearly impacts the chances of scoring some cards. When I deemed that a card was affected by this, I re-coded the Field Requires Obj to reflect its scoring chances when the relevant warband places only 2 objectives. Finally, third phase objective cards receive a 0 in field Odds. Their actual odds of being scored in the third phase are stored in Field Requires Glory.

3. Methodology


For every warband in the scope of this document:

  • 600 decks are created. All decks are formed by 6 Surges and 6 End of Phase cards, and the chances of a card to be included in a deck depend directly from the Field Deck Frequency above.


For each of the 600 decks, the average glory it scores along a game is computed by running 100 fictitious games, as follows:

  1. Three cards are drawn. If no surges are drawn, a mulligan is done.

  2. For each surge in hand, a random number between 0 and 1 is drawn. If it is lower than Field Odds above, the card is scored, and a new card is drawn.

  3. The step above is repeated for each surge card drawn.

  4. For each End of Phase card in hand, a random number between 0 and 1 is drawn. If it is lower than Field Odds above, the card is scored.

  5. Combination Strike and Opening Gambit are resolved, if applicable.

  6. Solid Gains and Great Gains are resolved, if applicable.

  7. Non-scored End of Phase cards are discarded. Surges are kept. Hand is replenished.

Steps from 1 to 7 above are repeated 2 more times in order to simulate rounds 2 and 3. The only difference is that at the end phase of Round 3, third end phase glory cards are resolved as other end of phase cards. With this, we have a glory total for the deck in the simulated game. Then:

  • The average of the 100 glory totals above is taken as the glory linked to the assessed deck.

  • Then the glory distribution of the assessed warband is built using the 600 glory points derived.

  • The process detailed above is run twice per warband: Once considering the warband places 3 objectives, and once considering it places only 2.


4. Results


The glory distributions linked to every warband are plotted below. Green colored distributions stand for when the warband places 3 objectives, while blue colored distributions stand for when the warband only places 2. Each plot also shows the extra average glory a warband gets when placing 3 objectives (above) and the average amount of restricted cards their glory deck contains (below).

5. Analysis


The information obtained in the previous section can help us to dig deeper in certain areas of the game: 5.1. On the relevance of placing 3 objectives

The data above gives certain perspective on how much having three objectives impacts the ability for each warband to score their objective cards, unconditional to the meta. In particular, four tiers are observed:

  • Largest innate benefit from placing 3 objectives – The Grymwatch

  • Large innate benefit from placing 3 objectives – Thorns of the Briar Queen, Lady Harrow's Mournflight, Skaeth's Wild Hunt

  • Noticeable innate benefit from placing 3 objectives – Thundrik's Profiteers

  • Essentially no innate benefit from placing 3 objectives – Rippa's Snarlfangs, Stormsire's Cursebreakers, Hrothgorn's Mantrappers

If some of these results seem strange, keep in mind that these numbers only reflect how much having the objectives effects the ease of scoring objectives, and that the cards in the tested decks depend on the cards players used in Deckers for each warband. Some Thundrik's players, for example, took cards like Supremacy, Temporary Victory, and so on, making those decks prefer to have the objectives. Many Wild Hunt decks also contained objectives for holding objectives such as Purifying Rites, which also influence their numbers.


These results also do not take into account counter-play some warbands may have available, such as objective flipping/removal, they simply show the typical amount of glory a warband might expect to gain from their deck over many games.

5.2. Match-up Initial Bias

With the information above we can try to get a feel of the match-ups between the warbands in the scope of this exercise. In this sense, the table below gives the average glory differential between every single matchup. The warbands in the rows of the table are assumed to place 3 objectives, while warbands in the columns are assumed to place only 2 of them.

As an example, the third row, second column of the table shows a -0.65. This means that when Mantrappers place 3 objectives against Lady Harrow, ignoring all other factors, they are expected to score 0.65 less glory points through their glory deck than the banshees. The opposite matchup is displayed in the second row, third column of the table, and is indeed even better for the Mournflight.

The information above is the basis for the next two sections, which discuss the concepts of a Glory Decks Tierlist and the Glory Cost of Placing Boards.


5.3. Glory Decks Tierlist


Results from Table 1 can be used to derive an overall initial glory bias for each warband in the scope of this exercise. This can be done via aggregating the following two figures:

  1. Average initial bias when the warband places 3 objectives (this is, average of the relevant row of Table 1).

  2. Average initial bias when the warband places 2 objectives (this is, the opposite of the average of the relevant column of Table 1).

Below, the warbands in the scope of this exercise are sorted by their overall initial bias:

Even though the results should be taken with a grain of salt due to simulation noise, they seem to be clearly pointing to the following tier distribution:

  • Tier S – Grymwatch

  • Tier A – Mournflight, Thundrik's, Skaeth's

  • Tier B – Thorns, Rippa's

  • Tier C – Mantrappers

  • Tier F – Cursebreakers

Note that this does only take into account glory decks, so it should not be understood as a warband global tierlist, but a glory deck strength tierlist. Other factors, such how much glory a warband gets from kills, how little they give up in deaths, or glory from upgrades are additional factors that would have to be applied on top of these numbers.


5.1. Glory Cost – Placing Boards


The expected glory impact of placing 3 objectives in a matchup can be easily derived from Table 1. Indeed, we can obtain it via adding up the two figures from the table which are relevant for the matchup. For example, in the Mantrappers vs. Mournflight matchup, placing three objectives has a direct benefit of 1.47 0.65 = 0.82 glory points on average.


This figure can be seen as the Glory Cost of placing boards in a matchup. Indeed, as a rule of thumb, one should only choose boards over objectives when winning the roll-off if the benefit they expect from it exceeds the Glory Cost of the matchup.

The table below shows the glory cost of all the match-ups among the warbands in the scope of this article:

5.5. 3 Objectives Dependency

A magnitude of the overall benefit which each warband gets from placing 3 objectives in the current meta can be easily derived from Table 2. Indeed, one only needs to average the Glory Costs associated to all the possible match-ups involving the warband. The table below displays this information:

In this case, there seems to be two clear different tiers, with Thundrik’s somewhat in the middle. This is:

  • Strong Dependency on placing 3 objectives: Grymwatch, Thorns, Mournflight, Skaeth's.

  • Significant Dependency on placing 3 objectives: Thundrik’s.

  • Weak Dependency on placing 3 objectives: Rippa's, Mantrappers, Cursebreakers.

6. Conclusions

Along this exercise we have dug into the concept of Glory Distribution: the expected distribution of the glory decks belonging to the 8 warbands forming the meta of WU Beastgrave Q3 2020. We have obtained the Initial Glory Bias for all possible match-ups amongst these warbands, taking also into account which warband places 3 objectives. We have used this information to give a general tier list which gauges the strength of the glory decks of the warbands in the scope of this exercise. We have also defined the concept of Glory Cost of Choosing Boards in every matchup and used this information to derive the dependency of each warband to placing 3 objectives in the current meta.

7. Limitations

This exercise has two main limitations:

  • Data: The data used to build the decks used to derive the glory distributions which are the basis of this article comes from Underworlds Deckers. This means that the decks it includes range from competitive to less-than-casual. As a result, the frequency of certain cards can be unrealistic in a competitive Underworlds environment.

  • As mentioned in the data section, the field Odds represents the odds of scoring a particular objective along a round. These probabilities have been chosen by me in a case-by-case basis, and could be completely off-base in some cases. In any case, they can be found in tables in the annex, so comments and potential amendments are welcome. You can see all of these Field Odds in the input tables here.

Thanks, Khel!


I found this very interesting and I am sure the readers will as well!


If you liked this article, great! If there is anything you think we could have done better, let us know in the comments.

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