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Lemon Knuckles

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Everything posted by Lemon Knuckles

  1. Alright lads. Let's get to work. Spreadsheet attached, and full definitions included. Will try to keep this post updated with questions, changes, etc. as we go. Project Description: F.A.Q.s Design Principles Proposed Stages Proposed Level One Methodology The Formula Key User Inputs Changelog AoS Gunkulator v1-03.xlsx
  2. Lemon Knuckles

    Crowdsource Points Project: AoS Gunkulator

    This is a fascinating case, and a puzzle to try and figure out. On their own, gunk currently values them as follows (as a unit of 10): 71 Pink Horrors of Tzeentch 140 200 -60 -30% 7. Very Overcosted 72 Blue Horrors of Tzeentch 71 100 -29 -29% 7. Very Overcosted 73 Brimstone Horrors of Tzeentch 61 70 -9 -13% 6. Overcosted Obviously they are not worth their points on their own, but trying to figure out the value of their splitting ability is a tough nut. Doing so well, I think, involves calculating the resultant units in the context of tempo. The splitting is a very anti-tempo play and an amazing control ability, and I'd argue that the relative value of the Presence of the resultant Blue and Brimstone horrors is higher than it would be if those same effective wounds were present up-front in the Pinks. Likewise, I'd argue that the value of the Pressure of the resultant units is lower than it would be if that effective output was present in the Pinks. It's a very interesting thing to think about. It's also kind of interesting that the proportional value of the Blue and Brimstone's Presence decreases as their number increases due to the potential increasing effects of Battleshock. This is the case for any horde unit, and one of the reasons that the max size discount is not actually a discount per se, but more an accurate reflection of relative decrease in the value of a horde unit's effective wounds. At some point I need to better tackle the math around this.
  3. Lemon Knuckles

    4. Who's the Beatdown?

    @gronnelg, welcome! Glad you signed up. This is a great place full of friendly folks. I accept the criticism fully, and am aware. The abstract-ness was necessary for me to think through the idea. Can appreciate that it made reading it a chore. Kind of like listening to some guy muttering to himself in the corner. Hopefully as it continues to unfold it will get less and less abstract and more and more accessible. Kind of like building a house... a foundation is pretty boring and it's hard to visualize the house, but the more it's constructed, the more "interesting" and accessible it becomes. I hope!
  4. Lemon Knuckles

    4. Who's the Beatdown?

    Who’s the Beatdown? is probably the most iconic piece of MtG theory ever written. It has proven exceptionally fertile as the ideas within have been grown, developed and re-harvested again and again over time, and ported out and across all kinds of other game systems to varying degrees of success. It is not perfect. It is not scripture. But it was one of the first on the scene to look beneath the surface of the game and emerge with something truly fundamental, important and consistently relevant. I am aware of only a few attempts to apply Who’s the Beatdown theory to AoS. None of them have been completely satisfying. Yes, MtG is a very different game than AoS, but I don’t think that’s the problem. The concepts are relevant, even if they have to be reframed a bit to match a different context. The problem, I think, is that the current dearth of AoS theory makes it more difficult than it needs to be to fully develop Who’s the Beatdown in AoS terms. So buckle-up buttercup. We’re going to try to apply what we learned last time and see what sparks might fly. Breaking Down the Beatdown What’s at stake in Who’s the Beatdown is the idea that in any given game, and indeed, at any given point within a game, a player’s chance of success is significantly improved if they properly understand their role in game relative to their opponent. A player’s role can be fluid and can change match-up to match-up, and indeed, can change back and forth within a given match-up. Misunderstanding your role oftentimes means misunderstanding what’s important. Misunderstanding what’s important oftentimes means losing. Let’s start by reviewing a recent attempt to apply Who’s the Beatdown to AoS. For this, we’ll use the relevant excerpt from THWG’s new workbook, reproduced in the spoiler below. Please read through it before continuing on. While reading it, take note of what you understand from the concept as outlined, what you can take away from it to help frame how you see the game (concept, from Latin concipere, “to take in and hold”). I’ll share my take-aways below and we can compare notes, but I think it’s important that you meet it on your own terms first. For me, it seems like it gets some things right and gets some things wrong, and leaves the over-all concept a bit too blurry, and therefore less useful then it could be. But like Flores’ original piece, it does provide fertile ground to work on, to nurture and harvest and regrow the seeds that it plants. To do that work, I will have to introduce some new concepts. But staying faithful to the original methodology, these new concepts will be derivative from our three starting elements (Space, Time, Variability) and therefore connected to our three essential resources (Presence, Pressure, Projection). We don’t want to just create a pile of ideas; we want to create a framework within which each of our ideas are logically connected with each other, and through which a cohesive and functional perspective can emerge. What I think THWG’s piece really gets right here is the notion that risk is one of the key differences between how to play the two roles, and that advantage is one of the key elements in understanding what role to take. What I think the piece gets wrong here is the actual assigning of the roles themselves. What I think is under-developed is the defining and assessing of advantage and coming to grips with what’s important to each role. Let’s start with the roles. In Flores’ original piece, he defines two possible player roles: the Beatdown (or aggro) role, and the Control role. Although the notions of Aggro and Control decks existed as archetypes way before Flores, what was inspired in his article was the insight that within the context of a particular match-up, an Aggro deck might actually be better served assuming the Control role, or vice versa, the Control deck might actually be best served playing the Aggro role; that is, although you may have designed your deck to be Aggro or Control, the specific context of the game might require you to play otherwise. The key concept was to understand the power of the resources that you had available and that your opponent had available and their relationship to time. An Aggro role was required when the resources you had available were less powerful than your opponent’s but were able to be brought online sooner. The Control role was required when your resources were more powerful but required more time to deploy. Thus the Beatdown player was the one who had a short-term advantage and thus had to try and win now, before they became outclassed. They had to burn through their resources as quickly as possible and go for the throat. They had to push the tempo and get more done in less time because if the game dragged on too long, they would lose. The Control player, on the other hand, had to try and slow things down. They had a long-term advantage. Their role was to prolong the game however possible until the power of their late-game resources became overwhelming. If they could hang on long enough and “turn the corner,” they would win. If we want to successfully apply the lessons of Who’s the Beatdown to AoS, it is critical to preserve the element of time in our understanding, as it is critical to the entire original notion. We know from our previous work so far, that Time is one of the three essential elements in AoS, along with Space and Variance. Time is best understood as a measure of change. We use points to invest in Time whenever we buy Pressure. Pressure is used to attack Space, which we invest in whenever we use points to buy Presence. Space can be used to attack Time whenever Presence is used to control its vector speed, Projection. Here we can see that the fundamental difference between Pressure and Presence is their relationship with Tempo, which we will define here as the measure of the density of change generated per game-turn (how many moments they generate). Pressure promotes tempo, Presence reduces it. From here, we’re well positioned to start connecting the dots. The Beatdown role is a role properly assumed by the player who stands to benefit from increasing Tempo. The Control role is properly assumed by the player who stands to benefit from decreasing Tempo. In its most extreme example, we could ask the question, which player would win if no further time elapsed in game (e.g. if each player passed on each and every remaining subsequent phase). That player would be the one who would benefit from decreasing tempo, and as such, is the one whose chances of winning are best improved by assuming the Control role. The player who would stand to lose in this hypothetical situation would benefit from pushing the tempo, and as such is the one whose chances of winning are best improved by assuming the Beatdown role. They need to break the current game-state within which they are at a disadvantage. The bigger the advantage gap, and/or the fewer number of game-turns remaining, the more Risk should be assumed by the Beatdown player, and conversely, the less Risk should be willingly accepted by the Control player. Risk is the second new concept we need to introduce today, so let’s do that now before moving on to re-examine the examples from the spoiler. Risk is a derivative concept of Variance. Variance is an essential element of AoS. Pre-game, we are exposed to variance in the form of match-up uncertainty, scenario uncertainty, and (if you are using them) Realm rules. In-game, Variance manifests in two powerful ways: unit action and turn initiative. Almost all unit action contains some measure of randomness in order to quantify its effect: charge rolls introduce Variance into Projection; to Hit and to Wound rolls introduce variance into Pressure; save rolls introduce Variance into Presence, etc. The sequence of play is also subject to Variance, as the turn order between rounds is determined by a roll-off. Risk is the concept that we will use to talk about the implications of Variance on game-play. We say that a play is advantaged when its odds of succeeding are greater than 1/2, and significantly advantaged when they are greater than 2/3. Likewise, we say that an action is disadvantaged when its odds of succeeding are less than ½, and significantly disadvantaged when it is less than 1/3. In a completely neutral game-state, we should consider action whenever it is advantaged, and avoid action when it is disadvantaged. However, as our appetite toward Risk changes, so too should our assessment. In high Risk situations, it may be completely appropriate for the Beatdown player to pursue significantly disadvantaged action (some chance of winning is better than no chance of winning), just as it may be completely appropriate for the Control player to avoid all but the most significantly advantaged actions. Further, in high Risk situations it may be completely appropriate for the Beatdown player to plan for a sequence of events as if he was going to win the next turn initiative roll, just as it may be appropriate for the Control player to plan for a sequence of events as if he was going to lose the initiative roll. Our Risk defines our disposition toward Variance—my chance of winning either depends to some extent on getting lucky, or my chance of losing depends to some extent on getting unlucky. If the former, I need to consider ways of setting myself up to capitalize on that opportunity. If the latter, I need to minimize the impact Variability can exert on my current position. Let’s return to our two examples. Example #1 seems to be a match pitting a high Presence army (elite, re-rollable saves) against a high Pressure army (MW output). There’s not really enough information provided to be clear about the situation, but if we take the example at its word and assume that the MW units will be able to produce an overwhelming advantage in 3 turns, then it’s pretty clear that the Presence army has to assume the Beatdown role. It needs to drive the tempo quickly before its resource allotment in elite Presence is overwhelmed by the opponents investment in MW Pressure. It’s a tough situation for the high Presence army since it is an army designed to play a Control role. But that’s the importance of Who’s the Beatdown. Fail to recognize the role you are actually in (as opposed to the role you had in mind before the game started), and you are much more likely to lose the game. The army now needs to abandon its preplanned strategy and adapt to the situation at hand. It needs to drive tempo and beatdown if it is going to win. Conversely, the Pressure army needs to assume more of a control role than it might have been planning for. As was articulated in the example, it needs to protect its two MW units, and protection is always an anti-tempo play. It is the strategic use of Presence (place) to control circulation and threat, and thin out an opponent’s capacity to create a flurry of moments in their turn. In example #2 we see a match-up of a horde army with high Projection against a high Presence (tanky) army. The strategy articulated in the example seems spot-on: assume an immediate Beatdown posture relative to claiming the objectives, using initiative and superior projection to establish an advantage in Space that, if unanswered, will become inevitable over the long-term. But note that as soon as that advantage is secured, the horde army needs to pivot and assume the Control role. Once they have the advantage on objectives, they are no longer looking to play Beatdown. They are looking to preserve the current state of affairs as much as possible. Their primary concern from that point on is to slow the tempo of the game and ride out the victory, a task that they are well-suited to doing, since as a horde army they have a natural aptitude for controlling space through an abundance of place. The tank army, on the other hand, is in an unenviable position. They are forced early on into a Beatdown role for which they are poorly equipped. The tanky army wants to play the Control role. That’s the way the army is designed to work. However for the player to succeed in this context he must identify that the roles have shifted, and do it early. He must adapt to the situation by recognizing what’s important, what’s at stake, and what approach yields the best possible chance for success. (Note, if they are playing a scenario with no central objectives, like, say, Total Commitment, the tanky army could conceivably reject the Beatdown role and play for the minor victory by committing to a Control role focused only on its own objectives. If the horde army misplays, or if Variance produces some very favorable deviation, the path to a major might reveal itself). What’s interesting in these examples is that in both there are armies that, in order to improve their odds of winning, must adopt a style of play that is probably not what their owner envisioned when putting the list together. It reinforces the key insights of Who’s the Beatdown? In every game, and in every game-state within that game, there are two roles available to players. The first is the Beatdown role, which corresponds to the player with long-term disadvantage. Their best hope is to push tempo and maximize the benefit of their resources while they can in order to change the game-state into one with better long-term implications. The second is the Control role, which corresponds to the player that has long-term advantage. Their hope is to decrease tempo and preserve as much of the current advantaged game-state as possible. The bigger the long-term advantage, or the nearer it is to becoming inevitable, the more each player increases their unique disposition to risk, taking on more in the case of the Beatdown player, or taking on less in the case of the Control player. Let me know what your thoughts, reactions, criticisms or questions in the comments.
  5. Lemon Knuckles

    Crowdsource Points Project: AoS Gunkulator

    So, finally had a chance to rework the sheet to account for the tempo difference between melee and missle weapon profiles, and a few tweaks to the way range modifies pressure. The results are, well, interesting and shows the water-balloon effect in all its majesty. Seemed to fix the issues with range valuations noted quite nicely, but it did introduce some downstream effects. Problematic units that gunk seemed to identify correctly remain problematic, but a bit less variance than before: Girmghast Reapers, Morrsarr Guard, Witch Elves, Dire Wolves, Evocators, Sequitors, etc. Overcosted range units are now in-line with the exception of Kurnoth Hunters, and artillery was not broken in the process Arkanughts, Endrinriggers, Judicators, Arrowboys, etc. Some previously balanced units are now unexpectedly over/under costed VLoZD, Arkhan, Nagash, Skyfires, Lord of Change, etc. Some other big outliers are suddenly back inline Dragonlord, etc. Some other unexplained outliers from before remain outliers As always, if you can make sense of anything that seems off, and patterns therein, feedback appreciated. Updated Output:
  6. Lemon Knuckles

    1. Introduction: Why Theory, and Why Should I Care?

    @SuperHappyTime I just posted entry 4 and used "dearth" again. I guess I've unofficially started a campaign to bring that word back in circulation. Your point #2 is interesting, and resonates with my own experiences trying to get into the game. There is so much benefit from simply learning the rules, learning the units, etc. You will be overwhelmed and out of sorts if you don't do all of that work. But I'm hanging on to the belief that there are theoretical principles that subsist across all of these surface differences. I make analogies to MtG a lot, so here's another one. In MtG, there are way more possible cards and sets than in AoS with units and factions. But despite all of that, there are really only 9 fundamental deck archetypes that get recycled over and over again. Someone that has a grasp of MtG theory can quickly acclimate and understand an entirely new MtG environment. I'd love to see if we could replicate something like that for AoS. I'll probably be working toward your point #3. I just want to get there naturally on pace with the ideas that I'm trying to develop. There's lots out there available to help on #4. The Honest Wargamer and Just Saying are two AoS podcasts that are really great for that, and there are many other resources out there.
  7. There is a surprising dearth of theory regarding Age of Sigmar. I’m not sure why that is exactly. There’s certainly a lot of effort spent on list building. There’s a lot of effort spent on finding combos and unlocking synergies. There’s time spent on “creating a plan.” There’s time invested on computation aimed at solving very specific problems (aka math-hammer). There’s even a good amount of discussion about actual tactics and tactical play. But there’s next to nothing about theory. I suspect that’s one of the reasons that some people think that AoS is a game without any strategic depth. I disagree. I think the depth is there. What’s missing is the theory (the concepts and the framework) that makes thinking and talking about it easier, more accessible and more fruitful. I’m going to use this blog to try and build some momentum on this topic. I don’t know right now how it will turn out. It could be that the naysayers are correct and the game lacks substance. Or it could be that this will help map out some uncharted conceptual space “beneath the surface” from which we players can engage each other and the game in productive new ways. The endeavor will kick off in earnest with the next post. For now, I’ll just lay down some definitions for anyone who might not be completely comfortable with what we mean when we talk about theory, and how theory relates with strategy, tactics and having a plan. Theory is about the creation of concepts that have explanatory power. These theoretical concepts provide a clarifying lens through which we can look at the game in a way that helps us to understand it better. Strategy is about deciding on the best use of the resources available to us in order to win. Tactics are about how we specifically do each action we make in order to maximize the benefit of each decision made. Or simply, we can say: theory explains, strategy evaluates, and tactics execute. Or even simpler: Why, what, how. Considered this way, it’s perhaps a bit easier to understand why theory is a neglected part of AoS discourse, and to understand the implication of this neglect. Imagine your typical newcomer to the game. They are drawn in by a specific faction, by its lore or its look. They have some fun painting and modeling, but don’t have much success on the table-top. So they plug into the community and ask for help. Here’s my current list, help me make it better. Lots of people chime in with advice that helps the newcomer solidify a better plan. Drop this unit, add that unit, take this artefact, combo this thing with that thing and you will be able to do this really cool thing. The newcomer gets a few more models, makes these changes, and enjoys a bit more success on the table. Soon they are back asking for more help: I can’t beat army X, help! Again the community jumps in, and now their advice is more tactical. Make sure you screen like this and deploy like that, etc. And again, the newcomer takes the advice and applies it and enjoys a bit more success. And then the meta shifts, new armies are released, and the process starts all over. The point here is that the player is getting better with each step. They are learning what to do, and how to do it. And the rate of change across the surface of the game has sufficient velocity that the sense of learning and improvement can seem to go on indefinitely. If we can keep iterating on what to do (through list design), and how to do it (through improving tactical play), why do would we ever need to step back and think about why we’re doing it? The hope with this blog is that by exploring the why we allow for less imitating and more innovating. We flush out a strategic depth that persists across armies, and battleplans, and other superficial game changes. We improve our gameplay by expanding from just learning how to make a good plan better, to being able to ascertain, at any point, whether a given plan is still optimal, or even viable, and to successfully pivot to a new plan, to make different choices, in the moment, in the context of what’s most important right now. That’s the strategic depth that lies below the surface. That’s what I’d like us to explore.
  8. Nothing like a provocative title to kick things off. But sometimes the most important theoretical tool is the sledge-hammer. Sometimes old ideas have to be dismantled in order to create space for new points of view. Part of what I’m going to say grew out from the soil of discussions like this one. At stake in that conversation (which turned surprisingly passionate; so much so, that the mods had to intervene and yellow card the group) is the question of the relationship between a unit’s point cost and its value, and the relationship of that relationship to notions of fairness and balance. I was sympathetic to some of the assertions being made by both sides, but also deeply unconvinced by their conclusions. Resolving the problem, I think, requires looking beneath the surface and seeing the flaws in the foundational assumptions upon which the whole thing rests. The results have relevance to this blog and our efforts here to create a theoretical framework for Age of Sigmar. "We might say, the colour of the ghost is that which I must mix on the palatte in order to paint it accurately. But how do we determine what the accurate picture is?"--Wittgenstein One thing that everyone in the conversation agreed on was the fact that value (i.e. “tabletop value”) is contingent. Where people disagreed was on the claim that because of the fact that value is contingent, points, which are generalized, can never be “accurate” or “balanced.” A good example used in the discussion was the Bloodsecrator. How does one correctly cost Bloodsecrator given the “overwhelming” number of possible variables that could affect the computation of an ability like Portal of Skulls? The value of its +1 attacks component would not be the same if used to buff 10 Bloodreavers than if used to buff 80 Bloodreavers, etc., etc. Taken as is, problems like these seem unsolvable. But push the contingency of value to its extremes, and the assumptions underlying the problem become untenable. What is the difference in the value of the buff if the 10 Bloodreavers and the 80 Bloodreavers are both used successfully to take out a unit of 10 Skinks in a single combat phase? Even more to the point, let’s crystalize as many variables as possible to really flush out the contingency of value. The game is in the second turn of the fifth round and both players are tied on victory points. Player A has a unit of Skinks remaining. Player B has a unit of Bloodreavers and a Bloodsecrator remaining. The Skinks and Reavers are engaged in combat at the start of the turn. If the Skinks are holding an objective and the buff from Portal of Skulls is needed to ensure that the Reavers will inflict enough damage to outnumber the Skinks and take control of the objective, then its value is absolute since it is a decisive element for winning the game. If the Skinks and Reavers are locked in combat 9” away from the objective, then the value of the buff is zero since the Reavers need to retreat from combat past the Skinks and onto the objective in order to win. The combat itself is irrelevant. If the Bloodscrator is equipped with an artefact and starts the turn 7” away from the objective and the scenario is, say, Places of Arcane Power, then the value of the buff is absolutely negative, since activating it will prevent the hero from moving to claim the objective and win the game. There is nothing specifically unique about the Bloodsecrator in this example. The notion of the contignecy of value applies to any unit in the same way, and to the same possible extremes. The issue is not that abilities like Portal of Thrones are “complicated” and produce computational challenges; it is rather that questions of value are theoretical in nature, not computational, and that the domain of value is composed of actions and their consequences, not the units themselves. It is very often the case that nominal differences in calculated output yield no difference in theoretical value at all. Unlike value, points represent the investment required to obtain the capacity to do things; they represent a currency used to purchase resources. Points strive to create balance not through high-fidelity prediction of in-game value, but by creating an economy where access to key resources is restricted by a budget and a rational pricing scheme. I use points to invest in the capacity to create value in-game through intelligent play, but that capacity is not itself the value. Value and points are different things and are expressed in different languages. I consider it a design mistake whenever a battle-plan or a tournament ladder uses kill points as a scoring mechanism. Not because it isn’t “fair” (i.e. some armies will be better predisposed to offensive tactics than others), but more importantly because it serves as a poor heuristic for good gameplay. A strategy focused on forcing favorable exchanges of points is better than no strategy at all, but it is nonetheless a flawed strategy. Once we decouple the concept of value from the concept of points, we are free to rethink the game in a more theoretical way. My approach here will be to strip away everything down to its absolute foundational principles, and then proceed to slowly rebuild it, bit by bit, blog by blog, using only what flows naturally from these roots. So here comes my second provocative statement of the day: Age of Sigmar can be reduced to just three essential components. Everything else (everything!) is derivative. The first two essential elements are Time and Space. All notions of what we call Value derive from these two elements. The third essential element is Variability, which is an irreducible characteristic that governs the nature of play in the game. Derivative from Time and Space are the three essential capacities available to players as a means of generating value. The first is Presence, which represents a scalar investment in Space. The second is Pressure, which represents a scalar investment in Time. The third, Projection, is really a component dimension of Presence and Pressure by virtue of which these capabilities can be mobilized to contest an opponent’s Time (in the instance of Presence) or Space (in the instance of Pressure). We can say in purely abstract terms that Pressure attacks Presence, and Presence attacks Projection. In practice, our access to these capabilities is mediated through units (and the abilities, spells, effects that these units can mobilize), and all units necessarily contain some magnitude of Presence, Pressure and Projection. There is no such thing in actual game terms as “pure” presence, pressure or projection, although theoretically it is sometimes useful to think of them in pure terms in order to better understand their nature. Time, Space, Variability, Presence, Pressure and Projection. Six essential building blocks from which we hope to construct concepts useful for better understanding the game, and from which we hope to derive strategies to help better evaluate between the different choices that present themselves to us in game.
  9. Lemon Knuckles

    3. Housekeeping

    So in the last entry, we threw out some provocative statements and introduced a lot of terms in a way that seemed counter-intuitive to some people. This time around, I want to do a bit of house-keeping and tidy things up by unfolding these concepts a bit more fully and hopefully bring them into sharper focus. These concepts are important for what we are going to be doing, and if we ever do end up “doubling-back” (as one commentor cautioned me), then it will be less a regression and more a synthesis. So let’s revisit our six essential elements form last time: Space, Time, Variability, Presence, Pressure and Projection. Age of Sigmar is played on a Battle-field (usually 6’x4’ but not necessarily so). Take the meaning of the word field literally, and we can understand that the game plays out over a set of discrete, contiguous points of Space and Time. An individual point of Space is called a place and is understood by its relative position to all other places. An individual point of Time is called a moment and is understood by its relative change from all other moments (e.g. if I elect to “pass” during my shooting phase, for example, nothing has changed, no new moment has been created, no time has elapsed. David Byrne understood this when he wrote “Heaven is a place where nothing ever happens”). An individual point of battle-field (space-time) is called a game-state. Points (not points of the field, but points in the GHB… see how tricky words can get?) represent the currency I spend to assemble the resources with which I will play the game. For purposes of simplicity, let’s imagine an economy where 1 point = 1 degree of magnitude of a resource. There are, as we mentioned last time, three resources available to us. The first is Presence, which represents an investment in scalar Space. Investing in space means claiming a place, occupying it, asserting control of it and dominance over it. The degree of investment made represents the grip-strength with which I control that place. The size of place that my investment claims is determined by the base size of the model used to represent that investment. My control of that place is inviolate; no other model may occupy any part of that place. It is mine and mine alone. The most basic expression of Presence is Wounds. Imagine if a warscroll had only one stat, and that stat was Wounds. We could say of my purchase of a Witch Aelf, for example, that I invested 1 point to buy 1” of place at Presence 1. If I bought a unit of 10 Witch Aelves, we could say that I invested 10 points to buy 10 1” places of Presence 1, with a further qualification that the position of each of those 10 places relative to each other is constrained by the rules for unit coherency; or we could say for simplicity, that the 10 Witch Aelves form a unit and therefore represent an investment of 10 points for a Place with 10 Presence. If I add a second stat to the warscroll and give the Witch Aelves a Save of 6, I can now say of the unit that it represents an investment of 12 points for a Place with 12 Presence. If I add a third stat to the warscroll and assign the Witch Aelves a Bravery of 7, I can say that I have now invested 7.2 points for a Place with 7.2 Presence. Note that both the second and third values for Presence are subject to our third essential element of AoS, Variability. We can ignore Variability for now, but it will become relevant later. The second resource available to us in Pressure, which represents an investment in scalar Time. Investing in time means investing in the capacity to cause change. If I take my unit of 10 Witch Aelves and eliminate everything from their warscroll except the stats Attacks 2 and Damage 1, I can say that I’ve invested 20 points for the capacity of 20 Pressure. If I now add To Hit 3+, I can say that I’ve invested 12 points for the capacity of 12 Pressure. If I further add To Wound 4+, I can say that I’ve invested 6 points for the capacity of 6 Pressure. The third resource available to us is Projection, which is the introduction of the missing element (Time or Space) to the present element in both Presence and Pressure in order to create a vector of the two and by means of which we can mobilize these resources to interact with and effect the game-state. The Projection of Presence is movement. I change my place. The Projection of Pressure is range. I change your place. Projection is a dimension added to Presence and Pressure such that they can be expressed as a vector and has no independent value on its own. Projection increases the unit cost of the resource to which it applies. I pay a premium for each degree of Presence or Pressure I buy for each degree of Projection through which I can apply it in-game. 1 point of Presence costs less in a vector with movement 4 than it does in a vector with movement 8. All other elements of a unit’s warscroll can be seen as variables in these resource equations. Indeed all other elements that can interact with units in any way like artefacts, spells and abilities can also be thought of in the same way. When we flush out the complete warscroll for the unit of 10 witch aelves, we can say that the cost of the unit is the cost of the total investment in a particular bundled allocation of magnitude Presence and magnitude Pressure modified by magnitude Projection. Or: it represents a specifically allocated investment in space and in time proportional to their respective magnitude and vector speeds. Age of Sigmar is an objectives-based game. The win-conditions for AoS are outlined in various battle-plans, themselves subject to the principle of variance. Underlying the differences between battle-plans, however, is a common theme. There is specific space (places) capable of generating changes to the game-state (attribution of Victory Points) that advantage the player. A provisional and imperfect formulation would be to say that the point of the game is to have more Presence, persisting through more Time, in more of the places that matter, than your opponent. Which brings us to the most contentious part of the previous entry: the claim that units cost points but have no value. This claim is deeply problematic, and I remain conflicted about it. Someone I respect on the forums recently noted that my insistence on this point is frustrating. I will abandon it if it proves itself a useless notion, but until that happens I remain committed to playing it out and seeing what I has to offer. To do that well requires some reframing. How in game terms do we define value? It is a critical question, because strategy is quite literally the art of evaluation, the art of identifying one possible way forward as being more valuable than the others. It should be clear that we cannot simply calculate value in the same way we calculate points: differences in degrees of magnitude of Presence or Pressure or Projection do not necessarily yield differences in value the way they yield differences in cost. Further, the value of a game-state wherein a unit is screening or tagging a key threat, or occupying the critical space in a bottle-neck of terrain, or claiming an objective, is different than one wherein the exact same unit is not as relevant, even though there is no difference in that unit as unit (as a bundled allocation of resources of specific magnitude and vector). We can perhaps say of a unit that it is “valuable” in the same way that we can say of a Lego block that it is “buildable,” although that is still somewhat insufficient. I’ve been coached to try and keep these blog entries shorter. I’ve obviously failed, but will stop here so at least I can at least fail less. Please comment if you have thoughts. Your interactions definitely have “value.” Until next time!
  10. I've moved around a lot, but live in Colorado now with some family in Eastern Canada. Yes, Colorado is legal for recreational use, and no, I don't think that's why I write the way I do . I also travel a lot on business. Would be quite happy to sit with you and share some beer if the stars aligned.
  11. I'm sorry if it's been frustrating. I guess I'm chasing an elusive notion and pissing people off in the process. Sorry if that's the case. You've been generous in the discussion and I've learned a lot.
  12. We're both wondering that a lot, aren't we? To be clear, my "disagreement" is academic and not political. I don't have a stake in the outcome, I'm not advocating to change anything. I just want to understand and explore things. In that context, you've been fantastic to talk with. Any disagreement you sense on my part comes down to the question of Why? If points can never be accurate to value in the way you define (I agree) then it's logically clear that points cannot equal value. But it seems important to you to maintain that points equal value, and I guess I'm just trying to grasp what's at stake for you. Why is it important? What are the negative consequences to assuming the more logical view, or what benefit is lost if we abandon the less logical view. They Why? to me is the source of confusion, and disagreement such as it is is really just a desire to understand. I think the conversation has left Gunk far behind, but if it's at all helpful, I can tell the story. Gunk started, as most of these kinds of things do, as a little crunch I did to try and help me understand what I was buying and help shed light on list-building ideas. It originally had nothing to do with points at all. I just wanted to quickly calculate how much force I could bring to bear with different units, under different conditions. What the effect of this kind of buff or artefact might bring, etc. It then led me to comparisons, and then comparisons of different aspects, and finally to points efficiencies. If I needed "something" in my list, I could compare how much of that something I could get on a per point basis. It was one of those things that I imagine a lot of people do in different ways. An interesting thing happened when people started posting in the GW Wants Feedback for GHB 19 points discussion. People would say things like, "I feel Unit X should cost 20 points more/less," etc. And when out of curiosity I ran the unit through gunk, they were often "right" (whatever that word means in this context). Which is to say, people's feelings on what a unit should cost overlapped in a large degree with what gunk happened to say it should cost. Not always, and not exactly, but in the majority of cases, and directionally so. It made me curious the way people felt about units seemed to converge with what an objective math process said about those units. Which brought up the idea to focus on gunk and see if it couldn't be used to crack the code and reverse engineer the GW points system. If it couldn't help "explain" the system. The methodological premise was always that the GW system was (mostly) correct, but that there were outliers (as evidenced by people giving opinions on points updates) that could perhaps be better understood and contextualized once we understood how points currently work. So, in that sense, it was never about balance, but that doesn't mean it was against balance. Had a chance to read it today. Good, well-written article, and credible. Reminded me of my own experiences getting into AoS. I am late to the tabletop world. Never played WHFB or any other tt game. My initial experiences were completely overwhelming. I remember my first game. It was against a Slyvaneth list, and I had my hands more than full just trying to remember the rules and sequence of actions, and trying to remember what my guys did and when they should do it, and where they should be relative to other units in order for things to work. After deployment, my opponent had some allegiance ability that let him basically move all his guys around before the game even started. Blew my mind. And my mind kept being blown. You guy can do that? You have an ability that lets you do that? etc, etc. So much time spent looking at the app, at my books, at his books, at FAQs, etc. I think we played for 3.5 hours and barely managed to finish round 2. I get that complexity is a barrier to entry, and I think I've always advocated in other conversations for less complexity and less book-keeping. That's why I thought the Swedish Comp thing you shared was interesting but misguided. It's also why I said in my first theory blog that although thinking about the game theoretically can be creative, interesting and even fun, it will rarely be valuable in the sense that we'd be much better served from a "play better" standpoint by spending our time on just staying informed and current with the knowledge of what things exist and how things work, and by studying tactics. (I do hold out hope that theory can ultimately be applied to simplify the game and simplify in-game decision making, although the process of getting there might not be simple). Anyway, I get the sense from your sharing that article in particular, and also form the way you've used the Man A/B/C example in a way that wasn't how I was thinking it when I wrote it, that your Why? has something to do with balance, and community. I'm not sure I connect the dots to the points discussion though, as I think those kinds of concerns are much better addressed in rules design, battle-tome design, FAQs, rules overhead, etc. But I take those kinds of concerns seriously, even if I don't yet see the connection.
  13. Lemon Knuckles

    1. Introduction: Why Theory, and Why Should I Care?

    I have to switch gears a bit to follow, but I can tell you that the image of Liberators building latrines was worth the price of admission alone.
  14. I think everybody knows it. Every single person who has participated in this discussion readily acknowledges it, and no one has ever even hinted at suggesting otherwise. Points can be any way you design them to be. It is certainly possible to derive them mathematically. Yes, they will not accurately reflect value, but there is no methodology of deriving points that will. No matter what way you choose to design them, context will always matter, since value emerges from context. In fact, I'd rephrase what you said as "If points equaled value, then context wouldn't matter. Since context always matters, points do not equal value." By logical necessity, points exist outside of context. Now you might say, hey, we can analyze lots and lots of context and try to abstract something from that and then import that abstraction back into the points system. But there are at least two insurmountable challenges with this: Given the variety of people, strategies, context, etc., it will never be accurate on an individual level (maybe you could argue that it is accurate to some statistical abstraction) And more importantly, points themselves are part of the context. The second you import that abstraction back into the points system, you've changed the economy, and thus you've changed the context, and thus it is no longer even accurate to a statistical abstraction of what the game will be like going forward. New strategies and new valuations will emerge. It is infinite regress.
  15. Lemon Knuckles

    2. Your Units Cost Points but they have no Value

    @JackStreicher, @Overread Capacity is capacity. It is the potential to generate value. The string of a bow is capacity. If I notch an arrow, pull back on the string, aim at my neighbor and then release the string, it may or may not have generated value, depending on how you feel about my neighbor. Look, I am painfully aware that I am swimming upstream here. But the sledge-hammer metaphor is sincere. Words are not the things they refer to; words only define what we are allowed to think about the things they refer to. Creating the possibility of thinking about things in a different way necessarily involves reframing the meaning of certain words. For example, if you understand time as what’s on your watch, what I said about presence, pressure or projection is not going to make much sense. It would be hard to even understand how that kind of time could ever be an essential principle of AoS. But what is time in the context of the game? Allowing yourself to understand it differently, opens up the possibility of seeing the game differently. I don't promise anyone that the effort will be worth it. This may fizzle out, or run head-first into a wall. I don’t know yet where the implications of these concepts will lead. I will try to unfold them better and more clearly each time, and count on people like you to keep me honest. Appreciate the feedback!
  16. Completely agree with you It has its price driven by those things, not its cost. Its cost is its cost, regardless of perceived value. Its price is a reflection of the fact that we have a free economy, unlike points which is a closed economy. I did hold up the notion of a free market for points as perhaps as good a model as we could get to have points work the way you want them to, but it does seem impossible for practical reasons. Again, I completely agree. It remains a mystery to me how we agree on so much but follow those beliefs to two very different places. Although all these other factors are doubtlessly real, I'd like to continue to ignore them as relevant to the points system. Do see any problem with that? Thanks, I'll read it and let you know if I get anything from it. I also read this that you wrote earlier, and find it very, very relevant to our conversation.
  17. I am glad that we might be finding orbit with each other rather than just streaking past each other in the night sky. Perhaps it is reasonable to say that points reflect value the way chemistry reflects biology? I'm not entirely sure that lines up with what I have in mind, but good enough for now. The only thing different there versus a game like say MtG is the hobby aspect, the investment of time and emotion. I agree that it is a difference, but I'm not sure how relevant it is to competitive play. The minute we start talking about points, we are focusing on one type of gameplay only. And although these feelings exist, I'm not sure they are relevant in principle. They may be relevant because we want and agree for them to be so, but they are not relevant by necessity. When I played MtG, I was a mostly a Johnny, and favored the homebrew rogue deck over any of the established decks. My decks were rarely as competitive, but that's my choice and not a question of the balance of the game. Similarly, and touching on an example I used way back, the NHL is a competitive hockey league that creates "balance" through the implementation of a salary cap, and through a structured draft process. I think it is wrong to say that the league is unbalanced given that some teams are better than other teams, when that difference is due to differences in scouting, player evaluation, contracting, talent development, and coaching strategy. Indeed, the "meta" and "tiers" of the NHL are fluid, and change over time. There are no real dynasties anymore. That is definitely true, and opens the door for us to make normative claims about what we want points to be, rather than what they are, if we so choose. On what basis do we make that assumption? And what happens to balance the moment players realize that the can buy a Maserati for the same price as a rusted Jalopy? Players are smart enough to find and exploit that market efficiency. They will seize on it. Take the example of the most broken MtG card that was around back when I was playing standard... Skullclamp. It seems innocent enough on the surface as none of its effects seem particularly overpowering. But it was capital B broken precisely because it was priced wrong, because of the assumptions they made in playtesting about what people would do with it, instead of pricing it simply for what it was. But only because of the way you are defining accuracy. The Maserati gives me everything I need to price it. Labor, material, infrastructure and supply-chain costs. The price can't be effected by what I do with it. Why would a Maserati cost me less if I decided to park it on my front lawn and grow daises out the sunroof, or indeed because someone, somewhere might decide to do so? The value of the Maserati is emergent. The cost of the Maserati is self-contained.
  18. There is no underlying assumption about those things. They do not belong within the domain of what points refer to. We have all agreed that it is impossible for points to do so. You see the impossibility as a computational problem, and your answer is to go fuzzy, squint hard and guess. I see the impossibility as a conceptual problem borne from being slave to the notion that points = value, and therefore it exists only insofar as we are thinking about the problem incorrectly. It is akin to trying to solve a quantum mechanical problem with classical mechanics. It's impossible. But it's impossible because they are different languages, and the rely on different assumptions and different conceptual understanding. As soon as you recognize that it is not the job of classical mechanics to describe quantum phenomena, the problem disappears. You can insist that it should, and fudge a whole lot, but that is not a problem with the math, that's a problem with being stubborn and dogmatic. I have explained what balance is for me, in terms of value, a few times at least. Points by necessity can only speak about what's there. They can only speak of the unit. Value always has context, and must always speak beyond the unit. Balance in the pointing system occurs at the unit level. Balance in terms of value, in terms of an actual game state, does not. The game would be unbalanced if one strategy dominated all others. If Alpha Strike always won, if there was no reliable counter-play, then those armies best capable of playing Alpha Strike would always be advantaged, even in the abstract absent a definite game state. That would be an unbalanced meta. I don't think balance means that there should never be an advantage inherent in any initial game-state... there will always be good and bad match-ups. I also don't think it means that all armies and all strategies are equally viable across all metas... there will always be tiers. But the meta and the tiers are fluid, and change through time as things shift. As long as no one strategy is dominant, as long as multiple strategies and therefore multiple armies are viable, then the meta is balanced. And as long as the meta and tiers remain fluid, then the game is balanced.
  19. Three men each buy a brand new Maserati. Man A drives his down the Autobahn and says it's great. Man B drives his across a desert and says it's alright. Man C drives his through a lake and says it's terrible. Who's right?
  20. I wouldn't call it stark, and I definitely wouldn't call it a dichotomy. They are not opposed to each other, but they are different things, and necessarily so. Here's how I understand you: Balance = Accuracy Accuracy is when Points = Value You have said that Value can be influenced by things like scenario, terrain, opposing army, player skill, opposing player skill, etc, etc. This conversation has been focused a lot on how perfect accuracy is not possible, but it is perhaps more illuminating to imagine what things would look like if it was possible. Because as far as I can tell, such a thing would look like a game where any two players, regardless of differences in individual skill, could play any two lists, regardless of how well or how poorly constructed, from any two factions, regardless of how coherent or incoherent their respective battle-tomes, and have a equal chance of winning the game. There's already a game that's pretty much like that. It's called Heads or Tails. Now I know that this is not what you mean. But it seems to be the end result of what you are saying. And what I am saying is that if the logical consequence of framing things like accuracy and balance and value in this way leads ultimately to an absurdity like the above, then we need to pull out the sledge-hammer and redefine our assumptions. Because the assumptions here are not doing us any favors.
  21. I think this is an excellent thought experiment. Chess is an almost perfectly symmetrical game, except for initiative, the impact of which is effectively minimal. I think everyone would agree that it is balanced in the sense that the chance of white winning is equal to the chance of black winning, all of the time. If we turn Chess into an asymmetrical game in the manner you describe where each player could build their own material using points, then balance cannot possibly mean the same thing. It cannot mean that white and black are equally likely to win regardless. If that's what we still mean, then we are essentially saying there is no difference between a symmetrical game and an asymmetrical game. In fact, one way to understand the difference between the two is precisely through the reframing of concepts like balance. Now humor me as I get repetitive. Where I see a big problem with what you are saying is again when you conflate points with value, and where you ascribe value at the unit level. Points are the means of creating a restrictive economy wherein I must make decisions. I must make choices. Given the budget I have to work with, I need to decide what resources I want to assemble. The value of those resources is best thought through in terms of their relevance to my strategy. Units cost points, strategies generate value, units advance strategy through tactics. Our asymmetrical chess game would not be balanced if there was one strategy that could consistently beat all other strategies most of the time, especially if that strategy benefitted from initiative. If that were the case, then, theoretically, white would have an overwhelming advantage, regardless of what black chose to do or how black chose to spend its points. If, however, the value of all available strategies was directly influenced by the choice of opposing strategy such that Rock>Paper>Scissors>, it would be impossible to give either white or black an advantage in general, absent a specific instance of a specific game. What I've just written is not as precisely worded as I would like, and I'm a bit rushed for time atm, but the seed of what I want to call attention to is in there. I also think it is very important to reflect on how much you've hedged what you were saying earlier. You've introduced the concept of a "meta"-game in your last response, and I would challenge you to think about the implications of that, because to me it seems very, very relevant.
  22. I completely track with what you are saying. I don't track at all with why you are saying it. We seem to have radically different notions of what balance means. Within your framing of balance, everything you say is correct. But what you are saying is correct because is true by definition, and the "issue" is therefore insoluble, and unproductive. It seems pointless. I don't see the value of holding onto that conception of balance. I don't think any of it ultimately has to anything to do particularly with AoS, or even with math.
  23. Lemon Knuckles

    Crowdsource Points Project: AoS Gunkulator

    Thanks!
  24. @gjnoronh, @Fulkes, butting into your conversation..... I think it is a very false dichotomy. In fact, you had brought up the point previous that there could well be legitimate commercial reasons to introduce inconsistency into the points system as a means of driving sales for new product. Implicit in that statement is the idea that inconsistency yields greater inaccuracy (which under any reasonably constructed system it would). What that highlights is the problem with methodology, and it is the same methodological problem that I believe fulkes is making with his practical examples of how a consistent points system could work. It makes no sense to me to try and ascribe a points value to each and every individual stat in a stat-line. All stats are are variables in an equation. It is the output of the key equations that matter and that need to be pointed. Wounds, Saves, Bravery, Re-Rolls, Damage Prevention Rolls, Ethereal, Heals, Debuffs, etc., are all variables that calculate the Effective Number of Wounds a unit brings to the table. Attacks, ToHit, ToWound, Rend, Re-Rolls, Exploding Damage, Mortal Wounds, etc, are all variable that calculate the Effective Wounds of Damage a unit can output. The value of each and every one of those variables is directly influenced by all of the others in the equation, and it is meaningless to cost any of them on their own. Likewise, stats like Movement or Range or Fly have no value in and of themselves... their value is derived as a function of how they modify the utility of the Effective Wounds or Effective Damage with which they are associated. The problem I have here is with the notion that the insights gained from play-testing can be universalized into points in a way that can never be subsequently articulated mathematically. That just really doesn't make sense to me. It borders on a belief in magic. I absolutely agree that play-testing can and should be used to test and reform the mathematical assumptions, but what kind of knowledge is it that is gained from play-testing if we are forced to say of it "the unit should cost X but I don't know why?" I am highly skeptical and suspicious of this kind of assertion. Even if we say that X just "feels right," it seems wrong to say that it would then be impossible to solve for for a method that satisfies X. I certainly don't! That is part of the entire point of having different armies. I may want my Wanderers army to play like a Khorne army, and I am free to try and build it that way, but it would be wrong to demand of a points system to accomodate me in such a way that my Wanderers could do Khorne as effectively as Khorne could do Khorne. The obligation of any points system to ensure balance only extends so far. The players have responsibility too. Balance does not mean that I can just throw anything into a list and expect it to do just as well as a list that was carefully and thoughtfully constructed, regardless if both lists cost the same number of points. I take very seriously the assertion that AoS is more Rock/Paper/Scissors than it is Chess (I think you made that point, but I'm not sure). In that context, balance is not about ensuring Scissors and Rock are equally viable against each other, but rather about ensuring that Rock doesn't beat everything. All lists can do Rock, Paper and Scissors to varying degrees. Points is really about setting up an economy that governs how I choose to invest my resources into an allocation curve of Rockness, Paperness and Scissorness. If I decide to invest heavily into Scissorness, and part of the my scissorness comes from Rend, and I sit down for a game against Nighthaunt, all that means is I have effectively overpaid for Scissors relative to that game. It is basically an instance of "inconsistency" in resource price, but it is an "inconsistency" created by my choices as a player and by the game state, not by the points system. It may or may not impact value created in game, depending on play.
  25. I enjoy talking with you, however in this instance I feel like you've radically misunderstood what I've written. Of course the way we choose to allocate resources in army building is based on an assumption of projected value (and those who do it especially well do so within the context of a cohesive strategy). That's by necessity given how points and army building have to work in a universalized system with incomplete information. My intent with what I wrote was to explore the consequences of this assumption as assumption. The point, it seems to me, is that it is a mistake to continue this type of thinking once the actual game starts. It is wrong to play as if value in real game terms is simply an extension of the same mode of thought as points. They are different. How often do you hear someone say something along the lines of, "unit X is great... I killed 600 points with it yesterday." Does that necessarily tell you anything about the value created by that unit in that game? Within the pointing system, degrees of magnitude always represent degrees of projected value (to use your term). In game, however, incremental degrees of magnitude are often irrelevant. In game, entire vectors of force are often irrelevant if they lead to a less advantageous position. You seem to implicitly recognize this yourself when you mention target selection, unless you mean target selection as simply a computational exercise that projects value in the same way as points project value in army building. I think you are way too smart to mean that, though. If you don't mean that, then there are other principles at work in value, principles that are not in the domain of the points system.
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