Tuesday, July 12, 2011

The Math

Here's the plan for the math. I'll introduce it and then I'll explain what it all means in a bit more depth. You'll have to click to enlarge and might want to put it in a new window to be able to reference and read simultaneously.

The game spans 15 levels and is roughly broken into three tiers of 5 levels each. I am not planning a big shift in the game at each tier like 4e; it is one fluid progression. The tiers are used for when things are able to increase (for instance, an option to customize a monster adds +2 damage at 1-4 and +5 damage at 5th level and higher).

The first set of columns are core numbers that are relevant to pretty much everything. They are the level bonus (1/2 level) and your stocks. Stocks are received at every odd class (as opposed to character) level and, for the most part, improve attack and defenses by +1. Stocks also have a rider power, like granting a handful of hit points, increasing damage, increasing wound threshold, and so on. There is a bit more nuance to it all, but that is the framework.

The importance of the "primary stock" versus "secondary stock" is the order in which they are taken. Because you only get a single stock at first level, and a stock improves attack or defense, you have to decide which one to improve. The one you improve first is the primary. Looking back at the "secondary stock" column, we then see that the table assumes you improved the secondary stock at 3rd level (when you'd get your next stock if you are a single class character). This is illustrated more clearly in the table below. The titles "primary" and "secondary" have no meaning in the game--you don't *really* even call them anything different. They're all just stocks. The reason I include it here is for clarity and completeness.

The remainder of the table bases all math on the premise that you are using your primary stock. This means that at various points (about half the levels--look at levels 1, 2, 5, 6, etc to see what I mean) the math assumes you are +1 better than you actually are at about half the things you do. In light of self-selection in actions, this doesn't have a big impact (not to mention that the game can stand up to a +1/-1 variance with ease).

I want to dwell on stocks a moment longer and talk about the different ways a player can customize a character through the stock selection. The stocks a class provides build on each other and are designed to be a progression. They also have higher requirements. For example, the Rogue has the following progression of attack stocks:

Deft Strike 1 (Attack 1)
Gain a +1 bonus to attacks with light or agile weapons. Gain a +2 bonus to initiative.

Deft Strike 2 (Attack 5)
Requirement: Deft Strike 1 or 11th character level
Gain a +1 bonus to attacks with light or agile weapons. Gain a +2 bonus to move checks.

Deft Strike 3 (Attack 9)
Requirement: Deft Strike 2
Gain a +1 bonus to attacks with light or agile weapons. Gain a +2 bonus to initiative and move checks.

Let's focus on the parenthetical. The word "Attack" just means that this stock is an attack stock. You can only ever have 5 of any one type of stock. The number is the minimum Rogue score needed to be able to take the stock. In this way, you cannot dedicate all of your stocks to, say, attack because you aren't a high enough level. Finally, the stocks generally improve, so you are encouraged to complete your track for the payout of the higher stocks.

Here are some sample progressions for how a character could pursue stocks:

The first progression is the assumption of the game. You pick one stock as your primary and alternate back and forth. The second progression just shows that you wouldn't *have* to do it that way and you could jump back and forth if you decide that you want to improve defense twice in a row or whatever. The third progression shows an ambitious approach involving multiclassing. This character aggressively multiclasses to get more stocks (from 1st class level) and puts them all into attack. This gives him an early boost in attacking but will cost him later on in that he won't be able to take as many of the higher level stocks. Long term, the character is not much better off numerically and continues to miss out on the riders of the higher level stocks.

There are a number of additional limitations of this aggressive approach. Many stocks have a built in limitation (such as the rogue attack bonus only applying to light weapons). If you take too many stocks from too many classes, you'll end up limiting your overall versatility. An even larger limitation is that you are aggressively taking stocks to improve numerically, but by not developing any one class you limit the potential of your "edges." To discuss edges, we return to the table up top.

Edges are the second set of columns under "Attacks." The concept here is that we develop a base number for your attack (ability + stocks) and then, usually, add a single number to it. By only adding a single edge to an attack, we can cut down on the problematic synergies that arose when bard song + charge + flank + higher ground + etc turned into an auto hit. If you only apply a single edge, there is always a single meaningful tradeoff that you are balancing. Quick and easy.

The first column titled "Edge" is the expected value when you activate a power that helps only you. For example, "Careful Aim: Action Point; add your rogue modifier to your next attack roll as an edge." You can spend an AP to have a good chance to hit. The second column titled "Group Edge" is the value of abilities that characters can activate and other party members can piggy-back on without personally having to spend an AP. A classic example would be bard song, but many classes have similar powers. Sometimes you can just freely add the edge (note that it still fills the one-edge per attack rule) and other times you have to do something to add it like use a maneuver (move action) to move adjacent to the ally.

You ability + stock + edge basically equals your attack roll. It is possible for things to add subsequently, but they are fairly rare. More often a character will choose to forego an edge that increases attack for some other benefit, like an increase in damage or the ability to ignore DR. In this manner, the mechanical constructs of stuff like Power Attack are actually embedded into the math. Instead of subtracting from your to-hit, you just don't add anything. It saves a step and better keeps things in line.

The next set of columns titled Defense just shows the expected progression of magic item bonuses to defense or the inherent bonuses people will give out to keep things balanced. Similarly, the "Totals" set of columns just sums Level Bonus + Primary Stock + whatever the header of the column says.

The next set of assumptions comes under the "Attributes" section. The game presumes an average stat modifier of +2 across all defenses. It is unlikely that characters will actually have this (at least to begin). So then why assume it? Because of self-selection and the power of pooling resources. Players will find ways to minimize the importance of certain defenses to their character, rules will be developed that allow you to replace Strength with Cunning for Fortitude or whatever. What is expected is that the average of defenses *important to the character* will be +2.

The assumption on attack stat is similar but embeds the idea that some weapons are +1 proficiency weapons (equivalent to the +3 weapons in 4e). Characters will either have a +2 with a +1 weapon or a +3 attribute. Granted, some characters will have a +2 attribute with a +0 weapon and other will have a +3 attribute with a +1 weapon. This is an average.

Finally we get to the "resulting scores" that show the expected bonus to attack and defenses. The attack bonus is calculated on the "Group Edge" total and it is the group edge that is the presumed default attack mode. The impact of the resulting scores is shown in the "Hit rates by attack mode" set of columns. The darker green shows, again, the group edge hit rates which are the default assumption of the game. We see that it is 60-65% across all levels. If you expend resources to use a personal edge, that number ticks up to as high as 75%. In the alternative, if you use your edge for something other than a bonus to attack, your hit rate steadily declines. The benefits in lieu of attack are balanced accordingly and there are many ways to try and improve this through teamwork or exceptional powers.

As a final note just to tie some disparate ideas together--I recently talked about "a provoke" providing a generic benefit against the provoking creature. That benefit is that you can apply a second edge to the attack by using a provoke. Immediately, we see the potentially awesome scenario of using a personal edge to have a high hit chance and then a provoke to increase damage.


  1. Regarding edges:

    The difference in bonus between an edge and a group edge is 0 at lvls 1-2; 1 at lvls 3-6,12-15; and 2 at lvls 7-12.
    In other words, when you compare the difference between edges and group edges to the actual bonuses, the difference is non-existent to start, significant but not crippling for a while, and barely significant towards the end. These differences are blown out of the water by the ability to confer the group edge to multiple characters at once.

    Edges are tied to a limited resource, implying that there will be more rounds of combat than points to spend activating edges. So players will immediately try to find ways to maximise the number of "edged" character-rounds within the party. So for a group of 4 characters, activating a group edge gives 4 character-rounds of bonus per action point. If everyone takes group edges (and why wouldn't they with such a payoff?), the group can spend as many rounds as there are total action points among them with every character claiming edge bonuses. What incentive is there to bother with normal edges, when the bonuses are so small and erratic compared to group edges that benefit everyone?

    Have I misunderstood how/why edges will work?


  2. The math is premised on the belief that an edge will basically be applied every single round to every single attack (there are routes to get multiple attacks like two-weapon). Often the edge will be a group edge (like bard song) and that has the benefit of being a single resource allocation like you comment.

    I think you undercut the benefit of upping the attack by +1 or +2 by activating the personal edge, though. Think what people will go through now for a +2 bonus and then imagine if such bonuses are harder to come by. I also wouldn't describe them as erratic since they are entirely within the control of the player.

    To get a better handle on this, the two articles about the Indifference Line (and Difference in Indifference) help drive the point home. As you increase in level and damage is increasing, the value of any given +1 to attack also becomes more valuable. The game begins close to the indifference line so the variance among edges is similarly low. "Do I want +1 atk or +1 dmg?" They are about equal at low levels and so you are able to trade them freely. At higher levels, that +2 atk is worth +3 (or +4) more damage and so the relationship has to change.

    A few more points that are useful just in general. First, recall that flank is an edge that basically gives +2 atk. Since this is available at first level, it is actually one of the best things in the game to start. But, it requires a move action and an ally, so it isn't always possible. Sometimes you just don't have those resources.

    Second, many group edges aren't free to apply and similarly require a maneuver to benefit from. The straight up edges tend to be free actions in addition to providing a higher bonus.

    Finally, getting the group edge to +4 at the end takes a little dedication on the part of the character. They default at +3 but can get up to +4. The impact if you forego this opportunity is just to continue the relationship from 7-12 into 7-15.

  3. Maybe you have answered this somewhere but how many sources of edges do you expect a given character to have? Right now I count at least four mentioned (with some questions as well).
    -class power (from an Action Point)
    - the group edge (unsure how these work, an example would help me see why this isn't the best way to go from a party optimization sense)
    -combat maneuver (is it really better to flank than anything I can do with my action points until 3rd level?)
    - feats/things that duplicate power attack or whatever you mention in this post.

    While the edges themselves are simple enough to apply it seems like you could amass a great deal of them on a character that require some thought for each attack which only ends up slowing things down. I understand, and approve, of removing the subtraction element and the idea of stacking half a dozen bonuses, but in so doing this system runs the risk of making each attack have several considerations. Even more so, the fact that the system assumes you use an edge but each edge has a cost beyond the standard action (move action in a condition or an action point)- won't that complicate the decision making process even more than the problems you are trying to fix by going to the edge system?

  4. There isn't a set number, but I expect characters to have access to a number of sources (even at low levels) and gain access to more at higher levels. There is a natural deterrent from taking *too many* edge based power, though, in that you can only ever use one at a time. My gut is saying that it'll be in the 3-6 range for most of the game.

    To run through your list:
    -- Class power are the big source of the personal edge that provides the big modifier
    -- Group edges aren't really a term per se, it is just "an edge" but the modifier improves at a lower rate. For ease of communication at this stage, I'm using the term group edge but I sort of hope it does not catch on. I'll give two hypothetical examples (i.e. neither exist just yet).

    Bard Song. AP to activate, sustain move. Range close. Any ally can add +X (improving at group edge rate on the table) as an edge to attack.

    Master footwork. AP to activate, stance. "Your masterful footwork forces your opponent to leave himself vulnerable time and time again." Add +X (improving at NORMAL edge rate) as an edge to your attacks. In addition, all allies in the zone gain the following maneuver:

    Maneuver: "Wait for it..." Costs move action. Add +X (improving at group edge rate) as an edge to your attacks until the end of this round.

    So in the first instance the bard song is a clear choice for group optimization, but it costs the bard a fair amount. I also imagine that the bard will be the king of group edges. Most group edges are more similar to the second hypothetical where a beneficial rider follows on a selfish action--but the rider costs something extra (like a move action to activate a maneuver).

    In this way, group edges are commonly available but not always optimal. If you just entered a zone, you don't have a move action to spend on the maneuver. Sometimes other maneuvers are more attractive. Sometimes you want that incremental +1 that a personal edge grants.

    --Flank. Flank is strong at early levels but still not dominant. Recall the knight's example power of "Rally on me" that gives a maneuver to stand adjacent to the knight to get +2 defense. You could maneuver into flank (+2 atk) or maneuver next to the knight and use an AP for a personal edge (+1 atk, +2 defense). In addition, all of the discussion above about limited maneuvers pertains to flank. Finally, recall that some edges also provide bonuses to dmg and there are definitely times when you'd prefer dmg to atk. So lots of tactical tradeoffs.
    --Feats/things. More "things" than feats. I am even bantering around the idea of limiting some magic items powers by making them edges instead of straight bonuses, but not sure just yet.

    So all of that draws into your main question--won't this be complex and isn't complexity slow?

    There is tactical complexity, but it is choosing amongst basic decisions that are quick to apply and are applied to the same basic numbers. The familiarity breeds speed. Compare this to 4e where you have 5-10 powers but each power is basically its own sub-system with multiple moving parts. Or, compare this to 3e where the complexity came from micro-managing a dozen little benefits that build into something huge. You need complexity to sustain people's interest, but just because it is complex doesn't have to mean it is slow.

    Second, and I think this is important, the difference between the perfectly min/maxed guy and the casual guy is fairly small. The optimizer will be better, but still similarly challenged to his casual counterpart. The impact of this is that slower players can make simpler decisions without suffering or lagging behind.