I have recently been reading a book called How Life Imitates Chess by former World Chess Champion Garry Kasparov, in which he describes strategic analysis and decision-making as he has learned them in chess, and relates how the same techniques are applicable to decision-making in other areas of life.
In this informal article, I'm going to discuss how Kasparov's model for decision-making can help us to analyse lane-pushing games. Warcraft III actually gets a mention in the book as "a distillation of the MTQ concept", so I find this a particularly exciting and appropriate exercise!
MTQ stands for Material, Time, Quality. In the book, the factors affecting a decision are divided among these headings, and I will be applying the same categorisation to lane-pushing games. By analysing general approaches to decision-making, we can learn how to make decisions more interesting.
I am not focusing this discussion on any particular title, but I will draw on examples from various games (and chess) where relevant. I hope it might offer some fresh perspective on the genre.
"The fundamental building block of evaluation is material. Assets, stock, cash, goods, pieces and pawns, it's all material. We look at the board and the first thing we do is count the pieces. How many pawns, how many knights and rooks? Do I have more or less material than my opponent?"
In chess, Material equates to pieces. The game begins with a fixed number and distribution of pieces in play, and they are gradually removed from the board. In an RTS like Warcraft III, a match begins with almost nothing on the battlefield and players must build up their material over time: choosing soldiers and technologies according to their needs.
Much of this material will be lost in fights, but essentials like upgrades and factories are usually there to stay. Let's examine how material appears in a lane-pushing game:
- Like chess, we have material which will leave the board, never to return. Towers and other buildings exist from the start of the match, and are gradually demolished.
- Like an RTS, there is material which will enter the board and is there to stay. As players gain gold/experience, they form wealth which will materialise as items or talents. In general, players don't have established wealth taken from them, as this is snowbally and feels bad.
- Unlike chess or classic RTS games, some material will (re)enter the board at a fixed rate. Troops are a perfect example: no matter how many troops are lost, the fact that a team "has troops" won't change, even though in the short-term their quantity can vary. I refer to this as dynamic material.
Lane-pushing games use a lot of dynamic material, and that makes it an important subcategory for us to understand. Other common examples of it include:
- Jungle camps and bosses are valuable assets which can be defeated, but will respawn at a fixed rate.
- Wards and smokes in DotA restock at a fixed rate.
- Heroes flow back into the game after being killed, at a predetermined rate.
In the short-term, we can gain an advantage in dynamic material by eliminating enemy material. Killing enemy troops will result in having relatively more of our own; killing enemy heroes allows us to outnumber the survivors and get things done.
The fixed rate of re-entry is important, as it determines the window of time for which one team will hold advantage. While dynamic material flows onto the board at a fixed rate, the rate at which it leaves is variable and controlled by the players to create temporary localised advantages.
Often, dynamic material has some soft limit on how much will flow into the game. For example, troops tend to collide and annihilate, jungle camps do not spawn if there is an existing camp, and there is a limit on how many wards will be in the shop at once.
Players need to make a conscious effort to circumvent these limits. If this wasn't the case, the map would end up swamped with units!
Non-dynamic material, which is permanently gained and lost, is known as long-term material, or just Material. Surprisingly, most lane-pushing games have only the two types mentioned earlier: wealth and towers.
DotA additionally has super-creeps or mega-creeps, whichare a permanent advantage once achieved. Contrast with League's super-minions, which are dynamic because they only last for a limited time. It is valid to consider the rate of a dynamic material as a long-term material.
For example: consider that a jungle camp could be "destroyed" by reducing its spawn rate to zero. Simply reading that sentence is a bit jarring, because of how pivotal such a mechanic would be.
That's enough about dynamic material. For the rest of this article, we are primarily interested in long-term material.
In chess, both armies start out in tight formation, with the more powerful pieces boxed in behind a row of pawns. As the game progresses, players develop their pieces: getting them off the back lines and into the field where they can pose a threat.
Kasparov brings up the notion of board time: how many moves it takes to get a piece from A to B, or to get several pieces in position. Since players take turns to move, it would seem that both players should be moving or developing at the same rate, but in practice this isn't the case.
For example, suppose there is a white pawn with no pieces defending it. A black knight could capture this pawn on one turn, white might develop a piece which threatens the knight, and then black's knight retreats to its previous square. This would have no net change for black's position, and hence contributes nothing to black's development.
White might be happy to let the enemy knight run, knowing that the 'extra' turn bought time to move pieces into a better position, or eke out some other advantage. This is an example where the white is exchanging Material for Time. In the right hands, board time is a very valuable commodity.
Being a move ahead allows one player to set the pace of the game, forcing the other player to react. The seemingly tiny asymmetry in chess of white moving first has great statistical significance:
"At the Grandmaster level, white wins 29% of the time, black 18%, and 53% of games are drawn."
In a lane-pushing game, a time advantage must be quantified in seconds, since the game happens in real-time. Every action, like pushing down a tower, or running across the map to defend it, takes a certain number of seconds.
When one team can accomplish an objective before the other team can arrive to stop them, that's a time advantage in action. The simplest case of a time advantage is the enemy being too far away from an objective to intervene, but a more damning case is when the enemy is simply dead and unable to act until they revive.
It doesn't matter how much material a team has, if they can't put it to use where it counts. We can draw a link between time and mobility, particularly on the global scale. If heroes could teleport freely around the map, no-one would ever be late for an engagement!
Since the maximum time lead in a lane-pushing game is rather short, using and maintaining a time advantage is difficult. The onus is on the players not to dawdle, but instead to milk every second they've got, particularly when material has or is being exchanged to keep the enemy players at a distance.
"Space created!", yells the dead player who has kept the enemy team occupied with hunting them down; leaving it to the rest of their team to make use of the extra time that has been bought.
Indeed, "space" and positioning are intertwined with the Time heading. Outpacing the opponent in chess is more comparable to outmanoeuvring in a lane-pushing game than anything else.
"We often talk about having a 'good' bishop and a 'bad' bishop, and this jargon provides insight into the qualitative differences of material things. The bishop can travel as many squares as it likes in any diagonal direction, but only on one colour of the board." "If many of the squares of the bishop's colour are occupied, its mobility is extremely limited. Such a bishop is called 'bad', but its intrinsic nature is no different from when the game started. Its quality has been diminished by the circumstances around it."
Quality is defined by usefulness, given the situation. Players should always be looking to improve the quality of the material they have.
Of course, there are an enormous number of factors that affect the any given unit's usefulness, all of which must be evaluated in real-time. The difficulty of this calculation is one of the greatest challenges of the genre, and also one of its great attractions.
In chess, the intrinsic quality of each piece is fixed: a Queen is strictly better than a Rook. But chess is a very positional game: a Knight might be trapped uselessly at the side of the board for most of the game, and then suddenly become relevant later on. Even the humble pawn can rise to the power of a Queen if the board is right.
Fundamentally, quality is always defined relative to the board state. How does this manifest in lane-pushing games?
We know that a carry will find greater relevance in the late-game, because its intrinsic value increases exponentially with each item due to multipliers.
The increasing game clock is one way in which the board state is changing, but what about others? Towers fall, the number of troops might increase, and certain niches like split-pushing or defending base entrances become more valuable... but the change in game structure is relatively minor compared to chess, and I wonder if more could be done to explore heroes becoming relevant in new situations.
In most lane-pushing games, board state is largely determined within menus. Drafting and character selection set out the initial pieces, with choice of items/talents adding variations throughout the game.
Having these choices wrapped up in the UI, which are mostly made relative to other choices that were made in the UI, means that Quality is a much less tangible category than material or time. If we want to change this, there would need to be a way to influence the board state in a meaningful way.
Being able to affect the element of League of Legends' elemental dragons, or a means to permanently modify the terrain could be potent examples that affect further item choices. Lane equilibrium and warding/vision count as part of the board state. These are generally short-term concerns, but are certainly important.
Intrinsic to the MTQ system is the idea that material, time, and quality can be interchanged, and practical decision-making involves evaluating what we have, what we need, and where we're willing to make trade-offs to exchange one for another to achieve better utility.
To theorise, the ideal "most interesting" game might support a system in which all three categories are constantly being weighed against each other, with players making calculated trades and compromises between them to defeat their opponents.
It is important that trading be inefficient and rationed, otherwise having an abundance of one category would give teams the flexibility to convert to exactly what they need on-demand. But, is allowing interchange between all three really the best approach? Let's break things down by considering each of the possible exchanges:
Material for Time
DotA makes for an interesting case study. It's standard practice to invest gold (material) in teleport scrolls, a consumable which allows players to save time when moving around the map. The item is cheap enough to almost always be worthwhile, since the resources gained while out in the field will almost immediately recover the cost. Only very late into the game will players consider exchanging time back for carrying more material; dropping their teleport item in favour of more damage.
What if teleporting in DotA didn't cost gold, but instead drew from the other long-term material on the map: tower life? It would be a harsher exchange and likely "less fun", but there is something clinical about it that would make people think.
A weightier mechanic than teleports is the buyback (pay gold to revive immediately), which can buy a lot more time, but at considerable material cost and severe limits on its usage. In the 6.83 patch, buyback availability proved to be the major consideration in high-level DotA tactics.
Buybacks generally count as an "inefficient" trade, since players can't recoup the full material cost during the time they bought unless they manage to net several kills. However, it is often still the right decision, to defend an objective or otherwise, which is what makes it add depth to the game.
It is important that buyback availability be limited, both to avoid large material leads negating time advantages, and to ensure deaths still matter as the game's narrative implies they should. It is also worth noting that reserving the gold for a buyback usually means not having bought an item, which means the hero has less material value.
In chess, threatening checkmate allows a player with a time advantage to force defensive reactions from their opponent, disallowing them from using their full army and even using their material against them as they struggle to manoeuvre around their own pieces.
Sacrificing some material can be worth it to mount an attack on the enemy king, because once in check, their army is only as good as the pieces that can usefully defend.
Time for Material
What about the reverse, exchanging Time for Material? In theory, this is happening whenever a player is in an unhelpful, poor, or immobile position, but gaining material as a result.
In a well-designed game, the more out of position a player is (the worse their Time), the more risk they are taking, and the more they should be rewarded for it (with Material). Sometimes this takes shape in the form of invading the enemy jungle to tap into an otherwise risky resource, or diving a tower at great risk to finish off an enemy hero.
Split-pushing also fits this definition, and often split-pushers are heroes with escape mechanisms to overcome the disadvantage and risk of poor positioning. The presence of teleports in many games reduces the Time cost in this exchange, as you're not running late until there's somewhere you need to be, and teleporting lets heroes arrive on time to respond, regardless of where they were.
Are teleports a healthy mechanic, if they make this type of trade too forgiving?
Material for Quality
Here, we'd need to let players pay material to enact changes to the board state. The simplest example is "buying wards", though vision is so precious that the material cost is rarely considered.
To imagine a more serious exchange of material for quality, suppose we could spend gold on terrain deformation, permanently altering the troops on a lane, or upgrading a tower to be immune to heroes but extra-vulnerable to troops.
Any of the above would change the way the remainder of the game would be played, though we must be conscious that players will look to optimise their use of these features and none should be able to reliably de-fang the enemy draft.
While this is relatively unexplored territory among the commercial games, many of Warcraft III's AoS maps allow players to spend their material on reinforcements (a dynamic material), repairing towers, or many other 'Quality' options (such as buying True Sight for their towers).
Time for Quality
Time equals positioning, so here we're inspecting bad positioning that produces a more favourable board state. Split-pushing again serves as an example here, as split-pushers often aim to force a favourable lane equilibrium at the risk of their safety.
Another benign example would be the ability for a hero to enter an uninterruptable state of stasis for 2 minutes, to seal an entire lane in stasis for 2 minutes. Being "down a player" puts the team in a bad position, but the change in board state might be a qualitative improvement as there's less lanes to defend.
Quality for Material, Quality for Time
It's a bit tricky to discuss "trading away quality", since that sounds bad by definition! It's also difficult to decouple a less favourable board state from a loss in material, since so often the board state is determined by which buildings are still alive.
To give at least one example, suppose players could choose to burn their ward items for a sum of gold or to repair towers: reducing their team's potential for vision (which forms part of the board state) but allowing them to amass more material.
We mentioned earlier in the article that there is both dynamic and non-dynamic Material, and we've seen examples of how these can be prioritised. The idea of dynamic versus non-dynamic also applies to Time and Quality.
If a player could not teleport for 10 seconds after dealing damage, then clearing an enemy troop wave would create an advantage in dynamic Material, but a short-term disadvantage in Time.
Ultimately, our goal is to provide players with a volume of options that is manageable, and to make sure that deciding among them is non-trivial.
Viewing the game through the MTQ framework helps us to describe the nature of each option as an exchange between two of the categories, and makes it easier to evaluate the results of that exchange, and how to tune its efficiency and limitations.
For me, one of the more interesting observations from writing this article is how towers have relatively little involvement with decision-making. It's quite rare that players can improve the quality of their towers, or "spend" them to gain advantages in other areas.
Considering they are the one case where we really are losing material (gold gain is often correlated with other choices, or recoverable), I feel they deserve to be experimented with more.