The Case for Score Systems in Single-Player Strategy Games




I have argued for a long time that score systems are superior to win/loss systems as endgame feedback mechanisms in single-player strategy games. I believe that there are significant advantages to score systems, and no significant disadvantages, so all single-player strategy games, going forward, should adopt score systems.

There are three main advantages that score systems have over win/loss systems. They 1) eliminate forgone conclusions, 2) provide better feedback on player performance, and 3) eliminate the need for multiple levels of difficulty.

Clarifications

Before going into detail about the advantages that score systems have over win/loss systems, I want to make it clear exactly what I have in mind when I make that distinction.

A "win/loss system" or "binary system" is any system in which there are exactly two possible outcomes to a given match, "win" and "loss", and a "win" is designated as a better outcome than a "loss". In a win/loss system, the player's goal is to end the game with a win.

A "score system" is any system in which there are more than two possible outcomes, and each possible outcome is assigned to a real number. This number is called the "score", and one score is better than another score if and only if it is greater. In a score system, the player's goal is to maximize their average (or "expected") score.

Some games that may look like they use a score system don't actually meet the criterion I've described. In particular, many games that involve "scores" expect and encourage the player to try to "beat" the highest score they've previously achieved. That goal is different from trying to maximize the average score, so I do not count these as score systems. In fact, they are a type of win/loss system, because the outcome of a match is binary: you either beat your previous score (a win) or you don't (a loss). I don't think this type of system is good, so when I refer to "score systems" in the rest of this post, I'm referring only to systems in which the goal is to maximize average score, not to pass a binary threshold.

In many cases, the only thing that incentivizes a player to aim for beating their precious highest score, instead of maximizing their average score, is the fact that the game software tracks their highest score, but not their average score. It's nice to have a single number as an emblem of a player's current skill level, both so that they can see their progress over time and so that they can be ranked on leaderboards. The highest score a player has ever achieved is a decent choice for such a number, but it isn't the only number you could use. Instead, you could calculate, after each match, the average score of the last few matches a player has played. That number will rise as a player improves their skills, so it can be used to show a player their progress over time, and it can also be used to rank players on a leaderboard. The difference is that this way of measuring player skill encourages the player to maximize their average score in each match rather than trying to beat a binary threshold. Micahel Brough's game P1 Select uses a system like this, as does my own game Brazen Berry Bonanza.

In most existing games with score systems, the score is a quantity that starts at 0 at the beginning of the match, and then increases by some amount each time some kind of event occurs in the match. Often there are many different types of events that increase the score by different amounts, but there is no reason that all score systems must be like that, and I think those types of designs should generally be avoided. In Brazen Berry Bonanza, there is only one action that increases score, and it always increases score by exactly 1 point: picking a ripe berry. Additionally, in most games with score systems, the score has no effect on the rest of the gamestate, and it never decreases. Again there is no reason that all score systems must be like that, and I also that those types of design should also generally be avoided. A score could be treated like a resource, which can be both gathered and consumed, or exchanged for other resources. A score could even be a quantity that doesn’t exist until the very end of the match, rather than being something that accumulates over time. All that a score system is, fundamentally, is a way of assigning a numerical value to the gamestate at the end of a match. Existing score systems, and the design patterns common to them, represent only a small corner of the space of all possible score systems, and more effort should go to exploring different types of score systems.

It is important to understand that when I say that players should "maximize" their score, I am referring only to the value of the score at the end of the match. A player should not care about their score before the end of a match, except to the extent that doing so helps them maximize their score at the end of the match. If a player is choosing between two plans, A and B, and they expect that plan A will give them 5 points immediately but result in an average score of only 20 at the end of the match, while plan B will give no points immediately but will result in an average score of 30 at the end of the match, they should choose plan B, despite the fact that their score will be lower in the short term. Decisions like these, in which the immediate score payoff of a decision can differ significantly from the long-term payoff, will occur regularly in any interesting strategy game with a score system.

There are some games that use score systems where a lower score is better, rather than a higher score. Examples include golf and speedrunning. This difference is superficial, so for this post I will talk only about score systems where the goal is to maximize the score, rather than minimize it.

This post focuses entirely on single-player games rather than multiplayer games. There are several reasons for this. For one, I'm personally more interested in the design of single-player games than multiplayer ones. Second, multiplayer games almost unanimously use win/loss systems, and it isn't obvious how a multiplayer game with a score system would work. Many multiplayer games do involve a quantity that they call "score", but generally this quantity is merely used to determine who wins and who loses, so each player still ultimately receives a binary outcome. There’s no fundamental reason why someone couldn’t design a multiplayer game in which players are intended to maximize their scores rather than aiming for the binary criterion of "beating" the other player, but such a game would likely be very unintuitive, and no examples of something like that actually exist, as far as I’m aware.

There are many strategy games that don’t fall nicely into either of these categories. For instance, some games normally end in a win or loss but occasionally end in a "draw" or "tie" (this is most common in multiplayer games, but some single-player games include it as well, especially those in which the player plays against an AI intended to simulate a human opponent). In such a system, it isn’t clear exactly what a player’s goal is. Presumably a draw is somewhat worse than a win and somewhat better than a loss, but how much worse or better is it? Generally, games don’t provide a concrete answer to this question, so the goal of the game is ill-defined. Similarly, some games give the player both a score and a win or loss at the end of the match. Systems like that suffer from the same problem as games with draws: the goal is ill-defined. Should the player try to get a win, or get a high score? Presumably they should do both, when possible, but in cases where the player has to choose between winning and getting a higher score, which should they prioritize, and to what extent? Games generally don’t explicitly answer this question. Cases like these, where the goal of the game is ill-defined, are ignored for the purposes of this post. Strategy games that are not match-based (by "match-based" I mean a game where play consists of a series of distinct matches, each of which is completely causally independent from all other matches) are also ignored.

Eliminating Foregone Conclusions

A forgone conclusion, in a strategy game, is a situation in which the player knows whether they will win or lose before the match actually ends. For instance, if you play very well or get lucky in first half of a match and you reach a point where you know that you're going to win, but you still need to continue playing the game for several minutes before you actually get to the end, the conclusion is forgone during those last several minutes. It's also possible to have a forgone conclusion where you know you're going to lose before the match ends.

Foregone conclusions are bad because the time between the moment when the player knows how the match will end and the moment when the match actually ends is wasted time. During this time the player just has to go through the motions to bring about the result they already know is coming. The player has nothing to learn during this time because they already know how the match will end.

Situations in which the player is not certain of what the outcome will be, but thinks that one outcome is very likely to occur (for instance, if they think they have a 99% chance of winning), are not quite foregone conclusions, but still represent a lesser version of the same problem.

Games with score systems don't have this problem. If you play well or get lucky in the early portion of a match, that just means that your score at the end of the match will be higher than it otherwise would, and if you play poorly or get unlucky, your score will be lower than it otherwise would. The conclusion isn't foregone because there is still a wide range of possible scores that you could get. Your actions in the remaining portion of the game can still affect the outcome significantly, so you still need to come up with good plans, rather than just going through the motions to get to a predetermined outcome.

For any particular win/loss strategy game there might be changes that a designer could make that would make foregone conclusions rarer or shorter. Such changes, however, will likely only be applicable to the particular game they were designed for, and perhaps to similar games, but not to most other win/loss games, and so solving this problem for a given game could require significant design effort. Further, I doubt that it is even possible, in general, to entirely remove forgone conclusions from a complex single-player win/loss strategy game (I don't know of any decent win/loss single-player strategy game that entirely solves the problem of foregone conclusions).

Conversely, it's possible to conceive of a game with a score system that has forgone conclusions. For instance, if a game has an upper cap on possible scores, and the cap is low enough that it can be achieved regularly by a good player, then such a player might reach a point in a match where they know they’re going to get the maximum possible score before the match is actually over. However, this kind of forgone conclusion is very easy to avoid: simply don't have an upper cap of possible scores, or at least not one that’s plausibly achievable. So while it is technically possible to have forgone conclusions regardless of whether a game uses a score system or a win/loss system, the problem is very easy to avoid when using a score system but very difficult (and perhaps impossible) to avoid when using a win/loss system.

Better Endgame Feedback

By definition, games with win/loss systems provide a single bit (in the information theoretic sense) of endgame feedback, while games with score systems provide more than one bit (Note: some games may provide extra "feedback" in addition to the win/loss bit or score, such as the number of enemies killed or how long the match took, but since these aren’t inherently indicative of a player's performance they aren't considered here). So score systems, by definition, give the player more feedback than win/loss systems do.

This difference is important because the point of strategy games is for the player to learn how to play the game well, which means learning what kinds of strategies are more effective than others and why. The purpose of the feedback provided at the end of the match, which either takes the form of a single bit (in the case of a win/loss system) or a number (in the case of a score system), should be to help the player discriminate between various strategies, so that they can learn which are better than others.

In a win/loss system, you know that strategy A is better than strategy B if A leads to victory and B doesn't. If both A and B lead to victory, or loss, then you don't have a way to tell which is better than the other (unless you play a large number of matches with each strategy and find that A leads to victory more frequently than B or vice versa). In a score system, on the other hand, you know that strategy A is better than strategy B if A leads to a higher score than B. It will be rare that any two strategies lead to exactly the same score, so a score system almost always lets you discriminate between two strategies. A match in a win/loss system, on the other hand, has only two possible results, so it's quite common for two strategies to lead to the exact same result, which means that it is much harder to discriminate between strategies.

When I've made this point in the past, some people have objected that this difference doesn't matter, because the player can tell which of two matches went better even if they both ended with the same outcome. It's true that players can have a sense of how well a match went, or is going, that is independent of the endgame feedback they receive, and developing this sense is an important part of learning how to properly play the game. However, a player’s perception of how well a match went is no substitute for the endgame feedback that the game provides because the perception is theory-laden. A player's perception of how well they did depends their strategic understanding of the game, and so if their understanding is flawed then that perception will be flawed too. Endgame feedback, on the other hand, doesn't depend on the player's understanding of the game. Instead, it’s an objective reflection of how well they played (though it can also be influenced by random events that happen during the match, so it is a somewhat noisey reflection). When a player’s strategic understanding of the game is flawed in a way that negatively impacts their perception of how well a match went, good endgame feedback to compare that perception to is an invaluable tool for noticing and correcting those flaws. So the fact that players have a sense of how well a match went that is independent of the endgame feedback doesn't mean that the feedback is unimportant. Having good endgame feedback is still very important, and for that purpose score systems are clearly superior.

No Need for Multiple Difficulty Levels

If you agree (as I do) with Keith Burgun's argument that the ideal winrate for win/loss strategy games is 50%, it's essential for any win/loss game to have multiple levels of difficulty for players of different skill levels. This means that a designer creating a win/loss game needs to either design many different levels of difficulty, each of which is effectively a version of the game with slightly different rules, or design a system that adjusts some parameters of the game to get to a desired level of difficulty. Either way, the rules of the game will change as a player progresses to higher levels of difficulty. This means that some of a player's knowledge of how to play the game will become obsolete, not because they've discovered better knowledge to replace it, but because they're now playing a slightly different game, and their old knowledge doesn't apply to this new game.

Games with score systems don't need to maintain a 50% winrate, because there's no such thing as "winning", so they don't have this problem. Players of any skill level can play the same version of the game without any issue. Instead of being distinguished by the level they can achieve a 50% winrate at, they can be distinguished by average the score they achieve. Of course, for that to work it's important that there be a wide variety of possible scores, and that higher scores require advanced knowledge to achieve. But that's equivalent to simply saying that it's important for a score game to have depth, and in that sense they're no different from win/loss games.

In a game with a score system that has only one level of difficulty, there’s no need for the rules to ever change. An expert player will be playing exactly the same game as a beginner. This means that, once the player has learned how to play the game, they never have to learn any new rules again, and they can instead focus purely on how to maximize their scores given the way the rules are (and always will be). A player’s old strategic knowledge may eventually become obsolete, but only when they come up with a new knowledge that usurps it. Their knowledge will never be obsoleted by any changes to the rules. And the player can always return to older strategies to explore or experiment with them more, and those strategies will always work just as well as they used to, unlike if they had been forced to drop a strategy because it no longer worked due to some newly introduced rules.

Potential Disadvantages

Even if you grant that score systems have the advantages I described above, you might object on the grounds that score systems also have disadvantages, and those outweigh the advantages. I don't think there are any significant, inherent disadvantages to score systems. There are significant problems with most existing score systems in games, but these problems are caused by specific bad design choices that can be corrected without abandoning score systems entirely. To demonstrate this point, I'll respond to a list of supposed criticisms of score systems from Keith Burgun's article Auro’s "Single-Player Elo System", each of which I think can be fixed without moving away from score systems:

I agree that indefinitely scaling match lengths are a problem, but games with score systems do not, inherently, need to have unconstrained match lengths. One can easily imagine a game with a score system in which match lengths are capped at, say, 10 minutes. In such a game, the player would get higher scores not by extending the match length, but using the limited time they have available more efficiently.

Keith mentions a secondary problem here, which is that the early game gets boring for high-level players because it's designed to be easy enough that new players can survive it. I also agree that this is a problem, but it isn't inherent to score systems either. This problem can be solved by adding opt-in challenges to the early game that provide some type of reward (such as an immediate score bonus, or a resource that will help the player get more score later in the match) when completed. Newer players can ignore these challenges if the early game is difficult enough for them as it is, while experienced players can opt for a harder experience, and receive a better score for doing so.

I agree with both of these criticisms, but they apply only to score systems in which the player is incentivized to try to beat their old high score. That isn't the type of system I'm advocating for. The player should be aiming to maximize their average score, not their chance of beating their old high score. This problem can be fixed simply by incentivizing the player to maximize their average score rather than trying to "beat" their old score. The UI shown between matches should reflect this incentive, by displaying the player's average score over the past few matches rather than the highest score they've ever gotten.

I agree that it's bad for players to have to choose their own goal, and that they should be able to focus solely on trying to make good strategic decisions. However, in the type of score system that I'm advocating for, the player doesn't have to choose their own goal, because the game has an explicit goal: maximize your average score (and, again, the UI can be designed to incentivize this goal). The player doesn't have to arbitrarily come up with a threshold and try to pass it, they can just try to maximize their score. That goal is just as just as well-defined and legitimate as any binary goal.

I disagree that it's "impossible to determine whether your skill is increasing or not" when there isn't a binary goal. When you start to get a better average score, you can tell that your skill is increasing. In fact you can determine this far better when a game uses a score system, because score systems provide far better feedback than win/loss systems.

Conclusions

Given the advantages of score systems that I've outlined, and the fact that there are no significant disadvantages to score systems (as far as I'm aware), I think all single-player strategy games from now on should adopt score systems. While it may be necessary to use win/loss systems in multiplayer games to avoid alienating players, there is already plenty of precedent for score systems in single-player games. The opportunity to use score systems is one of the great advantages that single-player games offer.

Existing single-player win/loss games shouldn’t necessarily be changed to use score systems, because it may be difficult to make that change without breaking other parts of the game. The decision to use a score system is something that should be made early in the process of designing a game, so existing win/loss games should probably be left as win/loss games. However, when designing rulesets for new games, we have free reign to make whatever design decisions we think will be best, and we should take that opportunity to adopt score systems.