Difference between revisions of "Scores"

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[[Category:Mechanical Patterns]]
 
[[Category:Mechanical Patterns]]
 
[[Category:Patterns]]
 
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[[Category:Needs revision]]
 
[[Category:Needs revision]]
[[Category:Needs examples]]
 
 
[[Category:Needs references]]
 
[[Category:Needs references]]
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[[Category:Staffan's current workpage]]
 
 
''Numerical values used in games to determine winners.''
 
''Numerical values used in games to determine winners.''
  
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[[Scores]] are used to determine the winner in [[Go]] but not in [[Chess]] (unless someone surrenders in [[Go]]). However, in tournaments [[Scores]] can be used based on winning individual game instances, and the rankings one can achieve through participating in organized games and tournaments can be seen as a type of meta [[Scores|Score]].
 
[[Scores]] are used to determine the winner in [[Go]] but not in [[Chess]] (unless someone surrenders in [[Go]]). However, in tournaments [[Scores]] can be used based on winning individual game instances, and the rankings one can achieve through participating in organized games and tournaments can be seen as a type of meta [[Scores|Score]].
  
Several [[:Category:Computer Games]] use [[Scores]] as ways of letting players of single-player games be able to compare themselves to other players and previous times they have played. Examples of such games include [[Bejeweled]], [[Icy Tower]], and [[Staries]]. "Deathmatch" version of [[:Category:FPS Games|FPS Games]] such as the [[Quake series]] and the [[Unreal Tournament series]] have the number of kills one has made as [[Scores]] (killing oneself is typically counted as -1 kill). Other games, e.g. [[Candy Crush Saga]],  don't have global [[Scores]] but which level a player has reached can function as a form of [[Scores|Score]] in them since it does show how far players have managed to progress.
+
Several [[:Category:Computer Games|Computer Games]] use [[Scores]] as ways of letting players of single-player games be able to compare themselves to other players and previous times they have played. Examples of such games include [[Bejeweled]], [[Icy Tower]], and [[Staries]]. "Deathmatch" version of [[:Category:FPS Games|FPS Games]] such as the [[Quake series]] and the [[Unreal Tournament series]] have the number of kills one has made as [[Scores]] (killing oneself is typically counted as -1 kill). Other games, e.g. [[Candy Crush Saga]],  don't have global [[Scores]] but which level a player has reached can function as a form of [[Scores|Score]] in them since it does show how far players have managed to progress.
  
 
Team vs. team play in the [[Left 4 Dead series]] give points to the infected team based on how far they managed to traverse a level. Since the teams have asymmetrical abilities and starting positions (like [[Memoir '44]]), the roles as reversed so both teams play as infected and the [[Scores]] they get are compared to determine winners.
 
Team vs. team play in the [[Left 4 Dead series]] give points to the infected team based on how far they managed to traverse a level. Since the teams have asymmetrical abilities and starting positions (like [[Memoir '44]]), the roles as reversed so both teams play as infected and the [[Scores]] they get are compared to determine winners.
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[[Scores]] are typically a numeric value attached to individual players or [[Teams]]. In games where [[Collections]] of [[Resources]] are used to calculate victory, this combination of patterns create a type of [[Scores|Score]] system. However, some other attributes can be viewed as [[Scores]] so games without explicit [[Scores]] can have them implicitly. [[Character Levels]] is one such example since they can represent how much effort and skill players have put into the gameplay. [[Handicap Systems]] used in [[Go]] and [[Golf]] is another example since these can be seen as [[Scores]] in the [[Meta Games|Meta Game]] of being a good player in these games. In games where players progress in unlimited by lives over time and try to complete [[Levels]], e.g. [[Candy Crush Saga]] or [[Peggle]], the scoring of which [[Levels]] one has completed in [[Abstract Player Constructs]] serve a similar function to [[Scores]] in other [[Single-Player Games]].  
 
[[Scores]] are typically a numeric value attached to individual players or [[Teams]]. In games where [[Collections]] of [[Resources]] are used to calculate victory, this combination of patterns create a type of [[Scores|Score]] system. However, some other attributes can be viewed as [[Scores]] so games without explicit [[Scores]] can have them implicitly. [[Character Levels]] is one such example since they can represent how much effort and skill players have put into the gameplay. [[Handicap Systems]] used in [[Go]] and [[Golf]] is another example since these can be seen as [[Scores]] in the [[Meta Games|Meta Game]] of being a good player in these games. In games where players progress in unlimited by lives over time and try to complete [[Levels]], e.g. [[Candy Crush Saga]] or [[Peggle]], the scoring of which [[Levels]] one has completed in [[Abstract Player Constructs]] serve a similar function to [[Scores]] in other [[Single-Player Games]].  
  
Generalizing, [[Scores]] are typically increased as [[Rewards]] for succeeding with goals and decreased as [[Penalties]] for failing to succeed with goals. [[Pick-Ups]] and [[Combos]] are two patterns which quite often are directly linked to providing increased [[Scores]]. The actual update or finalization of [[Scores]] may be a [[Death Consequences]] but dying may in itself result in [[Scores]] decreasing so the patterns can modify each other. [[Handicap Systems]] can be used to both offer different starting [[Scores]] for players or to modify how they are given and removed, in both cases to create [[Player Balance]].  
+
Generalizing, [[Scores]] are typically increased as [[Rewards]] for succeeding with goals and decreased as [[Penalties]] for failing to succeed with goals. [[Pick-Ups]] and [[Combos]] are two patterns which quite often are directly linked to providing increased [[Scores]]. The actual update or finalization of [[Scores]] may be a [[Death Consequences]] but dying may in itself result in [[Scores]] decreasing so the patterns can modify each other. [[Handicap Systems]] can be used to both offer different starting [[Scores]] for players or to modify how they are given and removed, in both cases to create [[Player Balance]]. [[Revoke Rules]] are a special case of [[Penalties]] that apply to players for failing to follow rules (typically in games with [[Trick Taking]]).
  
 
While increasing one's [[Scores|Score]] can be a goal in itself, games sometimes provides [[Rewards]] for reaching certain [[Scores]]. A common examples is increasing the number of [[Lives]] one has when reaching certain [[Scores]]; [[Pinball Dreams]] does this through providing a jackpot value common for all players that can provide [[Lives]].
 
While increasing one's [[Scores|Score]] can be a goal in itself, games sometimes provides [[Rewards]] for reaching certain [[Scores]]. A common examples is increasing the number of [[Lives]] one has when reaching certain [[Scores]]; [[Pinball Dreams]] does this through providing a jackpot value common for all players that can provide [[Lives]].
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[[Scores]] can be seen as [[Investments]] in games where players have choices between trying to improve their possibilities to affect future gameplay, i.e. create [[Gameplay Engines]], and getting points for their [[Scores]]. Players of both [[Dominion]] and [[Race for the Galaxy]] need to make decisions of this nature as part of considering to do a [[Construction/Scoring Phase Shift]]. When [[Scores]] can intentionally be decreased by players as a way of performing others actions ([[Murano]] is an example of this), [[Scores]] become [[Resources]] (so they can be both [[Resources]] and [[Investments]] at the same time).
 
[[Scores]] can be seen as [[Investments]] in games where players have choices between trying to improve their possibilities to affect future gameplay, i.e. create [[Gameplay Engines]], and getting points for their [[Scores]]. Players of both [[Dominion]] and [[Race for the Galaxy]] need to make decisions of this nature as part of considering to do a [[Construction/Scoring Phase Shift]]. When [[Scores]] can intentionally be decreased by players as a way of performing others actions ([[Murano]] is an example of this), [[Scores]] become [[Resources]] (so they can be both [[Resources]] and [[Investments]] at the same time).
  
[[Scores]] can affect all types of [[:Category:Winning Patterns|Winning Patterns]], by being [[Tiebreakers]] for games with [[Winning by Ending Gameplay]] and by being general [[Progress Indicators]] in [[Unwinnable Games]]. They are typically the prime way of determining winners in games using [[Winner determined after Gameplay Ends]] but may be complemented by [[Tiebreakers]]. While [[Scores]] in [[Multiplayer Games]] rather obviously give players ways of having [[Competition]] against each other, they can work the same way in [[Single-Player Games]] through the use of [[High Score Lists]] to let players compete against themselves or others through comparing [[Scores]] between game instances (an example of using [[Scores]] as [[Trans-Game Information]]).
+
[[Scores]] can affect all types of [[:Category:Winning Patterns|Winning Patterns]]. For games with [[Winning by Ending Gameplay]], they can either be the cause of gameplay ending when a player reaches a certain [[Scores|Score]] or be [[Tiebreakers]] if several players can end gameplay at the same time. For [[Unwinnable Games]] they are a form of  [[Progress Indicators]] while they are typically the prime way of determining winners in games using [[Winner determined after Gameplay Ends]] but may be complemented by [[Tiebreakers]]. While [[Scores]] in [[Multiplayer Games]] rather obviously give players ways of having [[Competition]] against each other, they can work the same way in [[Single-Player Games]] through the use of [[High Score Lists]] to let players compete against themselves or others through comparing [[Scores]] between game instances (an example of using [[Scores]] as [[Trans-Game Information]]).
  
The possibilities of increasing [[Scores]] can be set up so that they become [[Risk/Reward]] choices, typically that one takes higher risks of not getting any points (or a risk of getting negative points) for the chance of getting more points if one gets any points at all. The distribution of  individual ways of increasing (or decreasing) [[Scores]] can be set up to follow [[Arithmetic Progression|Arithmetic]], [[Geometric Progression|Geometric]], or [[Discontinuous Progression]]. Motivations for the which of these progression schemes as most suitable depend very much on the specifics of a game design but [[Geometric Progression]] may be more suitable in cases where a design should have [[Higher-Level Closures as Gameplay Progresses]].
+
The possibilities of increasing [[Scores]] can be set up so that they become [[Risk/Reward]] choices, typically that one takes higher risks of not getting any points (or a risk of getting negative points) for the chance of getting more points if one gets any points at all. The distribution of  individual ways of increasing (or decreasing) [[Scores]] can be set up to follow [[Arithmetic Progression|Arithmetic]], [[Geometric Progression|Geometric]], or [[Discontinuous Progression]]. Motivations for which of these progression schemes as most suitable depend very much on the specifics of a game design but [[Geometric Progression]] may be more suitable in cases where a design should have [[Higher-Level Closures as Gameplay Progresses]]. [[Time Limited Game Instances]] can be used to put implicit maximum limits to the [[Scores]] possible and let players compete on being as quick as possible in gathering points rather than as efficient as possible.
  
 
[[End State Scoring]] and [[Secret Scoring Mechanisms]] are two general ways of modifying how [[Scores]] work in a game, both promoting [[Tension]] and [[Uncertainty of Outcome]]. [[Scores]] can easily be tied to [[Extra-Game Consequences]] through [[Gambling]], i.e. through requiring payment in money to play and offering payment back as [[Rewards]].  
 
[[End State Scoring]] and [[Secret Scoring Mechanisms]] are two general ways of modifying how [[Scores]] work in a game, both promoting [[Tension]] and [[Uncertainty of Outcome]]. [[Scores]] can easily be tied to [[Extra-Game Consequences]] through [[Gambling]], i.e. through requiring payment in money to play and offering payment back as [[Rewards]].  
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== Consequences ==
 
== Consequences ==
[[Scores]] are probably the most basic and most used elements in [[Abstract Player Constructs]]. They make games have the [[Continuous Goals|Continuous Goal]] of [[Collecting]] points which can also be seen as a [[Races|Race]] to either first reach a certain [[Scores|Score]] or have the highest [[Scores|Score]] when gameplay ends. They make easy value to use as [[Trans-Game Information]] in [[Tournaments]] which can result in [[Player Elimination]] for those with low [[Scores]], and can easily act as [[Tiebreakers]] in games built to use [[Back-to-Back Game Sessions]] ([[Memoir '44]] being an example of this).
+
[[Scores]] are probably the most basic and most used elements in [[Abstract Player Constructs]]. They make games have the [[Continuous Goals|Continuous Goal]] of [[Collecting]] points which can also be seen as a [[Races|Race]] to either first reach a certain [[Scores|Score]] or have the highest [[Scores|Score]] when gameplay ends. Through this they act as [[Facilitating Rewards]] in the sense that they facilitate players in being able to end or win games. They make easy values to use as [[Trans-Game Information]] in [[Tournaments]] which can result in [[Player Elimination]] for those with low [[Scores]], and can easily act as [[Tiebreakers]] in games built to use [[Back-to-Back Game Sessions]] ([[Memoir '44]] being an example of this). In games with phases, a focus on increasing one's [[Scores|Score]] as much as possible it typically a characteristics of an [[Exploitation]] phase.
  
When publicly accessible, they simultaneously are a type of [[Progress Indicators]] and [[Game State Overview]] which create [[Stimulated Planning]] and [[Tension]]. This can give rise to [[Dynamic Alliances]] working against a [[Predictable Winner]] in [[Multiplayer Games]]. While wanting to win over other players can be sufficient reason for [[Multiplayer]] games to have [[Replayability]], [[Scores]] in [[Single-Player Games]] can promote [[Replayability]] in trying to beat one's own [[Scores|Score]] from previous game instances and this can be seen as a weak use of [[Trans-Game Information]] (a stronger such use of [[Scores]] is through the use of [[High Score Lists]]).
+
If [[Scores]] can be used as [[Resources]], they are typically [[Non-Localized Resources]]. When publicly accessible, they simultaneously are a type of [[Progress Indicators]] and [[Game State Overviews]] which create [[Stimulated Planning]] and [[Tension]]. This can give rise to [[Dynamic Alliances]] working against a [[Predictable Winner]] in [[Multiplayer Games]]. While wanting to win over other players can be sufficient reason for [[Multiplayer]] games to have [[Replayability]], [[Scores]] in [[Single-Player Games]] can promote [[Replayability]] in trying to beat one's own [[Scores|Score]] from previous game instances and this can be seen as a weak use of [[Trans-Game Information]] (a stronger such use of [[Scores]] is through the use of [[High Score Lists]]).
  
 
[[Save Points]] and [[Save-Load Cycles]] tend to not work well with [[Scores]] since players can go back repeatedly in attempts to maximize their scores.
 
[[Save Points]] and [[Save-Load Cycles]] tend to not work well with [[Scores]] since players can go back repeatedly in attempts to maximize their scores.
  
 
== Relations ==
 
== Relations ==
[[Time Limited Game Instances]] - modulates
 
 
 
=== Can Instantiate ===
 
=== Can Instantiate ===
 
[[Abstract Player Constructs]],  
 
[[Abstract Player Constructs]],  
 
[[Collecting]],  
 
[[Collecting]],  
 
[[Continuous Goals]],  
 
[[Continuous Goals]],  
[[Game State Overview]],  
+
[[Exploitation]],  
[[Higher-Level Closures as Gameplay Progresses]],  
+
[[Facilitating Rewards]],
 +
[[Game State Overviews]],  
 
[[High Score Lists]],  
 
[[High Score Lists]],  
 
[[Investments]],  
 
[[Investments]],  
 +
[[Non-Localized Resources]],
 
[[Player Elimination]],  
 
[[Player Elimination]],  
 
[[Progress Indicators]],  
 
[[Progress Indicators]],  
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[[Replayability]],  
 
[[Replayability]],  
 
[[Resources]],  
 
[[Resources]],  
 +
[[Rewards]],
 
[[Stimulated Planning]],  
 
[[Stimulated Planning]],  
 
[[Tension]],  
 
[[Tension]],  
 
[[Tied Results]],  
 
[[Tied Results]],  
[[Trans-Game Information]]
+
[[Trans-Game Information]],
 +
[[Winning by Ending Gameplay]]
  
 
==== with [[Extra-Game Consequences]] ====
 
==== with [[Extra-Game Consequences]] ====
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[[Penalties]],  
 
[[Penalties]],  
 
[[Pick-Ups]],  
 
[[Pick-Ups]],  
[[Rewards]],  
+
[[Revoke Rules]],  
 
[[Risk/Reward]],  
 
[[Risk/Reward]],  
 
[[Score Tracks]],  
 
[[Score Tracks]],  

Revision as of 10:58, 9 August 2016

Numerical values used in games to determine winners.

Many games determine a winner for each game instance, or at least an ordering of how well players managed to reach the goals offered by the game (which can include having people tied in how well they succeeded). Games that do this through providing each player or team with a numerical value uses Scores.

Examples

Many Board Games use Scores to determine a winner. Some, e.g. Hare and Tortoise and Settlers of Catan, end when a player has a high enough Score while others, e.g. Carcassonne, Egizia, Race for the Galaxy, and Ticket to Ride, end due to specific requirements and Scores are then counted. Scenarios in Memoir '44 are typically not balanced between the two sides but through using scores for each game players can switch sides after a first game instance and compare their results of two game instances to get a balanced combined score.

Scores are used to determine the winner in Go but not in Chess (unless someone surrenders in Go). However, in tournaments Scores can be used based on winning individual game instances, and the rankings one can achieve through participating in organized games and tournaments can be seen as a type of meta Score.

Several Computer Games use Scores as ways of letting players of single-player games be able to compare themselves to other players and previous times they have played. Examples of such games include Bejeweled, Icy Tower, and Staries. "Deathmatch" version of FPS Games such as the Quake series and the Unreal Tournament series have the number of kills one has made as Scores (killing oneself is typically counted as -1 kill). Other games, e.g. Candy Crush Saga, don't have global Scores but which level a player has reached can function as a form of Score in them since it does show how far players have managed to progress.

Team vs. team play in the Left 4 Dead series give points to the infected team based on how far they managed to traverse a level. Since the teams have asymmetrical abilities and starting positions (like Memoir '44), the roles as reversed so both teams play as infected and the Scores they get are compared to determine winners.

The "ticket system" in the Battlefield series can be seen as an inverse Score. Each time starts with a certain amount and lose 1 ticket for each death in their team and not controlling enough flags result in tickets being removed at regular intervals. The amount of tickets the winning team has is through this basically a Score like Scores in other games.

Using the pattern

Designing a system for Scores in a game consists of deciding when players Scores are adjusted, how much they are adjusted by, and if there are certain Score values which activate events, including ending the game. The last case is shows how Scores often can become Races (but see King of the Hill for an alternative).

Scores are typically a numeric value attached to individual players or Teams. In games where Collections of Resources are used to calculate victory, this combination of patterns create a type of Score system. However, some other attributes can be viewed as Scores so games without explicit Scores can have them implicitly. Character Levels is one such example since they can represent how much effort and skill players have put into the gameplay. Handicap Systems used in Go and Golf is another example since these can be seen as Scores in the Meta Game of being a good player in these games. In games where players progress in unlimited by lives over time and try to complete Levels, e.g. Candy Crush Saga or Peggle, the scoring of which Levels one has completed in Abstract Player Constructs serve a similar function to Scores in other Single-Player Games.

Generalizing, Scores are typically increased as Rewards for succeeding with goals and decreased as Penalties for failing to succeed with goals. Pick-Ups and Combos are two patterns which quite often are directly linked to providing increased Scores. The actual update or finalization of Scores may be a Death Consequences but dying may in itself result in Scores decreasing so the patterns can modify each other. Handicap Systems can be used to both offer different starting Scores for players or to modify how they are given and removed, in both cases to create Player Balance. Revoke Rules are a special case of Penalties that apply to players for failing to follow rules (typically in games with Trick Taking).

While increasing one's Score can be a goal in itself, games sometimes provides Rewards for reaching certain Scores. A common examples is increasing the number of Lives one has when reaching certain Scores; Pinball Dreams does this through providing a jackpot value common for all players that can provide Lives.

Scores can be seen as Investments in games where players have choices between trying to improve their possibilities to affect future gameplay, i.e. create Gameplay Engines, and getting points for their Scores. Players of both Dominion and Race for the Galaxy need to make decisions of this nature as part of considering to do a Construction/Scoring Phase Shift. When Scores can intentionally be decreased by players as a way of performing others actions (Murano is an example of this), Scores become Resources (so they can be both Resources and Investments at the same time).

Scores can affect all types of Winning Patterns. For games with Winning by Ending Gameplay, they can either be the cause of gameplay ending when a player reaches a certain Score or be Tiebreakers if several players can end gameplay at the same time. For Unwinnable Games they are a form of Progress Indicators while they are typically the prime way of determining winners in games using Winner determined after Gameplay Ends but may be complemented by Tiebreakers. While Scores in Multiplayer Games rather obviously give players ways of having Competition against each other, they can work the same way in Single-Player Games through the use of High Score Lists to let players compete against themselves or others through comparing Scores between game instances (an example of using Scores as Trans-Game Information).

The possibilities of increasing Scores can be set up so that they become Risk/Reward choices, typically that one takes higher risks of not getting any points (or a risk of getting negative points) for the chance of getting more points if one gets any points at all. The distribution of individual ways of increasing (or decreasing) Scores can be set up to follow Arithmetic, Geometric, or Discontinuous Progression. Motivations for which of these progression schemes as most suitable depend very much on the specifics of a game design but Geometric Progression may be more suitable in cases where a design should have Higher-Level Closures as Gameplay Progresses. Time Limited Game Instances can be used to put implicit maximum limits to the Scores possible and let players compete on being as quick as possible in gathering points rather than as efficient as possible.

End State Scoring and Secret Scoring Mechanisms are two general ways of modifying how Scores work in a game, both promoting Tension and Uncertainty of Outcome. Scores can easily be tied to Extra-Game Consequences through Gambling, i.e. through requiring payment in money to play and offering payment back as Rewards.

When tying events and Extra-Game Consequences to Scores it may be necessary to consider if Tied Results are possible and should be allowed. Tiebreakers is the solution to avoid having Tied Results.

Diegetic Aspects

Scores are often difficult to explain within a game's theme, so using it easily breaks Thematic Consistency and often thereby also Diegetic Consistency.

Interface Aspects

Scores are typically important information in games where they are used, and for this reason often part of Gameplay Statistics and Game State Indicators. Score Tracks is a specific interface (or visualization) component dedicated for this.

Consequences

Scores are probably the most basic and most used elements in Abstract Player Constructs. They make games have the Continuous Goal of Collecting points which can also be seen as a Race to either first reach a certain Score or have the highest Score when gameplay ends. Through this they act as Facilitating Rewards in the sense that they facilitate players in being able to end or win games. They make easy values to use as Trans-Game Information in Tournaments which can result in Player Elimination for those with low Scores, and can easily act as Tiebreakers in games built to use Back-to-Back Game Sessions (Memoir '44 being an example of this). In games with phases, a focus on increasing one's Score as much as possible it typically a characteristics of an Exploitation phase.

If Scores can be used as Resources, they are typically Non-Localized Resources. When publicly accessible, they simultaneously are a type of Progress Indicators and Game State Overviews which create Stimulated Planning and Tension. This can give rise to Dynamic Alliances working against a Predictable Winner in Multiplayer Games. While wanting to win over other players can be sufficient reason for Multiplayer games to have Replayability, Scores in Single-Player Games can promote Replayability in trying to beat one's own Score from previous game instances and this can be seen as a weak use of Trans-Game Information (a stronger such use of Scores is through the use of High Score Lists).

Save Points and Save-Load Cycles tend to not work well with Scores since players can go back repeatedly in attempts to maximize their scores.

Relations

Can Instantiate

Abstract Player Constructs, Collecting, Continuous Goals, Exploitation, Facilitating Rewards, Game State Overviews, High Score Lists, Investments, Non-Localized Resources, Player Elimination, Progress Indicators, Races, Replayability, Resources, Rewards, Stimulated Planning, Tension, Tied Results, Trans-Game Information, Winning by Ending Gameplay

with Extra-Game Consequences

Gambling

with Gameplay Engines

Construction/Scoring Phase Shift

with Multiplayer Games

Dynamic Alliances, Predictable Winner

with Winning by Ending Gameplay

Tiebreakers

Can Modulate

Back-to-Back Game Sessions, Death Consequences, King of the Hill, Lives, Multiplayer Games, Single-Player Games, Teams, Tournaments, Unwinnable Games, Winner determined after Gameplay Ends, Winning by Ending Gameplay

Can Be Instantiated By

Character Levels

Collections together with Resources

Handicap Systems together with Meta Games

Abstract Player Constructs together with Levels

Can Be Modulated By

Arithmetic Progression, Combos, Death Consequences, Discontinuous Progression, End State Scoring, Extra-Game Consequences, Gameplay Statistics, Game State Indicators, Geometric Progression, Handicap Systems, Penalties, Pick-Ups, Revoke Rules, Risk/Reward, Score Tracks, Secret Scoring Mechanisms, Tiebreakers, Time Limited Game Instances

Possible Closure Effects

-

Potentially Conflicting With

Diegetic Consistency, Save Points, Save-Load Cycles, Thematic Consistency

History

An updated version of the pattern Score that was part of the original collection in the book Patterns in Game Design[1].

References

  1. Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.

Acknowledgements

-