[Literature] Game Balance ch8 - Statistics and metrics

My notes from course 8 of the Game Balance class of Summer 2010, by Ian Schreiber.

Roll	2d6	1d11+1
Mean	7	7
Median	7	7
Std Dev	2.4	3.3
68% of rolls will be in	[5; 9]	[4; 10]

Statistics tell us that something is happening, but they do not tell why. The why comes when designing appropriate metrics. Causality can not be established from correlations! For instance, if there are less Troll players than Elf players, what can it mean?

• Trolls are less aesthetically appealing.
• Trolls are less fun to use.
• Trolls have a higher learning curve.
• Trolls are underpowered.
• ...

Remember that top score players are outliers.
Playtesters should be as similar as possible to the target market. Playtesting with metrics is an iterative process that needs to be planned ahead of time. Moreover, playtesting needs to be done on novice players (they try the system once or twice) and on expert players (they try it regularly for a couple of months). Experts are needed to check for emerging/unexpected strategies.

Metrics

Developers are mixed between using intuition and/or metrics:

Zynga's Mark Pincus: metrics-driven design,

Chris Hecker: intuition-driven design,

and Playfish's Jeferson Valadares: both.

One can measure how much impact a change in game design has on the customer base. A-B testing allows more control on external factors (eg players of a particular region may stop playing for a while if there's a natural disaster).

MAU versus DAU: a purely viral game will have MAU = 30*DAU (there are 30 days in a month, and people only play for one day, then leave) whereas an old and sticky game will have DAU and MAU close together.
ARPU differs from ARPPU. Plotting ARPU or ARPPU against time is a good way to check if the start-, mid- or end-game generate revenue or not.

[Literature] Game Balance ch7 - Advancement, progression and pacing

My notes from course 7 of the Game Balance class of Summer 2010, by Ian Schreiber.

Progression is ...	in games that are ...
absolute	PvE/single player
relative to other players	PvP/multiplayer

Flow has two problems: different player audiences have different skills, and players learn throughout the game.
Balance = overall game difficulty, does not solve these problems. Balance only matches audience expectation.
Progression/Pacing = keeping the player in the flow zone. As player skill increases, so do challenges. Progression ensures the game ends in the time frame said by the box (1min for arcade, 40h for RPG, etc.). If the game is endless, then progression = end-game rewarding structure(s).

When transitioning from mid- to end- or elder game, the objectives change from progressing to something else. Game designer has to find something for the player to do. Ex: WoW guild raiding or making your house cute in Farmville/Sims. Problems: some players may like the progression game but not the elder game. The power gathered during progression game should be available and enjoyable during elder game.
Tips:

• As playtesters test the game, they become experts => the game gets tuned harder => make the game easier at the end, and/or keep some playtesters for the end.
• Let players adjust the difficulty themselves (more challenging but also more rewarding levels or adjusting the difficulty level at any time). In PVP, difficulty adjustment should be voluntary (handicap, resources at the beginning, ...).

PVE

Perceived difficulty = (game power challenge + game skill challenge) - (player power + player skill), with:

• Game power challenge = stats (doubling opponents HP makes the game harder)
• Game skill challenge = new enemies or better AI, direct challenge to the player's skill (you need to play better) and not a player's power (you need more hit points to win). A game designer can control power-related, but not skill-related components of difficulty.

Large luck component or shallow mechanics: a short increase in player skill as the player masters what little they can at the beginning. Then skill plateau (player is as good as she can ever be). A minute to learn, a minute to master. This is the design of educational games (where skill is not the priority).

Giving practice zones where new weapons or powers are acquired makes players learn/increase their skill faster. Skill gating = progressively harder challenges, guarantee that if players complete a challenge, then they are ready for the next. Skill gating != practice zones.

Psychology: “reward schedule” or “risk/reward cycle”: you don’t just want the players to progress, you want them to feel like they are being rewarded for playing well. Reward not too rarely and not too often. Many small rewards are more efficient than a single big reward. Regular rewards = bad. Reward for something players were looking for (otherwise the game seems too easy) and not for a random event (eg "inflict exactly 123 dmg"). 3 kinds of rewards related to progression: increasing player power, level transitions, and story progression.

Increasing player power

If the most fun toy in your game is only discovered 2/3rds of the way through, that’s a lot of time the player doesn’t get to have fun. How do you actually keep the player engaged when you've given away all the cool toys early in the game? One way is if your mechanics have a lot of depth, you can just present unique combinations of things to the player to keep them challenged and engaged. Warning: this is really hard to do in practice. You can also use other rewards more liberally after you shut off the new toys: more story, more stat increases, more frequent boss fights or level transitions. Also, toy upgrades.
Better shorten the game than have it too long and boring.

Level transitions

Each level takes a little bit longer than the last: fast progression at start engages player into the game, later levels can be longer because player wants to know the end of the plot.

Story progression

Story really IS a reward. There should be a match between story complication/climax curve and the difficulty curve. Ex: tutorial = exposition scene, miniboss = rising action, final boss = final climax. Final boss should not be as demanding on player skill as kill 10 rats.

Pattern: do not reveal the story only during level transition; instead, revealing additional background story immediately after a fight (even an easy one) makes players feel like they earned it. (But do not do that all the time otherwise it becomes predictble!)

PvP

Acquiring more power than opponents = primary reward. PvP has more options to play with than PVE because everything is relative, there's no defined level/stats to reach to be "strong".

negative feedback loops => more power when behind and less power when ahead => best player alternates => depends on opponents, no one is left behind (ex: Mario Kart with dynamic difficulty adjustment).
positive feedback loop => more power brings more power => best stays best => independent of the opponents, game ends faster, bad start is deadly (ex: League of Legends).

	positive sum	negative sum	zero sum
Definition	sum of all player resources increases over time	players lose power over time. Goal = lose power more slowly than opponents.	fixed amount of resources on the table
Example	Catan, Agricola	Chess	Poker
Positive feedback
Negative feedback			Solution: Each player spends time in the lead before one player's final blow ends the game.

When both players have realized who is going to win, the game should end quickly.

[Literature] Game Balance ch6 - Situational balance

My notes from course 6 of the Game Balance class of Summer 2010, by Ian Schreiber.

If 10% of monsters are dragons, "double dmg to dragons" = 10% * 2dmg + 90% * 1dmg = 1.1dmg overall.
Situational balance = depends on the situation in the game; the cost is fixed cost, but the value changes depending on the situation. Ex: in DND, if atk + 1d20 >= AC then hit. Is +1atk (for player) balanced with +1def (for my opponent)?

• yes if 1 vs 1 (+1 on each side)
• no if enemies attack more often than player (because player will roll more often on AC than on atk) (eg 4 trash mobs vs one player)
• no if player(s) attack(s) more often than enemies (more rolls on player's atk) (eg player group vs boss)

=> Level design tip: player should be outnumbered half of the time, and outnumber the enemies half of the time if atk and def have the same cost and value. This adds replay value ("I could start a new game with 20atk/80def instead of 50atk/50def")

Versatility

In FPS, players usually have a close+strong+fast, a far+strong+slow and a far+weak+fast weapon. If player can switch weapons quickly, then it's as if the player had all of them at once. The overall price becomes the sum of all of these weapons, they should not be balanced individually.

A character/weapon is more versatile if it is able to handle more situations (Swiss-army knife). Examples:

• RTS: archer very strong against flying creatures and very weak against footmen. If wizard is (a bit) strong against flying AND footmen, wizard is more versatile than archer.
• FPS: knife = good in tight rooms VS snipers = good in large open-spaces VS machine gun = average on any map (= versatile weapon). Machine gun is the most valuable choice for players when they do not know which map is going to be played.

Solution against versatility: cost for switching can be time (it takes 5s to switch weapons), money, frequent weapon reload, etc. If switching is free, then player accumulates everything and uses each tool when he needs it. If inventory is limited, player will look for optimizations (eg only get fire and wind swords if you can only get 2 swords of the 4 elements). Balance depends on how fast player should be receiving new items.

• fast: price = constant (but player earns more and more as he progresses, so player gets swords quickly)
• faster and faster: "Since you’re such a good customer, you can have a 10% discount on all future swords."
• slow: prices increase

Two kinds of versatility:

• Ability of a single game object to be useful in different situations
• Ability of the player to change between game objects (if this type of versatility increases, then the value of each object's versatility decreases)

Shadow costs

Object cost = resource cost (how much player buys it) + shadow cost (maintenance, etc.). Shadow costs can be sunk costs or opportunity costs.

Sunk cost

Sunk cost = pre-requisites/tech tree costs. Examples:

• building a RTS unit may require buildings + techs. Building only 1 unit = lot of sunk cost, building many units = factored sunk cost
• WoW tech tree: powerful ability now VS weak ability now opening VERY powerful ability later?
• buying expensive shop discount card or a potion-making machine VS buying cheap potions repetitively?

Opportunity cost

Opportunity cost = how much versatility is reduced = when a choice prevents the player from taking another action later on. When an action adds constraint, how much is it as a cost? Examples:

• Protection from Fire costs 10 G. Protection from Ice costs 10 G. How much costs Fire+Ice protection?
  • 10G if player knows opponents' atk ahead of time,
  • 20G if player can not know,
  • 15G if player can not know but can purchase the other one if you guessed wrong.
  Giving hints (eg if player is told about a red dragon, she expects fire) reduces the cost.
• strong single-target VS weak AoE
• Alternates: Situational objects that can be brought into play if needed, but the player isn’t forced to use them when suboptimal.
• Metagame combo: not useful on its own, but useful if paired with something else (eg support class in MMO, building a CCG deck); the game should be balanced assuming optimal play, not average, because players will become good and play well anyway.
• RPG multi-classing and 'either/or' choices: lvl 10 thief = lvl 10 warrior = lvl 7 thief-warrior. Cost = more than either but less than both.

[Literature] Game Balance ch5 - The human-side of probabilities

My notes from course 5 of the Game Balance class of Summer 2010, by Ian Schreiber.

The more randomness in a game, the more casual it is: there are fewer strategic choices. Less randomness means more of the fate of the game lies in the player’s choices. That’s not always the case, though. Ex: TicTacToe has no randomness, but is not about skill. Other counter-example: a Poker hand is random, but there are skilled Poker players.
Skill dominates (over luck) if the player is rewarded for predicting and/or responding to the randomness. Ex: one can base his decision on probabilities in Poker, but not in Black Jack.
There is no skill in executing a difficult pattern that you’ve practiced (eg counting your hand or memorizing cards in BlackJack). Skill appears in planned, successful and unexpected decisions.
Luck can be carefully increased to even the playing field. Ex: headshots make it possible for weaker players to sometimes luckily kill better players. Head shooting is also a high-level skill. How much luck or skill a game should have depends on the target population: social games and kid games = luck, hardcore games = skill.
How to transform skill into luck:

• replace player choices by dice rolls
• throw less dices (so that there is no law of large numbers, hence less prediction)
• increase the impact of random events on the game state
• increase the range of randomness (like changing a d6 roll to a d20 roll)

Human biases

Humans tend to remember things that happen the least often, or forget those who are unpleasant (eg match loss), hence they tend to overestimate their level. Humans have a flawed understanding of probabilities, hence showing the actual probabilities will actually make them feel like something is wrong/broken. Here are a bunch of biases humans are subject to:

selection bias	improbable but memorable events are seen as more likely than they really are
self-serving bias	"unlikely" (5%) is interpreted as "nearly impossible" (0.01%) when the odds are in your favor. However, "unlikely" (5%) is interpreted as "possible" (30%) when the odds are not in your favor.
attribution bias	positive random result is assumed to be because of a player’s skill, negative random result is assumed to be bad luck/cheating
anchoring	over-evaluation of the first/biggest number seen. Ex: losing 2/3 of the trials is not as bad as losing 20/10 of the trials. Consequence: small base dmg but high bonus dmg = player likely to underestimate.
gambler's fallacy	assumption that a string of identical results reduces the chance the string will continue
hot-hand fallacy	assumption that a string of identical results increases the chance the string will continue

Ethics

Dishonest game design = make the players believe they are very likely to win. It increases excitement and anticipation of hitting a jackpot. Hence it keeps them engaged. Ex: dishonest car dealership: show VERY big prices first to anchor the customer, then show "normal" big prices: they look like small prices.
Honest game design = tell the player one thing, but actually do something else. Examples:

• If the player has 75% chance of winning, under the hood roll the number as if it were 95%.
• If the player gets a failure, make the next failure less likely, and the one after that even less likely (= avoid long streaks)
• Hot-hand streaks should happen in a positive feedback loop, to counteract the greater chance of a miss after a string of hits (ie give bonuses when series of wins)

But also, stay ethical as much as possible. Display wins, losses and various stats to enable players to grasp their actual skill and to "prove" the game is not unfair/imbalanced or that the AI is not cheating.

Saving

In a game where the player can save anywhere at any time, players are likely to save just before an important roll, and keep reloading until their roll succeeds.

• Naive solution: do not re-generate the random number each time they reload => new problem: players can now anticipate future rolls (the seed has not changed).
• Alternate solution: the player can save anywhere, but the total number of saves is limited (cf the original Tomb Raider) => new problem: players need to know how far apart they should save on average so that in the end of the game, they still can save.