I find several key elements in replayability in any game...
- Multiple routes to victory
- Multiple starting conditions
- Variable in-game activities
- Variable in-game events
- Variable action results
- Imperfect information
- Optional Rules
Multiple Routes To Victory
Multiple routes to victory is a key element in all games, not just cooperatives, and it can be assessed by reading the rulebooks for the victory conditions.
Multiple Starting Conditions
Multiple starting conditions means you don't always start the same.
Parchisi and Chess are classic examples of one start condition, as is Axis and Allies.
Risk, Shadows Over Camelot and Civilization are three different modes of variable starting conditions. In Risk, you have random allocation of starting countries. In Civilization, each picks their starting country, and then their starting space. In Shadows, you have a random assortment of starting white cards and one of 7 (or 8 or 16) characters with differential powers. In Flash Point, you have the option of fixed start for Family difficulty, or random start with any difficulty.
The more non-random variability in starting condition, the more likely people are to find one optimal, and the more control they feel, but likewise, that also reduces replayability.
The more random variability in starting condition, the more replayability, but also the more likely one is to be hampered by the random factors and be "losing from the start."
Again, this can usually be assessed by the combination of the component list and the rulebook.
In Flash Point, it's possible to lose the game in the first round from bad luck; if you lose 4 or more of the victims on the map during the first two players' turns, it's game over before player 3 gets to play. I've nearly had this happen - in a 3 player game, we lost two victims on the first player's turn; they straddled a starting fire marker, and that marker was hit. Roughly a 1 in 100,000 chance, but it was in my 4th play. That this could happen was evident in the rulebook.
In Game Activities
The more different things that can be done, the more potential replayability... If you have but two options per turn, that tends to reduce replayability somewhat over a game with 4-5. (Too many eventually results in unplayability, tho'.)
So, for example, in Shadows, one is either playing cards on a quest, playing cards on a siege engine, playing cards on a character, or moving between quests. Essentially, 4 options. Which, generally, hits my sweet spot for a board game.
In Wizards (Avalon Hill), each turn is spend AP on movement and/or casting... but the movement options are many, and the spell options quite a few.
In Flash Point, one is fighting fire or rescuing victims, with movement being required to do both. Only rescuing victims counts towards victory, but preventing collapse makes fighting fire a necessity. But there are several more actions listed; these are options relating to how to minimize travel time.
This is readily determined by reading the rules.
Things which happen to the player's position other than by choice.
Well done events can be a bonus to the replayability. Poorly done ones are a hinderance.
This is a hard one to judge without play; the quality and effect of the randomization (or lack thereof) can make or break a game; this is doubly true in cooperative games, where the competition is usually versus the events instead of the other players.
This has to be determined by a study of the components and/or multiple plays. For cooperative games, this is where the meat of reviews really becomes important.
Wizards has dozens of events, and uses a number of different random tables for them.
Dragonriders of Pern has at least one event every turn: the threadfall card. It also has players draw special cards, some of which are events. These provide most of the randomness needed for the replayability of this game.
Shadows over Camelot has the entire black deck...
Flash Point has only two randomizations, but they happen a lot: where the fire spreads, and where the next "point of interest" (POI) appears. Spread is every turn. POI appearance is whenever a victim has been rescued, or a victim is killed, or a POI is revealed to be blank.
Variable action results
The more potential results of a given action, the more replayability.
Generally, this is the result of randomizations in action resolution.
In Shadows Over Camelot, this is the random strength on the quest black cards, and the die-roll of the siege engine.
In Wizards, it's almost entirely die-rolls on tables.
In Dragonriders of Pern, it's random die-rolls on both thread fighting and diplomacy.
Flash Point has no variable results of decisions. All the random input is in where fire spreads, what's under the POI, and where POI's appear.
In a game with either variable setup or variable events, a lack of full knowledge tends to improve replayability. If taken too far, however, it impairs playability over all.
The amount of information is usually readily determined from a rulebook; its effect on play, however, isn't.
In Wizards, there's lots of imperfect information, but anything in play is perfect information. You don't know what's coming, but you know all that's on the board so far.
In SoC, the imperfect information is extensive; what events are forthcoming, what cards your fellows have, who the traitor is. In fact, the major victory issue is reducing the uncertainties. If a group can readily reduce the uncertainties by consistent use of language without breaking the "no game mechanics discussion rule," then the game is almost solved from the get go... reducing it to traitor hunt and race to complete quests in time.
In the competetive coop Dragonriders of Pern, the imperfect information about thread fall next turn makes the game much more tense; one option that reduces that is having a visibile queue of thread cards. It strongly changes the way experienced players play it in both the coop thread fighting and competitive diplomacy phase. The lack of information by the dice also inhibits long term planning.
In Flash Point, the information of the current state is almost perfect - the only thing you don't know is what a POI contains - it's either a victim or a blank. Future information is absent, since it's dependent upon random rolls and random draws.
In the end...
These factors combine to determine the most important singular qualifier:
Interesting choices that have multiple non-loss directions.
If you have an interesting choice, but one direction leads to loss, and the other to victory, once you learn the difference, the choice is no longer interesting.
If the choice points are always the same and always have the same results, once you've explored them all, they become uninteresting.
Of the four cooperative games I've mentioned (Shadows, Wizards, Dragonriders, Flash Point), I've found replayability a non-issue with any of them for infrequent plays.
Shadows, the choices are too similar in any two plays to play twice in a row, but separated by some time, the game remains interesting, especially if one doesn't replay with the exact same group every time.
Dragonriders, the game is a bit long, but the randomizations make the outcome in doubt right until the end, and despite very low starting variability, the high in-game variability makes the choices interesting and not a fixed-tree state. (It's also one of the few games that scales well 1-6 players)
Wizards is even more wildly open. highly variable board, massive randomness in in game events and outcomes. It's also bloody hard, and competitive cooperative. Everyone has to cooperate against the board, or everyone loses; only one will in fact win, however, so there is some PVP action. Many of the choices are less than interesting, and there are up to a dozen trivial choices per turn; interesting choices are range from one per 10 turns (while on certain long tasks) to several in a turn.
*Flash Point can be replayed in rapid succession, due to the high level of randomness coupled to near-perfect current state information. While there is only one victory condition, the challenge remains high.
The inclusion of playtested optional rules also gives some games more replayability. Because they change some aspects of the rules, they also change the experience somewhat.
Optional rules fall broadly into a few key areas: difficulty changes, thematic changes, and alternate conditions. An optional rule for difficulty change makes the game either harder or easier, while not changing much of the mechanics. A thematic change changes the thematic nature of the pieces, but often involves little to no change in game play. An alternate conditions option is a change in either how you start, or what constitutes a victory or a loss.
Optional rules need to be looked at carefully - sometimes, they are added because the game isn't long-term replayable without them; in others, they're there because they enable the game to be attractive to a wider audience, but don't really affect replayability.
Shadows has an alternate setup option called the "Squires" option that changes the beginning setup slightly. Likewise, it has an option for a pure co-op play, by not using the loyalty cards, and an option for a harder game by including two traitor cards plus a loyal card per player, and thus not knowing whether there are zero, one, or two traitors.
Dragonriders has a solitaire variant with similar but not identical rules. It also has the 7 player variant with the Harper Hall as a player, whose victory condition is by kingmaking.
Wizards has the option of changing the duration between evil advancing. Longer makes it easier to thwart evil, and shorter makes it harder. Further, how many tasks must be completed to thwart evil may be changed, also affecting difficulty.
Flash Point has a "Family Game" and an "Experienced Game" both in the basic rules. The family game is a fixed setup, and is simplified rules. The experienced game adds a number of additional mechanical complexities, including three difficulty levels, and is presented as a second section of the rulebook. A third section includes optional rules, including piecemeal adoption of the advanced game mechanics into the Family Game, and explicit permission to house-rule one's own additions to the game. The only option I've used is mixing in some of the expanded game into the basic game.