In our gaming group, Settlers of Catan is by far one of the games we've played the most, making it one of our favorite games. In my musings to understand what makes a great game, i've come up with a theory i'd like to posit here: Settlers of Catan is a great game because it "gives you the illusion of control, but is actually mostly based on chance." Let me explain.
Luck vs Skill
Most games usually involves luck and skill, which I see as a continuous line from all luck to all skill. Skill-based games give you sense of control and satisfaction that comes from the challenge of learning and playing against other skilled opponents. The classic example of an 100% Skill game is Chess. There is no element of chance and the seasoned player will win pretty much all the time. Every move you make has a direct result on the game outcome giving you a great sense of control. On the other end of the Spectrum is CandyLand which is 100% luck. Everything is dependent on the dice roll and you basically have no decision-making capability. A machine which rolled the dice and moved the pieces could play the game for you. The upside is that these games are very fair for new players. Hence, these games are fun because anyone can win (and they tend to be easier to learn the rules). Most games fall somewhere between of all-luck and all-skill, trading off the benefits of one for the other.
What about Settlers of Catan?
The reason we play Settlers so often is because there are many strategic options to explore, giving it great replay value. It is a very active game and there is very little down-time; you are constantly gathering resources and trading even when it's not your turn. At the same time, the game is very fair for new players and it is quite common that new players win the game over seasoned veterans (given the right initial conditions*). This is why we like to play the game at parties because even new players can have fun.
Because of this fact that new players have a good chance of winning over seasoned players, it gives good evidence that the game is actually mostly based on chance. However it doesn't feel like it because you are constantly doing stuff: drawing cards, trading with other players, and building roads and cities. You feel like you are always in control and allowed to pursue your own strategic agenda. Being a game that "gives you the illusion of control, but is actually mostly based on chance," give you the benefits of both Luck and Skill-based games in one, which I think is why Settlers of Catan is a great game.
*The biggest effect on outcome of the game is probably initial placement of settlements, which directly determines your chance of resource gathering from the dice roll. We found in our games that giving new players guidance on placing their initial settlements (on high pip count, 6 and 8's) makes the game fair for them to win. Also, it means they're very active throughout the game, constantly drawing resource cards, and thus they have fun playing, meaning they'll play again.
