For many years I've struggled to explain to people why I enjoy watching NFL football. Attempting to explain it forced me to develop some analogies and one in particular works really well - the chess analogy.
People unfamiliar with the sport, think it's something akin to rugby, violent sport where players push, shove and run and the team with the strongest, roughest players wins.
No doubt, that's one side of football. It is rough, requires strength and speed in abundance and teams with tougher players often have an advantage. However, there're more to football than that. There's the "chess perspective".
The Principle: Turn-Based Strategy
Because of the start-and-stop nature of American football, its discontinuity, there's opportunity to think, to plan, to apply intellectual analysis. Coaching staffs come up with designs that attempt to take advantage of unique capabilities of each of their players and create favorable match-ups. Each side picks an offensive play and the other side picks a defensive play to counter it, then they survey the result and move on to the next play.
That's very similar to chess (and to other TBS games). In chess players take turns making moves. Each having an opportunity to think in between, with limited time allowed.
Two coaches (or coordinators) are very much like two chess players directing their pieces against each other.
And what about the players? Aren't they in some way like the chess pieces?
There's the quarterback, arguably the most important player on a team - much like the queen in chess. One that can move far by throwing the ball (chess queen has the range also), one that can do two things - run or pass (queen in chess is the only piece that can move straight or diagonally), and one that has to be protected from harm - lest one lose the game.
There are the running backs, possibly second most important position - much like rooks are second most valuable pieces in chess. Running backs don't usually throw the ball, they take it and run - rooks can only move straight.
Wideouts would be bishops, they move far, but only in a specific way and serve a limited, albeit important function.
Tight-ends are knights, they don't have the range that wideout-bishops have, but they run short patterns and protect the quaterback when necessary.
And finally the linemen must be pawns. They form the line of protection around the quarterback, much like pawns do around the king and queen in chess. The also push forward and try to dominate the center and open up holes for their running backs to go through - again, all functions performed by pawns in chess.
Board and Positions
Both games are played on rectangular boards (though one is called a field and sometimes has real grass growing on it). Both are broken up into even sections: football into 10-yard stretches, and chess into 8 rows.
Both games are heavily focused on forward advancement towards opponents positions and being "pinned" deep in your own territory is never a good thing.
Line-up of the players/pieces is also very similar. In case of chess, the game starts with 8 pawns in the front, and all important pieces, rooks, knights, bishops, king and queen behind them.
In football, each play starts with linemen in front and most of the skill players (QB, RBs) "hiding" behind them.
Complexity of chess is well quantified and understood. The number of legal positions in chess is generally estimated to be between 1043 and 1047 (a provable upper bound), with a game-tree complexity of approximately 10123.
Tree-game complexity of American football (and any sport, really) is impossible to calculate and difficult to estimate, since various unique attributes of human players are at the moment not precisely quantifiable, and thus the average branching factor is not known. Likewise, a number of legal positions is potentially near-infinite considering that football field is continuous rather than discreet and each position has a large number of states (position, rotation and other attributes of the player).
Modern NFL teams carry playbooks that have in excess of 500 different plays on offense and up to several hundred on defense. We'll assume 100 defensive plays. Typical NFL game has an average of 130 plays. That yields 6,500,000 possible variations of the game, not counting playbook changes that all the teams undergo every year.
We must also account for the fact that each play specifies more than one action for each player, they may have multiple sequential assignments and may also have an assignment which requires them to change their actions based on opposing team's reaction/position. That increases complexity by a factor equal to an average number of assignments each player has on each play to the power of the number of players on the field. The number of assignments is high for some players (quaterbacks may have 4, 5 or even more) and low for others (blockers might have 1 or 2), so lets assume 2 on average. That's 211=2048 assignment variations.
The combination of 6.5 million variations with 2048 possible assignment situation brings the total number of all designed game variations to approximately the order of 1011. That may not seem like much, however it does not take into account the human factor. Since in this case the "pieces" are people that will bring a very large number of subtle variations into each play, we must assume the real number to be much higher - anywhere from 1014 to 1019, depending on what you believe a real number of behavioral patterns a player might potentially exhibit on a play - from hundreds to millions.
I'm sure one could argue with some of the assumptions I've made and the mathematical model selected, but it won't change the main point - the game is very complex.
Undoubtedly you can see the parallels. And the bottom line? NFL football is a very smart sport and in addition to showcasing great athletic abilities, it also puts on display an intricately designed, complex play system which engages the brains of the spectators (at least the ones that pay attention).
Of course I cannot compare the two games without pointing out the one important difference: cheerleaders!