In most sports, it's possible to use two basic principles to determine what strategy a team should follow.
The first principle is that the more times a given activity occurs, the more likely it is to conform to the average expected outcome. If you flip a fair coin ten times, it would be unusual but not unheard of to get heads seven times. If you flip a fair coin 100 times, it's very unlikely to be heads 70 times. If you flip the fair coin 1,000 times and get heads 700 times, you can probably conclude that it's not actually a fair coin.
The other principle is the risk/reward tradeoff. This principle comes from the world of finance, and it's something I think we all understand instinctively. The higher a return you want to get on an investment or activity, the more risk you have to take. A Hail Mary pass from a team's own 20-yard-line is risky because it's hard to complete and relatively easy to pick off, but if completed, it has a greater chance of turning into a touchdown than an off tackle handoff is from that same place.
These principles easily apply to basketball strategy. Think about a team that is a big underdog in a game.
All else equal, that team will want to play at a slow pace to minimize the number of possessions in the game. Because the opponent is a much better team, the average outcome of a possession in the long run will be in favor the opponent. Keeping the number of possessions down will make it possible for the result of the game to have an outcome that is far from that average—and the underdog pulling off the win is far from that average. The more possessions there are, the greater the likelihood of a result conforming to the average, i.e. that the better team will win.
Also all else equal, the underdog will want to take a lot of three-point shots. They're higher risk plays, but they bear a higher reward by being worth 50% more than a shot from inside the arc. Hoisting bad threes is always bad unless time is about to run out, but any time the underdog gets a decent look from deep, it should take that shot. Taking more risks increases the probability of a large blowout, but a loss is a loss in the standings. Taking more risks also increases the chances of a win.
On defense, the underdog will want to press the opponent in the backcourt. Pressing increases the chances of getting quick turnovers and therefore minimizing the number of possessions with a real scoring opportunity for the favored team. It dials up risk, since breaking the press often results in easy buckets, but backcourt pressure can lead to easy buckets for the pressing team too.
In short, the underdog team should try to use as much of the shot clock as possible, take as many good three pointers as it can, and press like crazy. Things change from there based on personnel and team style, but a coach who knows his team isn't very good should probably make his team a slow, three-point shooting squad that presses. Conversely, a good team should not be afraid to push the pace to increase the number of possessions in a game, should generally not take threes unless a good shooter is wide open, and should probably set up its defense whenever possible. In stats lingo, keeping the number of trials high and the variance low is a good thing for the favored team.
If you try to apply these principles to football, you'll find that they're in opposition to each other.
Keeping possessions down means keeping the clock moving. To keep the clock moving in football, a team will run the ball more because incompletions stop the clock. Any throws should be safe ones to maximize the number of completions and prevent those stoppages.
However, increasing risk to increase return means throwing more. For this piece, I took sacks and sack yards out of rushing and put them into pass attempts and pass yards instead. The best team in 2015 at rushing was Oregon at 6.69 yards per carry. That would've put the Ducks' rushing game at No. 52 on the yards per attempt list behind Washington at 6.71. Despite starting a true freshman at quarterback all year, the Huskies' pass attack got more yardage from its average play than the best rushing attack in the country did. Passing bears more risk—it's harder to complete a pass than complete a handoff or snap, and handoffs and direct quarterback runs can't be intercepted like passes can be—but it unquestionably offers a higher return in theory. It's part of why even the most run-oriented teams resort to passing frequently when they're down towards the end of games (clock stoppages on incompletions being the other reason, of course).
To keep the clock moving, you have to run. But to increase the variance, you have to throw.
Of course, that's just offense. A defense can try harder to strip the ball at the risk of more broken tackles or jump routes to try to get more interceptions at the risk of allowing bigger gains. It can also purposefully allow receivers an opening for short, easy catches over the middle to try to reduce clock stoppages from incompletions or players going out of bounds at a risk of allowing too many yards to end possessions.
Overall though, the fact that the general underdog principles of minimizing the number of interactions in a game and increasing the variance of those interactions makes underdog strategy in football less clear than it is in other sports. The question of what an underdog should do will never be completely straightforward in football until and unless incompletions no longer stop the clock.