tombonneau said:
Not to get engaged in this semantic debate, but I think the classic "Playing not to lose vs. playing to win" scenario is when you have a situation where a team is up by 4-7 point (i.e. >FG).
They are presented with the ball is respectable field position, i.e. their own 30-45.
The clock is in their favor and they know that if they get one first down--only one--the other team is at their mercy and they can take a win to clinch victory.
A coach who is playing not to lose, will run the ball three times in that situation even if he thinks there are plays in his playbook that have greater odds of picking up a first down and winning the game.
A coach playing to win will try a playaction or similar pass play that will increase the likliehood of picking up the first down and winning the game.
Every situation can be broken down into a percentage of winning the game. If it's 0-0 and the teams are even, and there's 15:00 left in the 1st quarter, each team's chances are 50/50.
If it's 10-0 and there's 5:00 left in the 2nd quarter, the winning team has say a 65% chance (just a rough guess).
If a team is up by 5 with the ball on their own 40 and there's 2:00 to go, the team probably has a 90% chance of winning on 1st and 10. If they run for 0 yards, and now there's 1:55 to go, maybe they have an 87% chance to win. If they pass for 7 yards and there's 1:55 to go, maybe they now have a 95% chance of winning. If they pass and it's intercepted, maybe they have a 55% chance.
But every play and every play call slides each team's chances of winning up or down. A coach who is playing not to lose may run the abll three times, but if that increases his team's odds of winning, he's not playing not to lose --> he's playing to win. If running three times decreases his team's chances of winning, he's not playing not to lose --> he's playing to lose.
The terms conservative and aggressive are much more descriptive of what you want here, I think. But there's no such thing as playing not to lose and not playing to win, unless you're kneeling on the ball with 30 seconds left in overtime.