In game theory, a pure strategy is where a player does not randomize between options. For many game situations, this is not an optimal way to play the game. Would a prison guard want to always to do his rounds in exactly the same fashion time after time after time? No because the prisoners will rationally expect him to continue his beat in the same way and the prisoners will do what they will do when he's away.
Mixed strategies, on the other hand, is randomizing between options. A prison guard might do his rounds at different times during his shift. He may even do more or fewer rounds than he usually does just to shake things up.
It's no different in sports. A pitcher who throws the same pitch gets hammered. A pitcher who "tips his pitches" also gets hammered. Teams have to shake things up to keep the opponents honest. A recent Columbia Daily Tribune on the Missouri Tiger running game shows how the coaching staff is using the tools it has at its disposal to craft an effective running game. An excerpt:On Saturday, Missouri (5-3, 1-3 Big 12) used the two-back look on 13 of its 75 plays from scrimmage, running out of it 11 times for 36 yards. The Tigers had more success trampling the Buffs with their more conventional one-back shotgun set (138 yards on 28 carries), but as Gary Pinkel’s team continues to deploy more two-back looks — a tailback lined up on each side of quarterback Blaine Gabbert in the shotgun — the running game discovers something it might have been lacking: unpredictability.
“It gives the defense a new look,” said tailback Derrick Washington, MU’s busiest runner against the Buffs with 99 yards on 22 carries. “Usually we line up with one back in the shotgun and we always run the ball to the opposite side. And some defenses just slant to that side thinking we’ll run there. But now, we keep them guessing because either back can get the ball and go either way with it.”
“It’s making it tough on reads,” added backup tailback De’Vion Moore, who chipped in 58 yards on eight carries, including the game’s longest run from scrimmage, a 31-yard dash in the opening quarter. “You see one back go one direction and another back go another direction. It’s like, ‘OK, which back are we keying?’ It’s all about speed on the field and players who can make plays.”
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