If even the lagging guard is denied the ball, the offense may run something like the “blind pig,” in which the weakside forward cuts out toward the ball for a pass that is redirected to the lagging guard, veering backdoor to the basket. If there has been no pressure and the triangle-side wing is free, the ball usually goes to him, and he initiates the attack. But if the wing is denied, the center could receive the ball in a passing option known as the squeeze while the wing makes a backdoor cut; then comes a screen by the triangle-side guard, freeing the lagging guard to receive the center’s pass for a shot.

Got that?

With every player the possible point of the newest beginning, crucial to the triangle are versatile athletes, with polished passing, movement and shooting skills allowing them to fulfill multiple roles. Jordan and Bryant scored from all over the court because their positioning varied from possession to possession.

A center capable of shooting from outside — Pau Gasol, for instance, or perhaps Frank Kaminsky, a senior at Wisconsin last season — is a coveted triangle commodity because he can give other players the opportunity to visit the post. O’Neal passed so well that he defeated the double teams his potent interior scoring skills attracted by operating like a lighthouse, locating the safe pathways ceded by the defense and beaming assists into the clear.

Winter empowers his players to read the defense and make situational decisions within the flow of the game, so the tricky part is that everyone must recognize the same opportunity and choose the same response. In effect, Winter wants five basketball Peyton Mannings on the floor, scanning the defense, deciphering its intentions, flashing around the court in well-spaced concert, exploiting vulnerability. Passes move faster than players, and Winter, like Carril, knows that defenses besieged by a ball in constant flight rarely sustain full effort for entire possessions.

The triangle offense is really more of a rubric than a system. “The Triple-Post Offense” contains a menu of options and counters sufficient to defeat any known defensive action. Winter has diagramed pages and pages of these discretionary choreographies, with the clarity and precision you’d expect from someone who studied architectural draftsmanship in the Navy.

Another red book requirement for playing under Winter is that players learn the exact dimensions of the court and even of the hoop itself. He has mapped the game, as it were, and he believes that if players become familiar with all of his coordinates, they will never lose control.

As an N.B.A. assistant, Winter was renowned for convincing professionals that it was in their interest to begin every practice with push passes, bounce-backs — the most basic basketball exercises.