The Two-On-One Fast Break

If you play basketball, what strategy do you use when defending a two-on-one situation? I always try to fake at the player with the ball, in hopes that this will slow them down allowing more time for one of my teammates to hustle back and help or so that the other team will make a poor decision. While I fake, I stay on the ball side of the basket, ready to take a charge or spring and steal/tip the pass. 

Here you see two circles representing the offense, the colored in one has the ball, and one "X", the defender. This picture shows how I would play defense: I stay in the dribblers lane to the basket, and have good positioning to react to a pass. 

DeVenzio has quite a different strategy than me: "The important thing is to stay near one player and keep the ball in the other player's hands, preferably the guy on the left side who most likely is right-handed and, therefore, more prone to miss the eventual shot or throw a bad pass from that side" (256). It has never occurred to me to try and keep the ball in one player's hands, nonetheless on the left side (I don't know why anyone would assume that a player would miss a layup, unless there was previous known knowledge). DeVenzio does agree with me, however, to fake and threaten the ball. Then at the last moment, he says, to get over and distract the shot, take a charge, or block the right-handed pass (256). 

The two circles are those on offense, the "X" is the defender, and the colored in "O" has the ball. This picture shows how DeVenzio recommends defending a two-on-one. Sticking closer to the player without the ball.  But easily seen here, this gives the player with the ball a driving lane straight to the basket. 

 DeVenzio's strategy doesn't make much sense to me. When I think about myself on offense, taking the ball down two-on-one, if the defender comes up to about the free throw line, I will pass the ball. If they stay down directly under the basket, I will take the ball all the way to the rim, looking at my teammate the entire time, then fake a pass just before I lay it up. Because this is what I personally would do on offense, I would keep my defensive strategy the same. It puts me already in the dribblers way, and my arm length gives me a safety net in case of a pass. 

Whose defensive strategy do you think is better, DeVenzio's or mine?

Citation:

DeVenzio, Dick. Stuff Good Players Should Know. 3rd ed. Stafford: PGC      Basketball, 1983. Print