Posted by ESPN.com's Mike Sando

Alex Smith had success throwing to rookie Michael Crabtree on third down when the 49ers rallied in the second half of their 24-21 defeat to the Texans.

Smith's success throwing to tight end Vernon Davis, the NFL's leader in touchdown receptions, had come on early downs.

The charts, produced by Hank Gargiulo of ESPN Stats & Information, break down Smith's passer ratings by receiver and situation. The first chart isolates first and second downs.

Alex Smith's passer rating differential by receiver on first and second downs Receiver Times targeted Passer Rating Rating to other receivers Differential Vernon Davis 10 142.1 72.1 +70.0 Josh Morgan 4 116.7 106.7 +10.0 Frank Gore 6 96.5 110.5 -14.0 Isaac Bruce 9 91.9 113.8 -21.9 Michael Crabtree 9 57.9 124.2 -66.4 Moran Norris 1 39.6 111.8 -72.2 Glen Coffee 1 39.6 111.8 -72.2

The second chart isolates third down. The information will become more useful the longer Smith plays. The third-down information in particular is quite limited, but it does line up with the overall impressions I've had, specifically in relation to Crabtree's potential on third down.

Alex Smith's passer rating differential by receiver on third down Receiver Times targeted Passer Rating Rating to other receivers Differential Michael Crabtree 3 106.9 59.7 +47.2 Josh Morgan 2 79.2 82.4 -3.3 Vernon Davis 3 70.1 89.6 -19.4 Frank Gore 1 39.6 91.7 -52.1

I'd appreciate feedback on the methodology here, specifically as to what tweaks might make this type of information more useful or reliable. Davis and Morgan were also the early-down leaders for Shaun Hill. Hill's third-down rating was best throwing to Frank Gore and worst -- by 60.5 rating points -- when throwing to Davis.