In the chart below are the total production ranking, offensive production ranking and defensive production ranking for USC from 2008 to week #5 of 2013 (Kiffin's last game at the helm of the Trojans). What stands out to me is that USC's defense has been less productive since Kiffin's arrival than in the last two seasons under Carroll. The season by season data is given below where all the analysis is derived from the Complex Invasion College Football Production Model.
2013
As of last weekend, USC was 3-2 playing against an average strength of schedule (SOS) as compared to the "league" as a whole. [I define all teams that are within one standard deviation of the league SOS as average]. USC is the #51 most productive team overall with the #46 most productive offense and the #56 most productive defense. Given that USC has not been in the top 10 in any category since 2008 and my guess is that current USC administrators did not feel that the program was moving in that direction, USC decided to fire their head coach. What will be interesting to see is if this change fundamentally changes USC's performance. I doubt there will be any real change this season; but this question will best be answered in a few years.
2012
The USC Trojans played against a SOS = 55.69, which was "tougher" than the league strength of schedule of 65.53. In the wins/loss column, USC finished the regular season at 7-5, with their best win (win over highest ranked opponent using the NCAA FBS Production model) was a 38-17 victory over Pac 12 rival #24 ranked Arizona State - avenging last years defeat, and their worst loss was to Pac 12 rival #61 ranked Arizona (36-39). USC subsequently lost to #50 ranked Georgia Tech (7-21) in the Sun Bowl. Not helping the situation, the model predicted that USC was the better team. The Trojans finished the 2012 season at 7-6. Overall, USC was ranked as the #46 team in overall production, with both the #42 ranked offense and defense for that season. While a ranking of 46th overall is above average - it is not in that "elite" status where the Trojans are competing for the Pac 12 conference title and a "national championship" or Rose Bowl berth.
2011
The Trojans finished the regular season at 10-2 (bowl ineligible due to NCAA sanctions). USC finished the season as the #27 most productive team using the NCAA FBS Production model, with the #16 most productive offense and the #47 most productive defense. USC played an average SOS = 63.75 compared to the average for the "league" of 64.29. For this season, USC's best win was a 38-35 decision over #8 ranked Pac12 rival #8 ranked Oregon Ducks and their worst loss (22-43) was to Pac 12 rival #63 ranked Arizona State. This was by far Kiffen's best team (in terms of production) during Kiffen's tenure at USC.
2010
Lane Kiffin's first year as the head coach for the USC Trojans, the Trojans finished the regular season at 8-5 (bowl ineligible due to NCAA sanctions). USC finished as the #52 most productive team with the #42 most productive offense and the #75 most productive defense, which is a substantial reduction in productivity from 2009. USC played against an average SOS of 61.15 compared to the league average of 63.10. The Trojans best win was a 49-36 victory over #13 ranked Hawai'i and their worst loss was again to the #87 ranked Washington Huskies by one point, 31-32.
2009
In what was Pete Carroll last season with USC, the Trojans finished the regular season at 8-4 and won their bowl game against #51 ranked Boston College (24-13) to finish 9-4. The Trojans played against a SOS of 58.08 which was average as compare to the "league" as a whole. USC was the #31 most productive team overall with the #33 most productive offense and the #36 most productive defense, all less productive than the previous year. USC's best win was a 18-15 victory over #9 ranked Ohio State and their worst loss (13-16) was to #76 ranked Washington.
2008
This was an excellent year for USC football. The Trojans finished 12-1, including a Rose Bowl victory over #4 ranked Penn State 38-24. USC was the #2 ranked team in the nation in terms of overall on-field productivity, with the #12 ranked offense and the #1 ranked defense in the "league". USC only loss was to Pac 10 rival #28 ranked Oregon State (21-27) and played against an average SOS = 56.92 as compared to a 62.92 SOS for the "league" as a whole.