Just to put what Yvonne wrote into numbers, I took the offensive stats from cfbstats.com for all the years they had data (2008 through the ND game in 2014), and calculated points, yards, and first downs per possession. I like per possession stats because you don't have to worry about the pace of play (a team like Oregon that scores quickly will get more possessions than a team like Stanford and would be expected to get more yards and more points, even if the offenses are equally efficient at turning possessions into scores. The system is not perfect, and doesn't account for the strength of the defenses faced, but I find the stats are very useful.
Since the data goes back to 2008, we can see the effect of having Andrew Luck in the backfield (three years, from 2009 - 2011) and the effect of having both Shaw (2011 to 2014) and Harbaugh (2008 - 2010) as head coaches. Most importantly, each head coach had an opportunity to coach Luck and one other QB (Pritchard for Harbaugh, and Hogan for Shaw), so it really gives us a chance to disentangle the effect of Andrew Luck from the effect of the coach. To be fair, I think Hogan is a better QB than Pritchard was, though I think that is balanced out by the fact that Harbaugh had Gerhart as running back, and this year, Shaw does not have a running back of the caliber of Toby. Note, I listed Hogan as the QB for 2012, even though Nunes started a number of the games.
Looking at the raw sats, it is clear that Andrew Luck was a difference maker; his three years we averaged 3.6 points per possession (a touchdown every other possession), 2.1 first downs per possession, and 42 yards per possession. In the other years, we averaged 2.4 points per possession (PPP), 1.6 first downs per possession (FDPP), and 31 yards per possession (YPP). In other words, Andrew Luck was responsible for a 47% increase in PPP, 31% increase in FDPP, and 30% increase in YPP.
Looking at coaches, having Harbaugh as a coach was worth 0.3 PPP (3.07 PPP for Harbaugh vs. 2.80 PPP for Shaw), 0.18 FDPP (1.93 vs. 1.75), and 2.5 YPP (37.6 vs. 35.1). However, Harbaugh had Luck for 2 out of his three years here, while Shaw had Luck only 1 year. If you do a multiple linear regression (sorry to be geeking out here), you get the following.
As for the question of whether the "trend has been worse since Luck left", we certainly took a big hit with Luck's departure. But 2012, 2013, and 2014 look pretty similar to me. Points per possession is down this year; probably a reflection of our red zone troubles early in the year (note, I think we were perfect in the red zone against Notre Dame (our botched field goal was from the 25; the problem was we didn't even make it to the red zone against ND). First downs per possession and yards per possession are between 2012 and 2014.
lm(formula = PPD ~ Shaw + Luck, data = o)
Residuals:
   1    2    3    4    5    6    7
-0.35765Â 0.45235 -0.14765Â 0.05294Â 0.22353 -0.27647Â 0.05294
Coefficients:
      Estimate Std. Error t value Pr(>|t|)Â
(Intercept)Â 2.2171Â Â 0.2805Â 7.904Â 0.00139 **
Shaw     0.1706  0.2930 0.582 0.59161Â
Luck     1.2794  0.2930 4.367 0.01199 *
---
Signif. codes:Â 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 0.3487 on 4 degrees of freedom
Multiple R-squared:Â 0.8395, Adjusted R-squared:Â 0.7593
F-statistic: 10.46 on 2 and 4 DF, p-value: 0.02575
Andrew Luck is worth 1.28 PPP (statistically significant); there is no statistical significance between Harbaugh and Shaw, though, in the model, Shaw actually gets 0.2 PPG more than Harbaugh. I won't throw the regression code up for FDPP (I can send it if anyone wants), but Luck is worth 0.51 FDPP with a p-value of < 0.01; there is no significant difference between Harbaugh and Shaw, and Luck is worth 10.4 YPP (p = 0.01), and again, a non-significant difference between Shaw and Harbaugh.
Obviously there are a lot of caveats here; while I adjust for Andrew Luck, there are a lot of other players and coaches involved, and it is certainly possible that Andrew Luck aside, Shaw might have had more talent at his disposal his three years than Harbaugh did. Harbaugh did have Luck his redshirt freshman year, where he was somewhat less effective than his other two years, and you might argue that an offense with Luck as a redshirt junior should have accomplished more than an offense with Luck as a redshirt sophomore (the offenses the two years were pretty similar in efficiency). Finally, none of this takes into account external factors such as the quality of the defense we were facing, how much of the game was uncompetitive (when we pulled starters and/or went with a conservative play calling), or weather, which was certainly a factor Saturday.
BC