I included Rhodes in pulling my data, but at the end of the day there wasn't anything significant to pull from his stats for that one year, so I'm not going to report them below.
I used ESPN split stats, which go back to 1993. They break down the passes and runs through an incredible number of situations. Holmgren and Sherman had six seasons each in the stats period, and McCarthy 5. So McCarthy's total numbers will be lower than Holmgren/Sherman, but the ratios should be comparable.
EXECUTIVE SUMMARY: All three coaches maintained a pass/run ratio 60/40 or below. Pass run ratios did not increase above this level until falling behind in a game. There was some running to put games away, but the impact was less than you might have expected. And McCarthy has the highest pass ratio when tied/in the lead, an indication he is the LEAST conservative of the three coaches (for those saying he has no killer instinct).
There has been a perception that McCarthy does not run the ball as much as Sherman and/or Holmgren. That perception is not supported by the statistics. Both Sherman and Holmgren had an overall 56/44% ratio. McCarthy's ratio was 57/43%, the difference is not statistically significant.
I also looked at the stats by month (Sep-Dec). The main difference is Sep, where McCarthy starts the season off with a 61% pass ratio, compared to Sherman/Holmgren's 56%. Doesn't sound like much, but it leads to a significant difference in attempts per game.
To normalize the stats, I divided McCarthy's stats by 5 and multiplied by 6, and he still ended up running 200 times less than Holmgren in Sep (476-673). The rest of the year (Oct-Dec), McCarthy's stats were similar to S/H.
That 200 rushes equates to a difference of between 8-9 rushes per game (6 years x 4 games in an average month). So for whatever reason, McCarthy starts out the first month of the season with significantly fewer rush attempts than his predecessors (or himself for the following months).
Sherman was the most consistent across the months, with Holmgren running at the highest clip in Dec.
The win/loss split did not provide the info I was hoping on the question of whether a team was running more because they were winning or winning because they were running more.
So I looked at ratios from 1st half/2nd half of games, as well as by quarter. Holmgren's ratio dropped more in the 4th qtr than I would have expected, and McCarthy's didn't drop as much as I expected.
Sherman was again the most consistent, with a 56/44 (1st half) and 57/43 2nd half. He showed almost no tendency to run at the end of the game to salt away a victory. Holmgren was the opposite, passing at the highest ratio in the first half (60/40), and lowest in the 2nd half (52/48), with his 4th qtr totals actually dipping to 47/53. McCarthy was in between the two, with a drop in the second half from 59/41 to 55/45 (53/47 in the 4th quarter).
So, there's some evidence of running to put the game away at the end, but the impact was less than you might think--4th qtr averaging 4% lower pass ratio over all three coaches.
Those who complain that McCarthy has no killer instinct and gets conservative when he has a lead might want to skip this next section.
McCarthy was the LEAST conservative of the coaches (at least as indicated by pass/run ratios) when both leading a game or tied. McCarthy when leading maintains a 52/48 ratio, and when tied 59/41. Sherman was the most consistent (and conservative), with a 48/52 ratio when ahead and 53/47 when tied. Holmgren was between the two with a 49/51 ratio when ahead and 57/43 when tied.
The biggest thing I took from these stats were that when tied, all three coaches maintained a ratio below 60/40. It wasn't until they were losing that the ratios increased above 60/40. That would tend to indicate to me that the desired ratio is below 60/40.
I also looked at stats to see what the mix for each coach was in a close game--when we were 1-7 pts ahead, tied, or 1-7 pts behind. In the close games, the highest ration was 60/40 (McCarthy--the least conservative again!), with Sherman the most conservative (56/44).
There was a slight difference in ratios between tied and winning by 1-7, but it was only 2% on two of the coaches (Holmgren 55-57%, McCarthy 57-59%) and 3% for Sherman (50-53%).
There was a large increase in pass ratio for all three coaches when the Pack fell behind. Holmgren went from a 57% pass when tied to 76% when behind by 1-7, Sherman 53% to 72% when behind by only 1-7, and McCarthy had the smallest change from 59% to 67%.
Again, my biggest takeaway was in a close game, the pass ratios for all three coaches were between 56 and 60%.
One thing I discovered was ESPN breaks out splits by formation for the years from 2007 on. They don't have the info for 2010 yet, so I just included 2007-2009.
The formations they listed were Shotgun, 2 RB split, 2 RB I-formation, and Single RB. Obviously, there are some issues since it doesn't seem to allow for GB's inverted Y formation with 3 RBs. They also added some splits for 4 WR sets, etc.
The below numbers don't add up to all of the runs/passes in 2007-2009, but I don't see how to figure out the other formation numbers. But even without that, I suspect something's wrong with the numbers, or McCarthy needs to change his play calling, because the splits from 2007-2009 indicated that the Packers did not pass a single time from a 2-RB formation (split or I-formation). Every single play from those formations were shown as a run. I would be shocked if McCarthy had a tendency like that, so I suspect that their formation numbers may have issues.