How important ARE round-trippers?

Point A:
The Yanks 2006 record when not hitting a HR: 18-27
win % .400
Which makes their HR-game record: 79-38
win % .675
That's a 27.5% difference. That is big.

Point B:
1-run record: 24-22
win % .520
Games won by one run with a Yankee HR: 16
which means a HR was the difference in 67% of those 24 1-run wins = pretty important.

Point C:
Tampa Bay was 11th in MLB in HRs, which puts them in the top half. However, they were the worst team in baseball.

Point D:
If we split all MLB teams into thirds by HRs (for 2006)...
Top 3rd. - Avg HR 209 - Win % .540 - Playoff teams 3
Mid 3rd. - Avg HR 177 - Win % .473 - PO teams 2
Bot 3rd. - Avg HR 154 - Win % .487 - PO teams 3

Interesting... The top 3rd does have the best teams, but the bottom 3rd is better than the middle 3rd.

In conclusion: HR are quite important, and most wins include a HR from the winning team, but I think they're more telling of good overall hitting/poor pitching, rather than being important solely for their run production. Conversely, when a team does not hit a HR (which is rare nowadays) they usually lose, but it's more because they couldn't get any offense going, rather than they're missing out on the run production of a HR(s). Does that make sense?