IMO, it does sound like a really good or bad 1st hole score may have an effect on the rest of the 17. These are some examples of a really good or bad 1st hole score effecting the rest of the round.
1. Start thinking about shooting a really good score after a good 1st hole and then blowing up.
2. Free-wheeling after a bad 1st hole and shooting a good round.
3. Getting more focused after a good 1st hole and shooting a very good round.
4. Losing focus after a bad 1st hole and shooting an exceptionally bad round.
When I say "effect" I mean a positive OR negative correlation with the rest of the round.
I am really impressed by how often Touring Pros seem to block things out and be able to play and execute 1 shot at a time regardless of what has happened previously, while many amateurs I see don't seem to have this skill.
I was replying to Fourputt specifically, not all the responses at that time. However, I would say the same thing to Carl Spackler. By "effect" I don't just mean good 1st = good round and bad 1st = bad round, but also guys who are more likely to play a good remaining 17 after a bad 1st hole or play a bad remaining 17 after a good 1st hole. If a high % of Carl's best rounds start with double, then maybe a bad opening hole has a positive effect on how he plays the remaining 17. With Fourputt, he indicated that he has trouble regaining focus when he has had a blow-up after a good 1st hole. This might only account for a small % of his rounds, but it seems as if something might be going on there.
Here is an example with numbers. Let's say a guy is a bogey golfer averaging 90 on a par 72 with a 1st hole of medium difficulty that he tends to average a bogey. Let's suppose he knows Erik and has played a million rounds at this course making birdie 3% of those rounds and triple bogey 3% of the time on the 1st hole. Given that we would expect him to averge +17 the remaining 17 holes, if the 1st hole score has no effect, then he should average 88 when he makes birdie on the 1st hole and 92 when he makes triple. If his averages are significantly different (higher OR lower) than either of those, then it would seem that the 1st hole score does have an effect on the 17 remaining holes. (Note- that effect may or may not be mental with a lower=lower or higher=higher correlation as it could just indicate that he is more physically on or off that particular day. There are also other factors that could be at play like weather).