Total points is the overall best team
To me, the best indicator of strength of team is all-play records. Total points can easily be skewed by one or two big (or bad) games. Head to head is, IMO, the weakest of the three though. I prefer the Victory Points system where you are awarded two points per victory/zero points per loss and two points for finishing top four in terms of points for the week/1 point middle four/zero points bottom four. So, if you lose, but have a good scoring week, you at least get two points from the deal and if you win but you have a bad week, you get nothing. But I'd love to play in an all play league if anyone know one.
I completely agree with you that head-to-head is by far the weakest way to determine the strongest team. (But I still think it is an important aspect to a league. It's fun to have the weekly centerpiece to focus on when it comes to rooting for your team and against the opponent. And that goes double or more in the playoffs.)If moving beyond that initial discussion to total points vs. all-play, I would agree without hesitation that all-play is the best indicator of
consistent week-to-week team strength, but I wouldn't say it always conclusively decides the best overall team. My distinction is that all-play recognizes consistency, but it can penalize volatility and insufficiently reward explosiveness. And while there are some things an owner can do to seek out volatility, like QB/WR combinations, etc., at least some of the time the volatility is out of the owner's control. So to me, there's a certain arbitrariness to all-play that does not exist with total points.
I am in an interesting battle in my main league. Currently, I sit 23 points in the lead for the season, averaging 91 ppg to the second place team's 89.2 ppg. Yet my all-play record is approximately .790 while the second-place team isn't even at .700 on the year. I have had fewer off weeks and fewer explosive weeks, and clearly that is where the difference lies, but I'm not sure I can credit my shrewdness when Detroit's defense racks up a huge day in Denver the same week many of my other players have off days, just to name one example. Having played FF for 20 years, I'd say the total points is the better indicator of the relative strengths of these two teams in this league this year, and it's really not close.
When you get down to it, while mitigating the unfairness of having one random matchup determine a win vs. a loss (and both lucky wins and unlucky losses therefore can and do result), all-play still has at its heart the issue of discretizing the continuous statistic that is total points. It should be fairly obvious that being the best team by 40 points in a given week shows greater strength than being the best team by 1 point in a given week. And in that context, when a team is in the middle of the pack in a given week, a few points here or there can be the difference between having a net plus vs. a net minus in terms of all-play wins for the week. And this puts us right back to where head-to-head is unfair, although to a lesser extent.
Last week on MNF, I jumped four teams due to a single Brandon Jacobs TD. Instead of being 2-9 (I had a rough week!), I ended up 6-5 in terms of all-play. Four teams vastly outscored me, including two teams that nearly doubled me. To me, total points clearly better captured the relative strength of the teams in this particular week.
Consider these two profiles:
Team A: 2 first place finishes, 4 2nd/3rd place finishes, 6 4th/5th place finishes, 3 6th/7th place finishes, 1 other
Team B: 5 first place finishes, 2 2nd/3rd place finishes, 3 4th/5th place finishes, 2 6th/7th place finishes, 4 other
Team A would definitely be ahead of Team B in all-play, but would they really be the better team, or only the more consistently good team? Clearly Team A was not the most often dominant team. A lot of people, when seeing the breakdown, might wonder how close the finishes were in the above profiles, and that's where total points would come in.
So perhaps it's just a matter of preference. And also, it could depend on the makeup of your league. If you believe the team that is most consistently able to finish in the top 4 weekly teams is the strongest, then you will want to use all-play exclusively. Otherwise, you might be inclined to use total points to try to eliminate all of the arbitrary point values that other teams happened to score in given weeks that can creep in with all-play.
Ultimately, I'd love to come up with a way to combine both all-play and total points, so that both consistently and raw strength are given value. Unfortunately, while good in concept, it's difficult to implement in practice, at least for me.