What Do Each of the 'Rank By' Options Tell Me?
GeneralNOTE: The numerical accuracy of the calculations is correct and is not suspect. But the textual information herein is new/preliminary and may change to improve the clarity ~and accuracy~ of the statements and descriptions. Be aware of this as you use the Hole By Hole Analysis Page. Feedback of any kind; questions, proposed re-writes and other opinions are all welcome.

In General, the goal of this page is always rank hole in order by hardest to easiest. So 'Rank' is the default setting in the 'List By' set of options and will, in most cases, satisfy the question you are trying to answer.
Note: Where Net Scores are used, the Player Handicap used was each Players Handicap on date of each round.
Avg Gross Easy. This simply averages all of the scores from each hole in the group you have selected. Selecting this and also selecting 'Rank' (or 'Par+Rank') you will see which holes have the most blow-ups in grouping of pars.
Par Delta Gross (PDG)This is similar to Avg Gross, but takes the Avg Gross Score for each hole and subtracts the Par Number from it. This then tells you which hole, overall, has the highest average Gross Score over Par.
Avg NetAnother Easy One. Similar to Avg Gross, this averages all of the Net Scores from each hole. Its interesting, mostly, only if you select just your scores. Doing so might tell you which holes you do or do not take advantage of using the full number of strokes you got during all the rounds analyzed.
Par Delta Net (PDN)Also Similar to the Avg Net. Again focusing on your or another individual players scores, this will tell you overall which holes you take advantage of the strokes you get from your Handicap.
Par or Better Gross (POBG)This analysis is interesting. This tells you which holes have had the least and most number of Gross Pars or Better in the group selected. If you compare the rankings of these holes with their current Hole Handicaps, this'll surprise you. Here something to ponder, if a hole is 'Hard' I might screw up and get a big number, but if I don't screw up and I can easily make a Par should I get a stroke there over another hole that I always struggle to make Par on?
Strokes Over Par Gross (SOPG)This is very similar to Avg Gross. But this one, absolutely defines which are the blow up holes. This sums up all the 'Strokes Over Par Gross' for each hole and assigns a rank in order from most to least.
Par or Better Net (POBN)Similar to 'Par or Better Gross' but calculates the number of holes that a Net Par was scored. Not too interesting, unless you are looking just at the scores of an individual players, or perhaps a Handicap Group.
Strokes Over Par Net (SOPN)Similar to 'Strokes Over Par Gross' but from a Net Score perspective. Also of limited interest, unless looking at an individual or Handicap Group.
Par or Better % Gross Differential (POBPCGD)From here and below can be considered the options for re-assigning and Hole Handicaps.

If you found 'Par or Better Gross' interesting, you will perhaps find this one more so. This calculates the 'Par or Better Gross' Value for two different Handicap groups, calculates the Percentage of Pars or Better for each group and then subtracts the two Percentages. Doing this ranks the 'differential' in Percentage of Pars or Better between the groups. And in all cases the first Handicap Group is the set of Handicaps from 0-8. The second set is defaulted to the set of Handicaps from 20-28, but you can select other Handicap Groups to see the result. If you consider this ranking as a potential replacement of the Hole Handicaps we now play with, the Par 5's would all become the #1 or #2 Handicap Holes. ~WHY~ our datashows this is a subject of another discussion and our data is limited in being able justify a definitive answer (e.g., should more of us should be playingfrom the Gold Tees?
Avg Gross Differential (AGD)This is also compelling as it also uses a 'Differential' between Low and High Handicap Player results. Thus, it is a decent predictor of the Average score results between which ever two groups of Handicap Players are selected. The issue in using this is that the results are skewed by blow up hole results. Doing this then assumes that because ~you can screw up a hole~ means you should get a stroke there. This, some believe, is a falicy because 1) if you screw up a hole and are looking a big number, you ~should~ lose the hole, 2) if you screw up a hole and are looking at a big number, getting a stroke against someone who isn't screwing up a hole ~isn't going to help you win, or halve, the hole~ and 3) if you don't screw it up it is likely an easy Par and you'll be in contention to win the hole anyway.
USGA Methods, GeneralThe following are the 3 optional methods offered by the USGA to re-assess Hole Handicaps. All of the USGA methods to analyze recorded Hole by Hole scores and rank holes for the purpose of suggesting Hole Handicap re-assignments. Note, when a course is new other methods are used. After collecting 400+ Hole By Hole scores the USGA allows that the following methods can be used. For the Comparison and Difficulty Methods, there should ideally be 200+ 0-8 Handicap player scores ~and~ 200+ scores by 20-28 Handicap players)
With sufficient data, the USGA believes that the results of these three methods each have statistical validity. Curiously, each of the three methods can have ~WILDLY~ different results. So which does the USGA think is best? They don't say! Instead the USGA leaves it up to 'The Handicap Committee' to pick whichever method it thinks is best... but then gives additional suggested direction about what results should and shouldn't be applied in actual Hole Handicap assignments (e.g., Hole 18 shouldn't be the number one Handicap Hole.... even if the selected method says it is....).
All this tells us one thing, the USGA hasn't decided upon a single or 'best' method for making Hole Handicap assignment and instead tosses the hot potatoe to 'the Handicap Committee' to make its own decision, because, obviously 'the Handicap Committee' is going to whatever it wants to do anyway!! (and should??)
USGA Regression Method (Regrs)From WikiPedia: ''In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. For more than one explanatory variable, the process is called multiple linear regression.[1] This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.[2] ....Linear regression models are often fitted using the least squares approach...''
The problem with using the USGA Regression method is that the resultant Rankings are skewed by the existing Hole Handicap assignments which could be quite wrong. The are also skewed in the same manner as for the Avg Gross Differential, above, Rankings by holes in which big numbers are often posted without regard to how many Pars or Better are posted (i.e., it might be an eacy hole to Par, if you don't hit into a penalty); more simply, getting a stroke on such holes won't help you much in competing with someone who hasn't screwed up.
USGA Allocation Method (Alloc)The USGA Allocation Method is also known as the 'Comparison Method.' In computation, it is very similar to the 'Avg Gross Differential' method.Examine the Hole Handicap Allocation chapter of the USGA Manual (Section 17) to understand the computation, to see it, use the link to that Manual Hole By Hole Analysis Page.
USGA Difficulty Method (Diff)The USGA Difficulty Method is also described as a method to be employed in Four-Ball, Best Ball and Stableford (points) competitions.In computation, it is very similar to the 'Avg Gross Differential' method. Examine the Hole Handicap Allocation chapter of the USGA Manual (Section 17) to understand the computation, to see it, use the link to that Manual Hole By Hole Analysis Page.