I have completed my preliminary investigation into the relative

So that everyone can see the year-to-year variation in the 19th century, here are those results.

Year--Lg---Hit----Hr----BB-----SO----H$----Avg

Oops, I just noticed that the H$ formula I typed above is slightly wrong. I did the calculations correctly in my analysis, but I typed the wrong formula in the post above. Of course, H$ should be written as (H-HR)/(AB-SO-HR).

I did another batch of runs of my voting simulation software. To look at the "minority voting bloc" issue (aka Ross Barnes and the like), I slightly modified my simulation. I still have 100 voters each ranking 1000 players according to their personal perceptions, which are randomly distributed around some "true" values for each player. People fill out their HOM ballots according to their personal perceptions.

The modifications are as follows. Now 20% of the voters are "minority" voters and give a sizeable additional value to 5 "minority" players. These minority players (aka Ross Barnes) are randomly selected among the 6th thru the 15th truly best players. The idea is that these minority voters will all vote for Ross Barnes, say, whereas very few of the majority will. The voting schemes will perform differently in the face of this minority issue.

Here are the results. Defns are given in my previous posts.

V1: 61.4 80.9 94.7 10-9-8-7-6-5-4-3-2-1

The way I interpret Rob's results, the differences are minimal between all systems except the widely disliked V5. I just don't see ballot structure as accomplishing anything significant to combat any "minority voting bloc" issue. (Which, as I said before, I do not think is an issue as the number of people who are going to engage in strategic voting in an election like this is incredibly small.)

On that note, we are registering voters, are we not? We will need to.

I _do_ think that asking the voter to put their judgment to good use in making disctinctions is better, and would prefer a (14 or 10)-9-8-7-6-5-4-3-2-1 ballot or a 20-19-18-17-16-15-14-13-12-11 ballot, basically anything that ensures that rank order candidates are submitted... it's part of the fun and it encourages closer study of the candidates.

I should note, by the way, that a long ballot (provided it is weighted in some way) will go a long way to neutralizing this "problem" because it ensures that the better players are ranked on all ballots. Given that we are considering 10 ballot slots for (usually) 2 or 3 candidates, I don't see a need to make it longer, but it would be a solution. But while 10 seems doable, if you ask people to put down 15 or 20 names you will start losing voters.

Many thanks to Rob, by the way, for such wonderful and detailed studies. These are great, and very helpful. But in general, Condorcet-type voting "deficiencies" or "paradoxes" are extremely tough to combat and in actual practice, are rarely problematic.

Thanks Craig for those kind words. Permit me to reply to one issue you raise. Thinking carefully about the ballot structure seems to me to be a very important issue (as you can tell by the time and effort I am putting into it). Even ignoring strategic voting and "Condorcet-type voting paradoxes", which I have done in my analyses, this may be a key issue.

What is the best way to reflect a group of experts' views on the most meritorious players throughout baseball history? I think it far preferable to delve into this issue with objective and systematic analysis (i.e., make assumptions and test different schemes) up front than have concerns linger throughout the HOM exercise.

As a personal aside, I just spent a year of my life with the Baseball Survivor group exercise in ranking the top 100 players of all time. The exercise was a lot of fun and very informative. However, in retrospect I now wish we had spent more time up front discussing the voting rules since many of our results were a direct result of our voting scheme rather than the "best" reflection of the groups' expert opinions.

Here's another report of results of my voting simulator. This time all the voting schemes force voters to vote for 15 players on each ballot so as to make the comparisons more fair. Plus the "minority" issue (Ross Barnes) is in play. See the previous post for descriptions. Results are averages over 1,000 trials.

V11: 60.9 81.6 96.9 15-14-13-12-11-10-9-8-7-6-5-4-3-2-1

Rob how about this scheme, a variation on the 7-6-6-5-5-5-etc.

7-6.25-5.75-5.33-5-4.67-4.3-4.1-3.9-3.7-3.4-3.2-3-2.8-2.6.

Obviously that's a pain in the butt. But it solves Craig's ranking issue. Acutally try this, it's practically the same, but whole numbers:

70-63-58-53-50-47-43-41-39-37-34-32-30-28-26. It's the same general scheme of making the distinctions smalled as you move down the ballot, which represents the widening at the far end of the bell curve (that was my idea when I came up with the system anyway) as you move away from the end. I think the difference between 1 and 15 is a lot closer to 70-26 than 15-1, which is probably why this system keeps showing up near the top of the charts. There is a substantial penalty for not being named to a ballot, but I think that's okay, if someone doesn't think you are one of the 15 best, you are probably not one of the 2 or 3 best, generally speaking.

I don't think 15 will be too tough, especially for the first ballot. There's quite a backlog. After that, it's just a question of revising your ballot based on:

-discussion (people will change your mind, or you'll change their's)

That is a really dorky looking system though. I can imagine how we'll be called a bunch of mathmeticians, etc. if that voting scheme ever made it's way to the more mainstream media (should this project exceed expectations and take off) outlets, and as Primer's audience grows.

Do you all think that's something to be concerned with as we decide on a system or not? I don't really care, I just want the best system we can come up with, but I suppose someone should worry about things like that.

actually, Rob, try this one:

70-63-58-54-50-46-43-41-39-37-34-32-30-28-26

Just tweaked the difference for a 4th and 6th place vote from 53 and 47 to 54 and 46. Now the difference as you move down is the same or smaller each step of the way

1st-2nd 7 points

I really really like that system. We don't need to worry about what the points look like, anyway. And in the end, as Chris F points out you as the voter just rank order 1-15 and let the point-scoring system take care of itself.

It seems to me that the "background" answer is 10-9-8 (or 15-14-13) since that is the MVP-style voting that was intended.

The question is, then, are any of the other voting systems preferable. Rob Wood's numbers don't seem to show a more than 1-2% advantage to any alternate system. That strikes me an insufficient to deviate from the norm. But, that's just one man's vote. Weigh it as you deem appropriate based on whatever voting scheme emerges as the favorite.

I assume this means that no one wants "extra points" anymore?

At the risk of beating this dead horse, here's maybe the last installment of results from my voting simulator. Per Scuff's request, I have added one more voting scheme. I also sprinkled a little more variability into the simulator to see if the tally metrics would spread out; this didn't happen though.

V11: 53.4 75.7 95.0 15-14-13-12-11-10-9-8-7-6-5-4-3-2-1

Voting summary as I understand it.

To manipulate MVP style voting, I would:

Yes Josh, you and Satchel P, Oscar C and Cristobal T are all eligible. Hopefully we'll get lots of discussion from the Negro Leagues experts in the group, so we can get a good idea of where to slot these players.

Thanks for the simulations. It looks as if there are a dozen or more formats that provide about the same level of discouragement (or not) to attempted manipulation. So I would hope, therefore, that we would choose a simple, intuitive system. (As suggested, if we simply rank our choices 1 through x, and they're converted to a 76-63-whatever-whatever calculation in tabulation, that is fine.)

As I think about this, though, a bigger concern has popped up for me. It's been suggested that a really deep ballot (15 names) makes manipulation harder. But it also forces me to vote for players who I know darn good and well don't belong in the HOF. And then I'm going to justify my ballot? What if I just plain don't think there are 15 worthies on the ballot?

Marc, the question we're asking isn't "is the player worthy of the HoM?". The question is "please rank the best X eligible players from 1 to X". 'X' is still to be determined, but will probably be somewhere between 10 and 15 (I like 15). We're only going to elect between 2 and 5 players in any given year.

Think of it like an MVP ballot. In almost any year, there aren't 10 players that deserve to win the MVP (or 3 that deserve the Cy Young Award) but they still put 10 names on the ballot. Same thing here.