Wow.
That blog post is something I could have written myself, if it were not for the fact that I usually don't spend time writing long and elaborate posts like that. In fact, long ago (shortly after the introduction of SoS) I
have written a shorter version of something like this myself on the old forum, where I suggested a new scoring system that has quite some similarities with this one. I am not exaggerating when I say that literally every point under "Part 2: Why A New System?" and "Part 4: Why Use the Two-Tier Scoring System?" directly applies to the scoring system I had suggested, and my reasoning behind suggesting it, as well.
It shouldn't some as a surprise that I agree with everything jay65536 says here, and I have nothing to add. I will now discuss the scoring system I proposed years ago as well as some details in the scoring system of jay65536.
My scoring system
The scoring system I had suggested years ago was based on the observation that there are 'two' types of draws:
1) A draw where every remaining player agrees to draw;
2) A draw where there is a solo threat and a stalemate line is formed. The game is in a deadlock and is drawn out of necessity.
If the draw is of type (1), the pot should be rewarded according to DSS scoring. If the draw is of type (2), the board leader should get half the pot and the rest of the pot should be evenly split between the other remaining players.
The challenge then is making a scoring system that properly differentiates between the two. One way of doing it is just making two draw buttons. Say, make a button 'Draw' that splits the pot evenly and a button 'Deadlock' that gives more to the board leader. I could see some problems in the implementation of that, though, since it is a requirement that everybody needs to understand the difference between the two buttons. Another possibility is to say that the draw is of type (2) if and only if the board leader is above a certain number of centers, e.g. 14.
Commentary on jay65536s Two-Tier Scoring system
I think this scoring system is better than both DSS and SoS, for the reasons you mentioned in "Part 2: Why A New System?" and "Part 4: Why Use the Two-Tier Scoring System?". I also like that it handles the situation where two players get close to a solo better than my scoring system does (if it had a way of handling that properly, I cannot remember).
I would suggest to change the following
jay65536s wrote:Points are split equally among draw participants in the following cases: (a) any 2-way draw (90 each); (b) any 3-way draw in which no one has more than 12 centers (60 each); (c) any draw in which no one has more than 6 centers.
into the following:
Points are split equally among draw participants if no one has more than 12 centers or in case of a 2-way draw.
I suggest this change for the following reasons.
1) My formulation is simpler. Players want to be able to easily calculate their score in different hypothetical situations, or at least get a feel for it. Therefore, all other things being equal, I think my version is better.
2) The reason you want to reward the board leader with extra points in some cases is because you don't want to disincentivice players to go for a solo attempt. However, if the board leader has no more than 12 centers, that would be a pretty weak solo attempt, isn't it? Hence that reason does not apply. So if no one is in 'solo-danger' territory, why not split the pot evenly?
Interestingly, if my above formulation is being used, it is only a little extra tweak to formulate Two-Tier Scoring as follows:
A solo is worth the full pot. In case of a draw, any player with more than 12 supply centers receives a proportion of the pot equal to the proportion of supply centers he or she controls. The rest of the pot is distributed evenly among the other surviving players.
It's simple, clean, and, I think, has the same upsides as the version of Two-Tier Scoring proposed in the blog.
Other commentary
As a remark, I have noticed that both DSS and SoS use the following formula to calculate your share of the pot in case of a draw. Your share of the pot is equal to the following:
(Your number of centers)^n / [SUMOVERALLPLAYERS (That players number of centers)^n]
In SoS, n = 2. In DSS, n = 0. Interestingly, we are actually only using extremes here. Why does no one use n = 1, which rewards point proportional to supply center count? We could hypothetically even use e.g. n = 1/2 (Sum of Roots scoring).