Relegations/Promotions

Suggestions to improve the concept of a PlayDiplomacy League

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Re: Relegations/Promotions

Postby nanooktheeskimo » 17 Apr 2018, 20:12

If the schedule is a multi-year setup, what is the point of having seasons a year long?
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Re: Relegations/Promotions

Postby mhsmith0 » 17 Apr 2018, 20:54

So I played around with the data a bit, and got the following 2-year rotation structure:

Year 1 Year 1 Year 1 Year 1 Year 2 Year 2 Year 2 Year 2 Map to
Player Round 1 Round 2 Round 3 Round 4 Round 1 Round 2 Round 3 Round 4


1 A A A A C B B C 21
2 A A B B A A A A 1
3 A A C C B A A B 14
4 A B A B A C A C 6
5 A B B A B B B B 8
6 A C A C C C C C 15
7 A C C A A C C A 7
8 B B B B C C A A 16
9 B B C C A A B B 2
10 B B A A A A C C 3
11 B C B C B C B C 11
12 B C C B B B A A 10
13 B A B A B B C C 9
14 B A A B C C B B 17
15 C C C C A B B A 5
16 C C A A A B A B 4
17 C C B B C A C A 18
18 C A C A B C C B 12
19 C A A C C B C B 20
20 C B C B C A A C 19
21 C B B C B A B A 13

Basically the concept being that the year 1 schedule is the same as I'd proposed, but that you re-arrange the rows in year 2 to ensure that there are no 0's across the whole set (i.e. no player skips another player in BOTH years 1 and 2). You DO get some instances of high #'s of double repeats (most notably, player 8 double dips against SIX opponents: players 2, 4, 12, 14, 17, and 20 - players 1 and 15 also double dip against five opponents). Some of this can be worked out by just being careful about how you define slots and where you put in newcomers though, so you SHOULD be able to ensure that you don't see actual repeats of more than say 3 per player, and usually quite a bit less.

More detailed structural stuff:
Functionally, in year one there's no inherent difference between slots 1-7, slots 8-14, and slots 15-21 as groups. So between years 1 and 2, you can call all of the people who played in round 1 game 2 as "slots 1-7" instead of round 1 game 1.

MOREOVER (and here's where the magic of the annual rotation I'd discussed pays off), you can define ANY seven players who all played together in a game as "players 1-7" (and then the other two games define players 8-14 and 15-21), so you have even more options to pick how you're slotting people year to year to try and account for who got relegated (and trying to minimize high #s of repeats among the remainers as a consequence). Similarly, you can arbitrarily order all of the other games in any way you wish, which means that you have even more flexibility in who goes where.

So for instance, player 2 is defined as the player who was in game A rounds 1 and 2, and game B rounds 3 and 4; player 4 is the player in game A rounds 1 and 3, and game B rounds 2 and 4; and player 5 was in game A rounds 1 and 4, and game B rounds 2 and 3. But which round is which is completely arbitrary, so functionally you can switch players 2/4/5 as you wish (though of course that also then switches players 3/6/7). So there are limits to the conceptual flexibility at work, but you can still redefine terms in a lot of ways.


I think I'll go back to the illustrative example of the league 1 promotion/relegation stuff later today when I have some more time.

PS Yes the above table was ugly, but you can probably copy it into excel and get a better idea visually of what I'm trying to display.
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Re: Relegations/Promotions

Postby mhsmith0 » 17 Apr 2018, 23:00

OK so to continue the earlier example, here are the 14 projected remainers in league 1:
Pootleflump
DirtyHarry
greggybear
bindlestiff
Verse9
jimbobicus
StarkAdder
bdferris1
mjparrett
V
Machor
WarSmith
prgm
GruGloG


Conceptually, we want to be able to map them into a structure that inherently minimizes the # of repeat double dips. So how do we do that? Well, let’s start with some key assumptions and data points:
1) We can semi-arbitrarily redefine order of games and the letters of whatever we define as “round 1” (we can’t fully redefine things because by structure, game A in round 2 has three people who were in game A in round 1… but we essentially have four different rounds that we can define as “round 1”, three different games in round 1 we can define as “game A” (and then game B vs C in “round 1” is arbitrary too), and then we can arbitrarily reorder the other rounds as 2/3/4 in any order… so that’s 4 (choosing round 1) * 3 (choosing “game A”) * 2 (order or B/C) * 6 (order of the remaining rounds) = 144 different, equally valid (mechanically), ways of structuring year 1 along the liens of what I’ve discussed. i.e. there are a LOT of different ways you can create year 2 given year 1, which means there’s a lot of ways to optimize year 2
Side note: this arbitrariness of ordering has the additional benefit of making it difficult to distinguish who should be in which game during the middle of the season. By round 4 it should be solveable, but round 3 and especially round 2isn’t, so if people want some anonymity protection as a concept, that’s pretty doable.
2) OK, so we know we CAN redefine stuff, but how then SHOULD we? Well, let’s look at the overall results of duplication. I’d noted that slot 8 has six repeats… but interestingly enough, players 9-14 in this model have a very unusually LOW # of repeats (the overall average is 3.9, but the average of the 9-14 set is 3.3, and player 12 is one of just two slots that only gets two duplication/repeats). So if possible, we’d LIKE to try and shoehorn six remainers into the 9-14 slots, while having slot 8 be a promoter.
3) For this particular group, there are TWO instances of precisely six remaining players being in a game together: round 2 game 3 (or “game C” as I’ve been defining terms), and round 2 game 4 game 3 (or “game C”). So if I can get one of those two games to fit the concept of as “round 1 game B”, I can fit most of the other stuff in as I’d like.
4) Complicating factor: the ACTUAL round 1 rotation wasn’t to the structure we’d discussed, AND multiple remainers didn’t fit (DirtyHarry, prgm, mjparrett, bdferris1). So we’ll need to work around that to a degree.
Anyway, let’s get cracking…

Let’s look at round 2 game C. If we redefine this as “round 1 game B”, we’d need to assign player slot 8 to a promoter… but to do that, we need to NOT have any other games where three people in this game meet up (since if that happened, then one of those three needs to be player slot 8). Unfortunately, round 4 has a game with three of these players (warsmith, prgm, gruglog), and so does round 3 (jimbobicus, V, warsmith).
Round 4 game C has a similar issue, as round 1 has a game with three from that set (greggybear, bindlestiff, jimbibicus), and round 4 game A has three (pootleflump, dirtyharry, greggybear).


So we actually can’t use this as a model. Instead, we’ll need to look at making a group of 5 players (i.e. redefining a game with 5 remainers as “round 1 game B”), and if that doesn’t work look at groups of 4:
Round 1 game C doesn’t work (round 4 game C, round 3 game A)
Round 1 game A doesn’t work (round 3 game C)
Round 3 game A doesn’t work (round 1 game C)
Round 3 game C doesn’t work (round 2 game C, round 1 game A)

So now we need to look at groups of 4:
Round 1 game B actually DOES work here, as no other round has 3+ members. So let’s just roll with that and see where it takes us…

Note that player 13 gets 5 repeats, so if possible we’d like that to be a promoter too. Player 13 is defined as B/A/B/A, so we just need to avoid having any of the four here fitting into that bucket. And ideally, we’d shoehorn the four into 10 (B/B/A/A), 11 (B/C/B/C), 12 (B/C/C/B), and 14 (B/A/A/B), since they all have 2-3 repeat slots (player 9 gets 4, which is acceptable if a bit suboptimal).
However, 10/11/12/14 as a group has 1-2 members player in each “game B” (that’s the game where 3/7 members of the “round 1” game B player together), and as it turns out, none of these four were in the “game B” of round2.
You get the same for the actual round 2 game B (none of them played in “game B” of round 1), the actual round 1 game A (round 4 game A doesn’t work with this), and round 3 game B (round 4 game B). So none of these work *QUITE* the way I’d like, we’ll just need to pick one to work with. Let’s roll with the actual round 1 game B.

So we can’t model slots 10/11/12/14, but we CAN model slots 9/10/12/14 (two rounds with two of them in game B, one round with none of them in game B), and that’s nearly as good. Also note… DirtyHarry and prgm were non-fits into the actual year 1 rotation (effectively, the two of them flipped what they “should” have been in either round 2 or round 4), so we’d actually like to minimize the number of “only play once in 2 years” slots, which means that putting them into slots 10 and 14 (each only have three others in the “play once in 2 years” mold), is good if possible. Unfotunately, they can’t do that, but they CAN fit into 9 and 10 (in either order – since we’re modeling this as they flipped one game or the other, it’s completely arbitrary which is which). Similarly, V and StarkAdder can fit into slots 12 and 14, again in either order (this will depend on which of the other groups is in “game A” and which in “game C” in round 1, note this for later).

Let’s just stick with the real round 1 game A being game A, ditto the real round 1 game C being game C.
Of the game A group, this makes Pootleflump player 6, Machor player 5, Verse9 player 3, WarSmith player 7, and bdferris slots into player 2 (here we model this as reversing game 3, where he was put into game C instead of game A, basically he flipped the assignment with mjparrett for that game)
Of the game C group, this makes jimbobicus player 15, GruGloG player 18, greggybear player 19, bindlestiff player 21, and mjparrett player 17 (again, with a particular game swap with bdferris).

(I played around a bit with modeling it otherwise but didn’t really see an improvement)


Resulting table (first four letters are this year's actual matchups, next four are what was set up for 2019):
Results Round 1 Round 2 Round 3 Round 4 Round 1 Round 2 Round 3 Round 4
DirtyHarry B A B C A A B B
prgm B C B A A A C C
V B C C B B B A A
StarkAdder B A A B C C B B
bdferris1 A B C B A A A A
Verse9 A C A C B A A B
Machor A B B A B B B B
Pootleflump A A C C C C C C
WarSmith A C C A A C C A
jimbobicus C C C C A B B A
mjparrett C B A B C A C A
GruGloG C C A A B C C B
greggybear C A A C C B C B
bindlestiff C B B C B A B A

This one is... actually not ideal. WarSmith plays five different people twice in each year (prgm, bdferris1, Pootleflump, jimbobicus, GruGloG), and bdferris1 doesn't play either GruGloG or greggybear in either year. However, it mainly does a good job mixing and matching people (the average remainer plays 2.3 others once over 2 years, 4.7 others twice over 2 years, 2.7 others three times over 2 years, and 2.8 others four times over 2 years).

As a proof of concept, I think this process works well enough. As a "we should actually do exactly this" model, it can be improved upon (most likely there's a better game to slot in as "round 1 game B", and it's PROBABLY solveable in one format or another to avoid having to have anyone never see each other in 2019, while still making a 2019 set of fixtures that will be able to go plug and chug in 2020 and beyond without worrying about the deviations from this instance).
Last edited by mhsmith0 on 17 Apr 2018, 23:29, edited 1 time in total.
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Re: Relegations/Promotions

Postby mhsmith0 » 17 Apr 2018, 23:28

Yeah that can be materially improved upon...

bindlestiff C B B C B C B C
Machor A B B A B B C C
mjparrett C B A B B B A A
bdferris1 A B C B C C B B
jimbobicus C C C C A B B A
WarSmith A C C A B C C B
V B C C B C A A C
GruGloG C C A A A B A B
Verse9 A C A C C B C B
prgm B C B A B A B A
StarkAdder B A A B A C A C
greggybear C A A C C C C C
DirtyHarry B A B C B B B B
Pootleflump A A C C B A A B

In that model, prgm and greggybear skip each other in both years (this is due to prgm and DirtyHarry flipping assignments in year 1, round 4, games A/C), and WarSmith double dips against four instead of five opponents (Machor, bdferris1, Verse9, Pootleflump), with no one else double dipping agianst more than 3.

Average Remainer plays:
0.1 others 0 times over 2 years
2.1 others 1 time over 2 years
5.1 others 2 times over 2 years
3.3 others 3 times over 2 years
2.3 others 4 times over 2 years

Probably it can still be improved further, but it's overall pretty reasonable as an illustrative 2019 outcome given this particular theoretical set of people staying in league 1.
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Re: Relegations/Promotions

Postby V » 18 Apr 2018, 02:28

Seeing as we might need mhsmith0 to do next year’s league 1 fixtures for us (on behalf of mjparrett) may I ask a couple more league 2 participants to step it up, considering mhsmith0 is currently in 5th position & promotion could be considered most inconvenient ;).
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Re: Relegations/Promotions

Postby mhsmith0 » 18 Apr 2018, 02:41

V wrote:Seeing as we might need mhsmith0 to do next year’s league 1 fixtures for us (on behalf of mjparrett) may I ask a couple more league 2 participants to step it up, considering mhsmith0 is currently in 5th position & promotion could be considered most inconvenient ;).


lol I guess you're happy I didn't try for the solo or 2-way last game then :P

PS A lot of this can be automated once it's explained how to work it, so I don't THINK I'd actually need to be directly in charge of randing decisions or the like. Also as long as we're debating removing inconvenient people, relegating at least one of our glorious leader (mjparret) or bdferris or prgm or dirtyharry makes the year 2 math a lot simpler :P
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Re: Relegations/Promotions

Postby Shyvve » 18 Apr 2018, 02:46

mhsmith0 lost me about five of his posts ago, which, probably means I'm slated for relegation at end of season. Jus' sayin'...
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Re: Relegations/Promotions

Postby mhsmith0 » 18 Apr 2018, 03:23

Eh no worries I've honestly been kind of rambly. I'll probably clean stuff up into a more presentable bit at some point, but the basic tldr is:

1) Long-term you'll see people in the same league never going two full years without playing each other (presuming we go with what I'm proposing)
2) Short-term you'll see some violations of this in 2019 because the 2018 schedule wasn't *quite* the same as it needs to be long term
3) Depending on who does or doesn't get relegated, you'll see some variance, but you can probably expect that long-term, year in year out you'll have on average about two opponents you'll see twice after having seen them twice the prior year (in league 1; in leagues 2/3, the # will be lower since there's newcomers on both ends of it)

I'll also note that this is with the current setting of relegation count. If we end up cutting relegation slots long-term, which is probably sensible, the #s will change. If you relegate six instead of seven, it'll be more like 2.3 people you'll see as repeat doubles instead of around 2.0 (probably a range between 1 and 4 most years), and if you relegate three, it'll be more like 3.0 people you'll see as repeat doubles (with a decent # of years you'll see four [and rare occassions you'll see five people], and a decent # of years you'll see 1-2). I obviously haven't run all possible scenarios, but I think that's about right for how the mechanics are likely to shake out.

So that's essentially a quantification of long-term structure:

For long term league members:
7 relegation slots = 2.0 repeat doubles per year (it might actually be a bit lower than this tbh)
6 relegation slots = 2.3 repeat doubles per year
3 relegation slots = 3.0 repeat doubles per year

Given that data, the question becomes what is the value of reducing the promotion/relegation slots (if you believe it will lead to more interesting gameplay), compared to the cost of increasing the # of times you see the same people more frequently. And THAT is much more of a "what do people want" sort of question, I can't really answer that one myself (I guess I'd like to see a small reduction in promotion/relegation slots, but I wouldn't want to go all the way to just 3 / year, for instance).
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Re: Relegations/Promotions

Postby rd45 » 18 Apr 2018, 12:03

nanooktheeskimo wrote:If the schedule is a multi-year setup, what is the point of having seasons a year long?

Exactly.

It's nice to see that a hand-crafted multi-year schedule can meet whatever goals, I guess, just as an academic exercise. But, given the constraints around overall player numbers, and the wildcards that are always going to get thrown in by promotion/relegation, then I wonder whether you've got anything that's any better than a purely random allocation for any given year's games.

Something like this looks like it would do an OK job, with very minor changes (where team => game).
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Re: Relegations/Promotions

Postby mjparrett » 18 Apr 2018, 12:29

boldblade wrote:
rd45 wrote:In reply to the OP - so far, based on the caution & draw-mongering that seems to be the early pattern, I completely agree that relegation-avoidance is probably driving too much aversion to risk. We need to give it a whole season, because there's a chance that the later games break that pattern in the way that Nanook said. But, it's also entirely possible that those few players who are desperate for a late win (and motivated enough to do anything about it) will anyway be trapped into dull drawn end-games with mid-table players who are doggedly defending their carebear points. If that's how it turns out - then we need a total re-think on the scoring. Zero for a loss, one point each for any size of draw, 10 points for a solo? Anyone who solos any of their games is automatically promoted, with a matching no. relegated from the division above?


I agree the whole season should be played before changes are decided on with certainty. But I am glad we are talking about some solutions now. Personally, I do believe an entire change to the scoring is needed. But the reason I brought the idea of this post up is that I think it could have some of the same effects and I expected it to be much easier to swallow for all involved. I'm still frustrated with the nature of how this discussion has progressed because the idea still seems largely to be weighed against the outcome folks like myself, GPD and rd45 are looking for instead of the value of the change itself. At least the last page or so of comments have mostly covered the one issue people have with lowering the number of relegations. And I do appreciate the mathematical folks chiming in to discuss how such an issue would be addressed.

mjparrett wrote:No-one really answered my point earlier (or discussed, as it certainly isn't a question that has one answer); is a solo and 3 losses definitely better than 4 3-way draws? I would love to hear one of the solo only types (rd45, GPD, boldblade it seems?) answer/argue this. I know I am being awkward for the sake of it, but one solo doesn't necessarily make you a good player. The 3 losses is possibly more a true indication of your skill. Someone with 4 3-way draws might be timid, might be a carebear, or might lack the true tactical awareness of how to turn them into solos, but is undoubtedly a decent player who gets the game and is capable/clever at building alliances and stabbing to reduce the number of players.


In my opinion yes but that will come as no surprise. I find it interesting you are willing to discount the single solo as it may have been against the lesser players of the league but don't consider that you should also discount at least one of the draws for the same reason. Not only that but assuming both players considered would have wound up in one of the four games with lesser league players then wouldn't the one with the solo victory be better when he soloed against them and the other was unable (or unwilling)? Now, I would agree that avoiding elimination in 4 straight games is impressive and should be rewarded. But is it equal to a solo win? No. Now, I must admit I disagree with rd a little in that I do think there is probably a number of draws that might be worth a solo. Maybe 7, idk I would have to think about it more. But, at the same time if you are in 7 straight draws and never once had the chance to solo I find that quite unlikely and instead think you simply lacked the balls to take one that was available to you. Which I do find problematic but will admit managing to avoid elimination in that many straight games is respectable.


Sorry you misunderstand slightly - I'm not saying 4 draws is better than 1 solo and 3 losses either :) I'm just saying it might be. I also agree that the 4 draws might be due to poor player performance, surrenders etc. I guess (as someone else said), there is a tipping point where n number of draws is better than a solo. 1 solo and 99 losses or 100 draws in 100 completed games? We both know how should be higher in the league table (and don't say the 1 solo guy!!). I'm just slightly playing devils advocate.

Yes the scoring system could be changed. Yes so could the # promotions/releagtions. I am more than happy to discuss and agree we have gone slightly all over the place in this thread. But you need a majority to pass. So if 90% (just making numbers up here) agree with my current system and not with you, you either need to grin and bear it, or (sadly) quit the league.

It is a shame more league players don't join in these conversations. Maybe they are lazy, maybe they don't read the forums. Maybe they like it how it is.

I'll do a little research.
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