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Khift

Issues with the Day 2 Cut math - (4-2's make the Day 2 cut, but it is impossible for them to make the Top 16)

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Statement: It is effectively impossible for someone with a 4-2 record to make the single elimination rounds of the World Championship unless their clan has almost no 5-1 players in which case such a player might have a chance at being the challenger.

Corollary statement: Every 6-0 player will make the Top 16 cut unless they take a modified loss. Considering that it is completely within someone's control whether or not their loss is regular or modified, every 6-0 player should end up in the Top 16.

The reason these statements are true is because FFG is keeping the day 2 strength of schedule separate from the day 1 strength of schedule and is using D2SOS as the first tiebreaker. Meanwhile, they are keeping the tournament points from day 1 to day 2. This, combined with the fact that there are only two rounds in day 2, creates some very unfortunate circumstances.

 

Consider the expected population. If day 1b has the same number of 6-0 players, 5-1 players, and 4-2 players as day 1a has, then there Day 2 will have approximately  5 (+/- 1) players who are 6-0, 30 (+/- 2) players who are 5-1, and 68 players (+/- 4) who are 4-2. Each player has 4 possible outcomes from day 2 -- WW, WL, LW, and LL. Each of these populations will actually equally distributed -- there will be the same number of 4-2WW and 4-2WL and 4-2LW and 4-2LL. Pair-downs and modified wins/losses screw this up some, but not by a huge amount, and those will be covered later.

There is one more factor that needs to be considered here - and that is whether or not a player's first opponent wins or loses their second match. This is the sole determining factor in a player's D2SOS after considering their starting record and their personal performance. So, all 4-2WW's whose first opponents win their second round will have the same D2SOS, as will all 4-2WW's whose first opponents lose their second round. So we will call the former 4-2WWW, and the latter 4-2WWL.

 

So, barring pair downs and barring modified wins/losses, this identifies all possible tournament point outcomes and all possible strength of schedule outcomes. Now we only need to rank them.

8-0 players consist only of 6-0WW's. There should be 1-2 8-0 players. They are guaranteed in the cut.

7-1 players consist of 6-0WL, 6-0LW, and 5-1WW players. Using Swiss logic it can be calculated that there will be 10 to 11 7-1 players; they too are guaranteed in the cut.

6-2 players consist of 6-0LL, 5-1LW, 5-1WL, and 4-2WW players. Using Swiss logic it can be calculated that there will be 0-2 6-0 LL players, 6 to 8 5-1WL's, 6 to 8 5-1LW's, and 16 to 20 4-2WW's. Three to five of these players will make the Top16 cut.

So, let's evaluate the D2SOS of these groups:

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And herein lay the issue. Every 5-1 player that goes 6-2 will have a higher D2SOS than a 4-2 player that goes 6-2, simply because they started out paired up against a 5-1 player and not a 4-2 player in the first round.

 

Now, I said that I was ignoring modified wins and losses and pair downs. So, let's consider these things right now. First, we can easily see that a modified win/loss or pair down will not affect whether a 8-0 or 7-1 player makes the cut unless there are several of them. Specifically, a 7-1 player with 3 modified wins, or 2 modified wins and 2 modified losses will end up beneath the mass of 6-2 players with no modified results. With less than that, the 7-1 player ends up above the 6-2 mass and is guaranteed in. There's only currently one 5-1 player with any modified anything, so it's true that if that one player gets two mod wins on day2 then they are out of the running but it seems very unlikely. Pair-downs only hurt the D2SOS, which these populations aren't relying on to make the cut, and so has no effect on the quantity of 6-2's that make the Top 16 cut.

So that leaves us with 6-2's. On a 6-2 player, a pair down has the effect of dropping their D2SOS by 9/16. Doesn't matter when the pair down happens or who you are, getting paired down will have that result -- it effectively drops you one row on the above chart. Getting paired down against someone with a modified result will have a similarly deleterious effect, but not so severely; instead of falling an entire row you fall in between the rows. So in short, a 5-1LWL with a standard pair down has the same D2SOS as a 4-2WWW with no pair down. Finally, because of how Swiss works, pair downs happen at most once per round per score category, and so they're nowhere near enough to get a 4-2WWW into the Top16 cut.

Instead it has to be modified wins/losses. Pretty much the entire 5-1WL and 5-1LW brackets need to have a modified result in order for a 4-2WWW to make the Top16 cut. And that's quite unlikely; we're hoping that ~12 people out of a population of ~14 to 16 receive what truthfully appears to be a quite rare result; there just are not that many of them floating around. Like I said, there is currently one 5-1 who currently has a modified result.

 

The only possible out for a 4-2 to make the single elimination rounds is as a challenger, but even then that is only going to happen if every single 5-1 in their clan makes the natural Top 16 (the 6-0's are guaranteed in). Currently that could happen for Lion (which has no 5-1's at the moment), Unicorn and Phoenix (who each have one 5-1), but seems absurdly unlikely for the rest of the clans.

unknown.png

 

I'm not entirely certain what the point of this post is other than an excuse to do math, but I do think that it's quite cruel to let 4-2's play in day 2 if they don't actually have a chance to make it into the single elimination rounds. Isn't this what a graduated cut is supposed to avoid?

Edited by Khift

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I did my own rough math (yours is much more elegant and complete) and posted it to facebook coming to the same conclusion as you did.

 

Why give people false hope? That is an ultimate negative player experience. 

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Making it to Day 2 awarded players prizes. Plus, top 32 get additional prizes, so even if they don't make it to top 16 there's still recognition to be won. I'm not sure I get why it's cruel to have the extra players participate in Day 2. Even if they can't make the top 16, they made it farther than many of the other competitors. If making top 16 was the only point, most competitors would/should just drop out after their 2nd loss. 

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55 minutes ago, TheItsyBitsySpider said:

They allow them in because there are other prizes besides just the title to fight over. Top of clan and earning wins for prizes from the prize wall are worth still fighting for.

 

29 minutes ago, Zesu Shadaban said:

Making it to Day 2 awarded players prizes. Plus, top 32 get additional prizes, so even if they don't make it to top 16 there's still recognition to be won. I'm not sure I get why it's cruel to have the extra players participate in Day 2. Even if they can't make the top 16, they made it farther than many of the other competitors. If making top 16 was the only point, most competitors would/should just drop out after their 2nd loss. 

The issue is that this entire conversation is unnecessary. Everything I posted about would be completely obviated if there was only one strength of schedule that spanned both days. Instead they split the SOS for no apparent benefit except cruelty.

And it's not even the only issue caused, either. Most or all of 5-1WLW players will make Top 16 - but few if any 5-1WLL players will. The difference between these two groups players is the outcome of a single game that they aren't even participants in. And it's all because FFG is just going to all but throw away all of the data from day 1. A player's entire D1SOS only matters, all six rounds of it, if their D2SOS ties with someone else while on the bubble.

The worst part is, I'm about 98% certain that the only reason it is this way is laziness on FFG's part. They don't want to have to handle merging the tournaments, so they just make a new one. And if so that's a real shame on their part.

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My friend attended the Imperial Assault World Championship last spring.  FFG didn't keep the SoS separated for that tournament; instead, they carried forward the SoS from the day one results into the day two eliminations.  My friend's first opponent in the day one tournament dropped out after the first or second round (I forget which) to go play in an X-Wing side tournament.  Because of the way SoS works in IA, that opponent, which my friend defeated, was considered to have lost all of the other games he would have played, for the purposes of calculating my friend's SoS.

Nevertheless, my friend made it to day two.  His performance (including SoS) in day two would *easily* have placed him in the top 32 (earning him a set of those sweet, sweet Worlds dice).  He might even have placed in the top 16!  But his SoS from that first day dropout dragged him down, so that in the end he placed 33rd.  Missed the dice.  Specifically because the SoS was carried forward from day one.

This isn't theorycrafting.  This isn't a what-if scenario.  I saw the numbers myself.  This actually happened to my friend, in the most recent Worlds IA tournament.

There are arguments for and against using any tournament scoring system.  My friend doesn't seem to be the least bit salty over the results.  And you've just finished providing some perfectly valid arguments for carrying the SoS over from the day one tournament.  The waters are muddy, I'm afraid.

If there were one unarguably best way to score these tournaments, FFG would use it.

And people would still complain. ; )

Edited by IndyPendant

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2 minutes ago, IndyPendant said:

My friend attended the IA World Championship last spring.  FFG didn't split the SoS for that tournament; instead, they carried forward the SoS from the day one results.  My friend's first opponent in the day one tournament dropped out after the first or second round (I forget which) to go play in an X-Wing side tournament.  Because of the way SoS works in IA, that opponent, which my friend defeated, was considered to have lost all of the other games he would have played, for the purposes of calculating my friend's SoS.

Nevertheless, my friend made it to day two.  His performance (including SoS) in day two would *easily* have placed him in the top 32 (earning him a set of those sweet, sweet Worlds dice).  He might even have placed in the top 16!  But his SoS from that first day dropout dragged him down, so that in the end he placed 33rd.  Missed the dice.  Specifically because the SoS was carried forward from day one.

This isn't theorycrafting.  This isn't a what-if scenario.  I saw the numbers myself.  This actually happened to my friend, in the most recent Worlds IA tournament.

There are arguments for and against using any tournament scoring system.  My friend doesn't seem to be the least bit salty over the results.  And you've just finished providing some perfectly valid arguments for carrying the SoS over from the day one tournament.  The waters are muddy, I'm afraid.

If there were one unarguably best way to score these tournaments, FFG would use it.

And people would still complain. ; )

A single question: How many rounds were in day 2?

Because if it's not 2, then it isn't relevant to the conversation at hand. The issue here is that 2 rounds of Swiss is woefully insufficient to generate any meaningful data.

I'm sorry about your friend's situation and that IA's SOS system was very clearly broken, but that doesn't make this situation not also broken.

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I'm not sure what you're saying, now.  I reread your post, and this seems to be the first time you've mentioned that 2 rounds of Swiss is the core issue (other than the "...combined with the 2 rounds of Swiss" comment, that is).  The rest of the post seems to be an argument to carry over the SoS from day one.  (And please note, I'm not saying your arguments were flawed, or even that I disagree; I'm just saying that was the message I received as the core problem here.)  I just wanted to provide a counter-example.  --And yes, I think IA's tournament scoring system is crap. ; )

Now, if your argument is actually that there should have been 3 rounds of Swiss on day two, to give 4-2 players a better chance at top 16...well, that seems correct to me!  (Edit) And iirc there were 3 Swiss rounds in IA's day two elimination.

Edited by IndyPendant

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16 minutes ago, IndyPendant said:

I'm not sure what you're saying, now.  I reread your post, and this seems to be the first time you've mentioned that 2 rounds of Swiss is the core issue (other than the "...combined with the 2 rounds of Swiss" comment, that is).  The rest of the post seems to be an argument to carry over the SoS from day one.  (And please note, I'm not saying your arguments were flawed, or even that I disagree; I'm just saying that was the message I received as the core problem here.)  I just wanted to provide a counter-example.  --And yes, I think IA's tournament scoring system is crap. ; )

Now, if your argument is actually that there should have been 3 rounds of Swiss on day two, to give 4-2 players a better chance at top 16...well, that seems correct to me!  (Edit) And iirc there were 3 Swiss rounds in IA's day two elimination.

A third round of swiss would obviate my entire set of arguments, yeah. I would still personally prefer that they carry over the SOS from the previous day, but it'd at least work. The primary issue is that there are too many people in the top cut to be properly sorted by only two rounds.

Think about it like shuffling; it's a very similar problem, except backwards. When you shuffle you're trying to destroy information. You want to make it so that each card could possibly have moved from its starting location to any other location. If you don't shuffle enough, you haven't accomplished that - there are limits to how far that card could have moved, so it isn't random yet. Swiss operates on much the same basis, except instead of each iteration destroying information it generates information. Only doing two rounds of swiss and then using just that as the basis to sort people just doesn't create enough information to sort them by.

To continue the shuffling metaphor, doing three rounds would be akin to riffle shuffling exactly 7 times in a 52 card deck. It's the bare minimum necessary to get that full movement... but I doubt people would stop there as it just doesn't feel like enough.

Edited by Khift

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@IndyPendant The main issue in your example is the way SoS is calculated. In LCGs, SoS is calculated only from played games, which means a bye doesn't bring down your SoS (by having 0 points) and a dropping opponent also doesn't (any more than their pre-drop record would).

@Khift Didn't you say there'd be about 100 players in Day 2? 3 rounds of swiss doesn't seem nearly enough to sort them.

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5 minutes ago, Khudzlin said:

 

@Khift Didn't you say there'd be about 100 players in Day 2? 3 rounds of swiss doesn't seem nearly enough to sort them.

It depends on what it means to say 'sort'. You're right that 3 rounds isn't enough to sort 100 players to the top 1 player -- but it does sort roughly 100 players into the top 12.5 players, which is smaller than the Top16 cut. Two rounds only sorts to the top 25 players, though, which is greater than the Top16 cut, which is what leads to these issues.

Two rounds of swiss with only the 6-0's and 5-1's would sort those ~36 players into the top 8, which is also sufficient. Which is why two rounds would be "enough" if they didn't include the 4-2's, and also explains why none of the 4-2's can show up in the Top16 with only two rounds.

Edited by Khift

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I don't know enough to comment on this rather impressive maths post but providing some tangential support the rating system the league uses states it is best to have 6 matches per player to get the best (most accurate) results from the algorithm.

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7 hours ago, Casanunda said:

Playing more games against good competition is a negative player experience?  You must really dislike this game.

I love this game, just as a competative tournament goer over the last 15 years (non FFG) I was really confused that their cut doesnt allow all people who make the cut a chance to take the overall win/#1 spot. All the eventa I attended in the past, you made the cut, you are a contender.

 

I said it was a negative play experience because had I not saw this post/done the math myself, if I went 4-2 and thought I had the opprotunity and then found out I didnt, I'd be pretty bummed.

 

All that aside, new game, new company, new rules. Gotta learn and adapt! I do hope FFG is more transparent on this for folks though so no one has false hopes.

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7 hours ago, Khift said:

The issue is that this entire conversation is unnecessary. Everything I posted about would be completely obviated if there was only one strength of schedule that spanned both days. Instead they split the SOS for no apparent benefit except cruelty.

Emphasis mine. I'm going to get a little emotional here, so bear with me.

How dare you imply a deliberate malicious intent onto the tournament organizers? All you have here are statistics. And there's nothing so easy to manipulate and twist around than statistics. Have you asked "Why?" to someone with knowledge of such things? If not, than you don't know what the reasoning was. I, personally, have never tried to organize and manage a 4-day-long tournament, so I can't even begin to imagine how challenging it would be to make sure everything is "fair." I put that in quotes because fairness is highly subjective. What is fair to one is unfair to another. And at the risk of getting personal here, it was trying to navigate someone else's concept of "fairness" that (among other things, of course) led to my divorce. So, yeah.

I'm guessing nobody was allowed to play in both days. If that's the case, then you have to split SOS. You can't possibly gauge someone from Day 1 against someone else from Day 2. They're two completely independent events.

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3 minutes ago, twinstarbmc said:

Emphasis mine. I'm going to get a little emotional here, so bear with me.

I'm going to pass on bearing with you. I have no interest in being subjected to a sermon.

 

3 minutes ago, twinstarbmc said:

I'm guessing nobody was allowed to play in both days. If that's the case, then you have to split SOS. You can't possibly gauge someone from Day 1 against someone else from Day 2. They're two completely independent events.

If you make the assumption that players in both days are drawn from the same population then no, it's perfectly reasonable to group them together. Maybe that assumption is wrong, an argument could be made that there is a difference in the quality of player that would play on a Wednesday vs a Thursday perhaps, but if that's the case then keeping the tournament points from one day to the next is also incorrect and they too should be dropped. But I see no complaints from you (or anyone) on that regard, so I suppose the assumption must hold if only for convenience's sake.

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1 minute ago, Khift said:

If you make the assumption that players in both days are drawn from the same population then no, it's perfectly reasonable to group them together.

It is not, because the two groups were unable to play against each other. They are, at that point, two isolated populations. It would be like taking a single tournament in London and comparing the players' SOS against a completely different tournament in Sydney. 

3 minutes ago, Khift said:

I'm going to pass on bearing with you. I have no interest in being subjected to a sermon.

I appreciate that I took the time to read your screens-long tirade, yet you will not provide the same courtesy to me and my single paragraph. Thank you kindly. 

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Just now, twinstarbmc said:

It is not, because the two groups were unable to play against each other. They are, at that point, two isolated populations. It would be like taking a single tournament in London and comparing the players' SOS against a completely different tournament in Sydney.

You realize that it is very possible that this situation arises in swiss rounds of insufficient quantity to have a single undefeated player yes? It's unlikely, especially given the size of the tournament, but if the swiss rounds don't run all the way to completion then random chance is perfectly capable of creating an orphan group that only ever plays into itself.

And again, your assertion that these two groups are from a different population just because you say so doesn't hold any merit. They aren't geographically separated. They aren't temporally separated. They were even randomly seeded into by the FFG random number machine from the same group of applicants. If that's not the same population then I don't know what is. You see this kind of thing in stats all the time, looking at both sub-groups as they are gathered and the entire sample set as a whole.

Also, you completely ignored my other observation. If these truly are different populations then all data from them are incompatible, and we should toss out the tournament points in addition to the SOS. Are you in favor of that? Because I don't think a single other person would be.

 

3 minutes ago, twinstarbmc said:

I appreciate that I took the time to read your screens-long tirade, yet you will not provide the same courtesy to me and my single paragraph. Thank you kindly. 

Courtesy is reciprocated. You showed absolutely none and got none in response.

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19 minutes ago, Khift said:

If that's not the same population then I don't know what is.

Its not the same population because one tournament had 49 players and the other had 123 and they could not interact with each other. This is flat out fact. Their SoS cannot be compared. They are functionally two separate events and are treated as such.

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Just now, TheItsyBitsySpider said:

Its not the same population because one tournament had 49 players and the other had 123 and they could not interact with each other. This is flat out fact. Their SoS cannot be compared. They are functionally two separate events and are treated as such.

Let's assume you're right.

So we drop all stats from one tournament to the next. Day 2 starts from scratch with everyone at 0 tournament points. We do 2 rounds of swiss and determine that 25 of the 100 people won their two games, and randomly pick 16 of them to make the cut.

Is this what you actually support? Because if not, then you're being hypocritical.

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18 minutes ago, Khift said:

Let's assume you're right.

So we drop all stats from one tournament to the next. Day 2 starts from scratch with everyone at 0 tournament points. We do 2 rounds of swiss and determine that 25 of the 100 people won their two games, and randomly pick 16 of them to make the cut.

Is this what you actually support? Because if not, then you're being hypocritical.

I'm not talking about the points, points are fine in a two day event as every player still had to play games and win them, its the Strength of Schedule tie breakers i'm talking about. Since having a different player base sizes means more likely to be matched with higher ranking players in the swiss, favoring one group's SoS over the other on the tiebreaker. the Strength of Schedule they have would need to be erased or minimalized to better form less bias tiebreakers going into the Day 2 cut.


I'm more responding to things you say like "And again, your assertion that these two groups are from a different population just because you say so doesn't hold any merit.", because they actually are different populations.  They are drawn from the same purchasable source, people buying tickets, but for the sake of Day2 they are two separate populations it is drawing players into.  The players in Day1Z and Day1A are not competing against each other in their events, they are competing internally and contributing their top cuts to the Day 2 event. This means that they ARE different. Day1Z did not have a single identical player as Day1A. Your trying to treat the numbers like a survey when it is a competition. Going 6/0 on Day1Z does nothing to stop a player in Day1A from succeeding, because they are isolated competitions. The high rankers are being pulled into the Day 2 event, and that then becomes its own unique population.

 

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