The 2011 Table - Magic Numbers, Tragic Numbers & Other Calculated Distortions [R]

I agree with this -- actually made a similar point in this thread's initial post. But let me drive this point home. There's been virtually zero movement on this table since I started this thread.

Code:

[B][U]   WK23       WK27[/U]
01  LAG    01  LAG
02  SEA    02  RSL
03  FCD    03  SEA
04  CMB    04  FCD
05  RSL    05  CMB
06  COL    06  PHI
07  SKC    07  SKC
08  PHI    08  COL
------------------
09  HOU    09  DCU
10  DCU    10  HOU
11  NYR    11  POR
12  POR    12  NYR
------------------
13  CHV    13  CHI
14  SJE    14  CHV
15  CHI    15  SJE
16  NER    16  TFC
17  TFC    17  NER
18  VAN    18  VAN[/B]

There's some minor shuffling within each category, but it's the same top 8, the same middle 4, and the same bottom 6 since Week 23.

Without those two "extra" spots, we'd be playing out a fairly boring end to this season.

I don't know whether the league got this right or whether they are just getting lucky, but the changes made to the playoffs this year actually are succeeding in making this regular season exciting and meaningful. Perhaps the league looked at last year's playoff race (the one whose non-existence I detailed on the previous version of this thread) and realized changes were needed. With higher disparity (and we have higher disparity) and a larger league, you're likely to end up with a more bimodal table -- more teams at the top, more teams at the bottom, fewer teams in the middle.

So the top teams secure their playoff berths early in the season. The bottom teams drop out of the playoff race early in the season. With only 8 spots, the middle tier teams are pushed out of the playoff race, which means there's no playoff race. The additional 2 spots means the middle tier teams still have hopes for a playoff berth. And it's mainly those teams that we've all been talking about on this thread for the last month.

 

It's a fair point, but I've never really been a fan of factoring in home and away performance into the projections (which should always be taken with a grain of salt anyway). First, when there are plenty of games remaining, factoring home and away performance is basically meaningless. (In fact, this has come up before.) Second, when there aren't many games left, the PPG projections themselves are suspect in their entirety. (This too, I think has come up before, but I don't recall when.) When you get down to just a handful of games flukes, anomalies and noise take over. The totally unexpected win isn't balanced out later by the totally unexpected loss, the strange result isn't submerged into a bunch of predictable results. One-off occurrences take over.

Looking at home and away performance thus far you'd expect something like the following for NYR and POR remaining games:

NYR: 1.41 PPG, for about 8 or 9 points, and 44 or 45 points total.
POR: 1.00 PPG, for about 6 points, and 42 points total.

Meanwhile, the usual PRJ I've got in the main table has both teams ending the season around 44 points.

So what are we really talking about here? The NYR projection is effectively identical either way. The POR projection is less by 2 points, less than one odd result. The difference between the disaggregated projections for NYR and POR is at most one flukey game. It's all less than one game.

For better or worse for their playoff prospects, both NYR and POR are perfectly capable of doing something unexpected in one of their 6 remaining games. And that's the only difference here: just one unexpected result in one game.

What's that tell me? Same as I said two years ago. Disaggregating the home and away PPG numbers gives you a "false sense of accuracy" -- early on because there are so many games left, and later because there aren't enough left.

 

A fair point too. It pays to be wary of all extrapolations of this sort as past performance is not a guarantee of future results. So, yeah, calculated distortions and all that ...

 

Nothing strange. Pretty ordinary statistics, in fact. (It doesn't have be balanced early in the season. Just balanced enough and with enough games remaining to override any statistical noise.) I think you missed the point about the small sample size at the end of the season when there are only a few games left. At that point the statistical noise (the unexpected result, the fact that sometimes you get heads 6 times in a row, etc.) very easily overrides the statistical trend or probable expectation. Flip a coin 6 times. You'd expect to get 3 heads and 3 tails. But sometimes you get heads 6 times in a row. With a bigger sample, that sort of noise will even out and you'll get 50/50 in the long run. But small samples are often very noisy. Same here when you have only a few games left. Maybe it's counter-intuitive to some, but that is the way the numbers work.

 

I'm not positive, but I think RSL is already in if they hold the 3-way tiebreaker vs NYR and HOU. I'll have to look further ...

 

RSL owns the 3-way tie-breaker.

Maybe they're in with an asterisk (some crazy 4-way tiebreaker in which HOU or NYR comes out ahead), but, in effect, they are in. Details later ...

 

... Failing Up-Date ...

Code:

[B][U]         GP  GR  W   D   L   PTS PPG   PRJ MPP SE# T#  M#  WS# HD#   AD#   CNF[/U]
[COLOR="Blue"]01  LAG  29  05  16  10  03  58  2.00  68  73  16  --  --  --  ----  ----  W[/COLOR]
02  RSL  28  06  15  06  07  51  1.82  62  69  12  33  01‡ --  ----  ----  W
03  SEA  29  05  14  09  06  51  1.76  60  66  09  30  01‡ --  ----  ----  W
04  FCD  29  05  13  07  09  46  1.59  54  61  04  25  06  --  ----  ----  W
05  CMB  29  05  11  08  10  41  1.41  48  56  --  20  11  --  0.80  0.81  E
06  PHI  28  06  09  12  07  39  1.39  47  57  --  21  13  02  1.00  1.01  E
07  SKC  29  05  10  10  09  40  1.38  47  55  --  19  12  01% 1.00  1.01  E
08  COL  30  04  10  11  09  41  1.37  46  53  --  17  11  --  1.00  1.02  W
09  HOU  30  04  09  12  09  39  1.30  44  51  --  15  13  02  1.50  1.52  E
10  DCU  27  07  08  11  08  35  1.30  44  56  --  20  17  06  1.43  1.44  E
----------------------------------------------------------------------------
11  POR  29  05  10  07  12  37  1.28  43  52  --  16  15  04  1.60  1.61  W
12  NYR  29  05  07  15  07  36  1.24  42  51  --  15  16  05  1.80  1.81  E
13  CHI  28  06  05  15  08  30  1.07  36  48  --  12  22  11  2.50  2.51  E
14  CHV  30  04  07  11  12  32  1.07  36  44  --  08  20  09  ----  ----  W
15  SJE  29  05  06  12  11  30  1.03  35  45  --  09  22  11  ----  ----  W
16  TFC  30  04  06  12  12  30  1.00  34  42  --  06  22  11  ----  ----  E
17  NER  29  05  05  12  12  27  0.93  32  42  --  06  25  14  ----  ----  E
18  VAN  28  06  04  10  14  22  0.79  27  40  --  04  30  19  ----  ----  W

Current AD-Baseline: 45^ (Unchanged since the last update.) [/B]

Code:

[B]GP = Games Played | GR = Games Remaining | PPG = Points Per Game
MPP = Max Points Possible = PTS + (3 x GR)
SE# = SS Elimination Number = MPP - (1st Place PTS) + 1 
M# = Magic Number = (11th Highest MPP) – PTS + 1
T# = Tragic Number = MPP – (10th Highest PTS) + 1
WS# = Wooden Spoon # = (18th Highest MPP) - PTS +1
HD# = Historical Despair Number = [URL="https://www.bigsoccer.com/forum/showpost.php?p=24203471&postcount=1"]Full explanation[/URL]
AD# = Actual Despair Number = [URL="https://www.bigsoccer.com/forum/showpost.php?p=24203471&postcount=1"]Full explanation[/URL]

- Sorted by PPG, then most GR, then REVERSE alphabetical.*
- Teams in [COLOR="SlateGray"]gray[/COLOR] have been eliminated from the playoffs.
- Teams in [COLOR="Blue"]blue[/COLOR] have clinched a playoff spot.
- Teams in [COLOR="SeaGreen"]green[/COLOR] are conference seeds.
- Team in [COLOR="Brown"]brown[/COLOR] has won the Wooden Spoon.
- Teams in [I]italics[/I] are conference champions.[/B]

Asterisks

* In the final weeks MLS tie-breakers will replace the final alphabetical sort. But until the final weeks it's seriously not worth the bother.

^ Set by DCU’s current 44 point (1.30 PPG) pace.

% SKC holds the first tie-breaker over VAN. Therefore, despite a WS# of 1, they have escaped WS contention.

‡ See below for a full explanation.

Notes

Let’s cut to the chase: amazingly, despite all those crazy games, despite all those blown leads, once again almost nothing happened.

DCU blew a two goal lead at home against one of the worst teams in the league and had to settle for a draw. (Seriously, DCU! How could you be so stupid? Step over here so I can dope slap you! Ugh!) NYR got trounced by one of the best teams in the league. POR couldn’t manage to hold onto a one goal lead and also had to settle for a draw. Terrible results all around. But because there were terrible results all around, nothing really changed. Everything remains pretty much where it was before these games (and, frankly, it remains pretty much as it was before the last round of games).

The middle of the table is just plain stuck. Nobody seems capable of breaking from the pack. And everybody seems to be in a contest to find out who can fail least badly. Maybe we don’t have a playoff race after all. Unless you consider it a contest to see who can back their way into the playoffs in the least ignoble way possible.

I wish I had some sort of snappy metaphor to describe the craziness of what’s happening with these teams. But I don’t. They all seem like they’re intent on drowning themselves in a shallow bathtub. But instead of actually drowning they’re all just drinking up the water making it that much more difficult for everyone to drown themselves! (Does that work? I don’t know, but it’s the best I’ve got!)

So NYR, POR and DCU, I’m pretty sure none of you deserve it, but you got thrown a lifeline for another week. Maybe you should use that lifeline to help yourselves instead of employing it as just another prop in this failed series of suicide attempts.

What else? No SS for DCU. And SJE’s draw means it’s now dropped beyond the point of mathematical return on the despair numbers – meaning see you next year SJE.

And there’s the issue of RSL and SEA and whether they’ve clinched.

I’d like to think that RSL has clinched and that SEA has not. I can almost prove both of these, but without going through the full range of tiebreaking scenarios (meaning 4 and 5 way scenarios) I can’t give a 100% definite answer. Let’s start with SEA.

SEA has 51 points. There are only 12 teams remaining that can match or exceed those 51 points. Of those, the two at the bottom, whose MPP is 51, are HOU and NYR. Let’s say SEA loses the rest of its games and ends the season at 51 points, and that both NYR and HOU win out and end the season at 51 points. Would SEA beat HOU and NYR on a 3-way head to head tiebreaker? If it does, then SEA would be guaranteed to be in the top 10, and hence in the playoffs. The answer is no.

Code:

[B][U]     W  D  L  PTS[/U]
HOU  1  3  0  6
NYR  1  2  1  5
SEA  1  1  2  4[/B]

SEA loses on the three-way tie-breaker, which suggests that they do, in fact, need that 1 additional point to clinch. But is there a 4 way scenario in which SEA would come out on top, or at least within the top 10? Maybe.

RSL is a bit different. They’re in the same 51 point situation as SEA. Under the same scenario, would they beat HOU and NYR in a 3-way head to head tiebreaker? Yes.

Code:

[B][U]     W  D  L  PTS[/U]
RSL  2  1  1  7
HOU  1  3  0  6
NYR  0  2  2  2[/B]

RSL wins this 3-way tiebreaker, which suggests that they’ve already clinched. But is there a 4 way scenario in which RSL would come out on the bottom, or at least below the top 10? Maybe.

(And I pity the fool who attempts to figure out all the 4 (and 5!) way scenarios.)

Lastly, I've been saying, just you wait and see, these next games are finally going to bring some clarity to the middle of the table. It's not happening. So I give up! I'm telling you right now, this weekend we're going to see NYR draw with POR (because apparently neither of those teams can win a game when they need to!), and in their respective games DCU and HOU will draw as well. That way nothing will change, and that seems to be the way the MLS world works these days.

 

I started working through the scenarios from GreatGonzo and ThreeApples late last night. And then I realized I'd be up half the night if I really wanted to check and double check everything to make sure there isn't any possible way it could be wrong. So I went to bed.

From what I did do, I think they look right. Maybe RSL and SEA truly have clinched.

But I think I might be better off just forgetting that I ever saw that stuff and hopefully it'll all be rendered moot soon enough.