Wednesday, April 1, 2009

The 2009 Diamond Mind Projection Blowout - American League Edition

Opening Day is almost here, so it’s time to present my annual Diamond Mind Projection blowout. The idea behind this is to take several projection systems and run the 2008 season through Diamond Mind Baseball, which I consider to be the most statistically accurate baseball simulator out there.

I’ve done this for the last few years. If you want to see how previous runs have gone, here are the links:


As you can see if you look at the prior runs, the results can be hit and miss, but that’s certainly understandable. This year, I’m again using six different projection systems, and I’ve run each one 1000 times for a total of 6000 iterations.

Before I present the projected standings, it’s disclaimer time.

1) Projection systems are inherently limited in their accuracy, particularly for pitchers. We can get a rough idea of how most players will perform by looking at their past histories and how similar players have performed, and factoring in aging and regression, but abilities/talent can change in ways that can’t be forecasted.

2) Playing time distribution in these simulations will not match the actual playing time of the players involved. I used the rosters and depth charts available at and Baseball Prospectus as my guide to set these up as realistically as possible, but it’s a possible source of error. Rosters were set up to have 35-40 or so active players per team, and to get a reasonable amount of playing time from the bench and extra pitchers, to more closely model reality.

3) We cannot predict injuries and/or roster changes. These simulations do include projected playing time based on past health issues, so someone like Rich Harden is not expected to make 30 starts. I’ve also included random injuries which may lead to some of the outlying results you see, but there’s no way to account for all the fluctuations that will happen with rosters this season.

4) These are the averages of 1000 seasons, so the results will tend to regress towards the mean. The final standings will not look like this, because they only play the season once.

5) These are NOT my predictions. These are projections based on running a computer simulation thousands of times with projection data that is inherently limited. If your favorite team doesn’t project well, don’t blame me, blame the computers and spreadsheets that projected them. I guess you can blame me for the CAIRO results if you want, otherwise you can take heart in the 2005 White Sox projecting to win 79 games, the 2006 Tigers projecting to win 80, or the 2007 Rockies projecting to win 79.

6) Since this is all automated, I don’t break ties. I simply award all ties a share of either the division title or wild card when it happens which is why you may see some funny decimal places in the standings that follow.

OK, so now that the disclaimers are out of the way, onto the projected standings. I am showing W-L to one decimal point to deal with displayed rounding issues and so I don’t get people asking me why the wins and losses don’t add up to exactly 2430, not to imply that these results are that precise.

There’s too much crap to fit it all into one post, so I’ve created separate posts for both leagues.
2009 Diamond Mind Projection Blowout - National League Summary

And here are the combined standings of all 6000 projections:

AL East W L RF RA Div WC StD W Std RF Std RA Median Mode 1 2 3 4 5 6 APW Std APW
NYA 95.9 66.1 853 711 2908.8 1776.2 90 - 102 813 - 894 673 - 749 96 98 3058 1897 963 74 8 0 100 95 - 104
BOS 94.3 67.7 837 703 2157.3 2053.4 88 - 101 796 - 879 667 - 739 94 94 2295 2205 1351 130 19 0 94 90 - 98
TAM 90.1 71.9 795 695 916.3 1591.2 84 - 96 756 - 834 659 - 732 90 89 1009 1735 2753 431 72 0 88 83 - 92
TOR 75.6 86.4 691 742 9.4 80.3 69 - 82 654 - 728 705 - 780 76 74 14 100 410 2979 2497 0 78 74 - 83
BAL 74.5 87.5 781 844 8.3 46.3 68 - 81 742 - 820 803 - 885 74 74 10 63 320 2457 3150 0 71 66 - 76

AL Central W L RF RA Div WC StD W Std RF Std RA Median Mode 1 2 3 4 5 6 APW Std APW
CLE 85.5 76.5 803 754 2958.1 110.7 79 - 92 763 - 843 716 - 792 86 88 3092 1619 775 378 136 0 89 85 - 94
DET 81.4 80.6 784 775 1526.9 77.7 75 - 88 745 - 822 736 - 814 82 83 1629 1751 1159 901 560 0 83 80 - 87
MIN 79.5 82.5 748 769 1017.4 75.1 73 - 86 710 - 786 729 - 808 79 78 1102 1378 1558 1262 700 0 79 76 - 82
KC 74.6 87.4 728 801 259.1 18.5 68 - 81 690 - 766 761 - 841 75 75 291 746 1328 1652 1983 0 75 71 - 78
CHA 74.1 87.9 751 826 238.5 17.5 68 - 80 713 - 790 787 - 865 74 74 266 676 1188 1674 2196 0 69 65 - 74

AL West W L RF RA Div WC StD W Std RF Std RA Median Mode 1 2 3 4 5 6 APW Std APW
LAA 85.4 76.6 777 734 3356.4 55.8 79 - 92 737 - 816 696 - 772 85 86 3498 1607 708 187 0 0 88 84 - 93
OAK 81.1 80.9 768 755 1563.4 60.3 75 - 87 728 - 808 717 - 793 81 82 1673 2155 1607 565 0 0 82 78 - 86
SEA 77.8 84.2 710 737 882.8 26.9 71 - 84 673 - 746 698 - 775 78 77 961 1631 1998 1410 0 0 77 73 - 80
TEX 72.1 89.9 776 879 199.1 10.2 66 - 79 737 - 815 835 - 924 72 72 227 672 1578 3523 0 0 70 64 - 75
Avg WC 93.3


W:Average wins over 1000 seasons

L:Average losses over 1000 seasons

RF:Average runs for(scored) over 1000 seasons

RA:Average runs allowed over 1000 seasons

Div: Number of division titles won over 1000 season. Ties are split (ie, if two teams tie for a division, they each get 0.5 Div)

WC: Number of wild cards won. Same deal with the ties here

StD W: Wins within one standard deviation either way

Std RF: Runs for within one standard deviation either way

Std RA: Runs allowed within one standard deviation either way

Median: Median win total

Mode: Mode win total

1: Number of times in first place

2: Number of times in second place

3: Number of times in third place

4: Number of times in fourth place

5: Number of times in fifth place

6: Number of times in sixth place

APW: Average placing wins. This is the average win total to take each place in the division

Std APW: APW within one standard deviation

Avg WC: Average victory total of the wild card winner over 1000 seasons.

I'll run through the divisions and teams briefly:

AL East
Regular readers know that this whole exercise is just an excuse to make use of pie charts, so I'll start off each division writeup with a pie chart showing the breakdown for how the division titles were distributed. The pie charts here are for the combination of all projections. To look at the same thing for each separate projection just go to the appropriate link(s) above.

Team: New York Yankees

Avg Prj W: 96

2008 Actual W: 89

2008 PythagenPat W: 87

W Diff: 7

PythagenPat W Diff: 9

Avg Prj RF: 853

2008 RF: 789

RF Diff: 64

Avg RA: 711

2008 RA: 727

RA Diff: -16

RF+RA Diff: 80

Division %: 48%

Wild Card %: 30%

Playoff %: 78%

High W: 98 (hbt)

Low W: 94 (marcel)

Gap: 4

Avg Div Plc: 1

Are the Yankees the best team in baseball? The numbers think so, although they thought so last year as well. The pitching and defense projects to be about two wins better than last season, but the bigger gain is on the offensive side (+65 runs) based on adding Mark Teixeira and Nick Swisher, plus more expected contributions from Robinson Cano, Jorge Posada and Hideki Matsui. So a projected 81 run differential improvement adds about seven wins to last year's actual 89 win team, and about nine to their PythagenPat 87 wins.
Why they might be better than projected: We can't predict injuries, but in order to handle some of the downside risk I restricted Alex Rodriguez's playing time to around 120 games and Jorge Posada to around 100 games. On the pitching side I assumed that they will not get full seasons out of any of A.J. Burnett (around 27 starts), Chien-Ming Wang (around 26 starts), Andy Pettitte (around 25 starts) and Joba Chamberlain (around 23 starts). If those four are able to make more starts than that the Yanks should be a little better.
Why they might be worse than projected: They're not as deep as they could be. Having the loser of the Nady/Swisher battle around for corner oF and 1B depth will help, but they're susceptible at other positions. Right now the rotation looks solid, and with Phil Hughes, Ian Kennedy and Alfredo Aceves around they have some decent projected depth, but it's a reasonable question how good any of those three may be in 2009 if pressed into duty. The bullpen has some talented arms who project fairly well, but aside from Mariano Rivera they all carry some risk.


Avg Prj W: Average projected wins

2008 Actual W: Actual wins in 2008

2008 PythagenPat W: 2008 PythagenPat Wins

W Diff: Avg Prj W - 2008 Actual W

PythagenPat W Diff: Avg Prj W - 2008 PythagenPat W

Avg Prj RF: Average projected runs scored

2008 RF: 2008 runs scored

RF Diff: Avg Prj RF - 2008 RF

Avg RA: Average projected runs allowed

2008 RA: 2008 runs allowed

RA Diff: Avg Prj RA - 2008 RA

RF+RA Diff: Projected run differential delta

Division %: Percentage of times the team won their division

Wild Card %: Percentage of time the team won the wild card

Playoff %: Division% plus Wild Card %

High W: Higest average W projection and system

Low W: Lowest average W projection and system

Gap: Gap between High W and Low W

Avg Div Plc: Average place in division

Team: Boston

Avg Prj W: 94

2008 Actual W: 95

2008 PythagenPat W: 96

W Diff: -1

PythagenPat W Diff: -2

Avg Prj RF: 837

2008 RF: 845

RF Diff: -8

Avg RA: 703

2008 RA: 694

RA Diff: 9

RF+RA Diff: -17

Division %: 36%

Wild Card %: 34%

Playoff %: 70%

High W: 96 (chone)

Low W: 92 (marcel)

Gap: 4

Avg Div Plc: 2

Boston returns just about all their key players from last year's 96 win PythagenPat team, but they are projected to score a few less runs and allow a few more, which knocks them down by a win. Given the margin of error we're dealing with here, I'd say they are basically even with the Yankees, although they're tough to project given the uncertainty of some of their off-season signings.
Why they might be better than projected: The biggest reason is Jon Lester. Lester was outstanding last year as he appeared to finally have regained his strength after his cancer scare. However, the projection systems don't care about why Lester struggled in his prior seasons. They just see that he did and that suppresses his projections in 2009. While the jump in his innings last year is a possible concern, I'd estimate that a healthy Lester should be at least a win better than projected. The projection systems also expect Dustin Pedroia and Kevin Youkilis to regress somewhat. It's tough to say what kind of contributions they'll get out of Smoltz/Penny and Saito, all of whom are talented but who are all working their way back from injuries. If any of them can rebound somewhat, that will help out a bit.
Why they might be worse than projected: Daiskuke Matsuzaka outpitched his peripherals last year and may struggle to match his efficacy of last season. David Ortiz is projected to bounce back a fair amount but it's possible that his wrist injury may make that hard. Jed Lowrie looks entrenched as the starting SS, and while his defensive metrics were very good in a very small sample size last season, his minor league scouting reports are less sanguine about his defense. It's entirely possible that none of Penny/Smoltz/Saito contribute anything meaningful. Still, I unfortunately have a hard time seeing them being much worse.

Team: Tampa Bay

Avg Prj W: 90

2008 Actual W: 97

2008 PythagenPat W: 92

W Diff: -7

PythagenPat W Diff: -2

Avg Prj RF: 795

2008 RF: 774

RF Diff: 21

Avg RA: 695

2008 RA: 671

RA Diff: 24

RF+RA Diff: -3

Division %: 15%

Wild Card %: 27%

Playoff %: 42%

High W: 92 (pecota)

Low W: 88 (chone)

Gap: 4

Avg Div Plc: 3

The upstart Rays (Tampa Bay fans have to be tired of the word upstart by now) surprised most of the mainstream media with their performance last season, although CHONE and PECOTA both expected them to be pretty good. The secret's out now, but this is a very talented group of players and they should be in the thick of the AL East and wild card race all season.
Why they might be better than projected: 23. 24. 25. 27. Most of their key players are young and have the potential for growth beyond what the typical aging patterns built into projections systems would assume. They've got a deep farm system which can help them patch from within or go out and trade for help if needed. David Price's projections are pretty conservative in general based on the little pro experience he has. Although he'll start the season in AAA, he has a good chance to be up soon and to contribute more than projected if you go by his stuff and his scouting reports.
Why they might be worse than projected: They got some out of character performances from several relievers last year, and some or all of them could digress a touch. Like everyone, injuries could hurt them, although their overall organizational depth should mitigate that. They're in probably the toughest division in baseball, although they're a big part of that.

Team: Toronto

Avg Prj W: 76

2008 Actual W: 86

2008 PythagenPat W: 93

W Diff: -10

PythagenPat W Diff: -17

Avg Prj RF: 692

2008 RF: 714

RF Diff: -22

Avg RA: 742

2008 RA: 610

RA Diff: 132

RF+RA Diff: -154

Division %: 0%

Wild Card %: 1%

Playoff %: 1%

High W: 77 (cairo)

Low W: 74 (pecota)

Gap: 3

Avg Div Plc: 4

Why they might be better than projected: Travis Snider is a very good prospect, but his average projection is only .255/.321/.426. He has the talent to exceed that although he's still very young. They have arguably the most valuable pitcher in baseball at the front of their rotation. Vernon Wells could play a full season.
Why they might be worse than projected: They've got a lot of question marks in their rotation, and their offense looks unimpressive. If Baltimore makes a leap forward, it will likely come at the expense of the Jays.

Team: Baltimore

Avg Prj W: 74

2008 Actual W: 68

2008 PythagenPat W: 73

W Diff: 6

PythagenPat W Diff: 1

Avg Prj RF: 781

2008 RF: 782

RF Diff: -1

Avg RA: 844

2008 RA: 869

RA Diff: -25

RF+RA Diff: 24

Division %: 0%

Wild Card %: 1%

Playoff %: 1%

High W: 76 (chone)

Low W: 73 (pecota)

Gap: 3

Avg Div Plc: 5

Baltimore's not really a bad team right now. Unfortunately for them, they're in the AL East. I calculate a rough dvisional penalty using the formula N - N/2 times Opponent's winning percentage, where N is the number of interdivisional games. In Baltimore's case, their collective AL East oppenents project to a winning percentage of .5495, so their AL East penalty is around 4 wins. Out of curiosity, I flipped Milwaukee with Baltimore and ran 100 simulations. Baltimore went from 74-88 on average to 81-81, and Milwaukee went from 83-79 on average to 75-87.
Why they might be better than projected: They have Matt Wieters 'Nuff said. Actually, that's lazy. They also have Nick Markakis, who's awesome, and Adam Jones and Felix Pie who have the talent to be awesome. Rich Hill looked like he was on the verge of being a solid lefty starter until his back and control deserted him. While the odds of it are small, he could return to where he was in 2007.
Why they might be worse than projected: Their rotation is full of question marks. Adam Eaton may actually pitch for them. They are going to have a crap load of tough games.

Team: Chicago White Sox

Avg Prj W: 74

2008 Actual W: 89

2008 PythagenPat W: 89

W Diff: -15

PythagenPat W Diff: -15

Avg Prj RF: 751

2008 RF: 811

RF Diff: -60

Avg RA: 826

2008 RA: 729

RA Diff: 97

RF+RA Diff: -157

Division %: 4%

Wild Card %: 0%

Playoff %: 4%

High W: 77 (cairo)

Low W: 72 (zips)

Gap: 5

Avg Div Plc: 5

Why they might be better than projected: Because they almost always are?
2005: +20
2006: + 8
2007: - 4

2008: +15

Those are the differences between the White Sox projections I've run since 2005 and their actual win totals. When a model misses once, it could be luck. When it misses twice it could also be luck. When it misses three times, it could conceivably still be luck, but more likely it points to some kind of systemic error in the model.

They may not project well statistically, but I think Kenny Williams and his scouts do well in identifying breakout candidates and players who are better-suited to their ballpark. I also think Don Cooper is one of the best pitching coaches in baseball and that helps them too. The projections generally assume regression from Carlos Quentin, Gavin Floyd and John Danks, but it's certainly possible all have improved tangibly enough to make those projections pessimistic given their ages (26, 26 and 23 respectively).

Why they might be worse than projected: Their young players could all hit/pitch like their projections say, and their older players like Jermaine Dye and Jim Thome could start to show the effects of their age.

Team: Cleveland

Avg Prj W: 86

2008 Actual W: 81

2008 PythagenPat W: 85

W Diff: 5

PythagenPat W Diff: 1

Avg Prj RF: 803

2008 RF: 805

RF Diff: -2

Avg RA: 754

2008 RA: 761

RA Diff: -7

RF+RA Diff: 5

Division %: 49%

Wild Card %: 2%

Playoff %: 51%

High W: 88 (chone)

Low W: 84 (hbt)

Gap: 4

Avg Div Plc: 1

Why they might be better than projected: After leading the league in OPS+ in 2004 and 2006, Travis Hafner's performance has plummetted. He's still fairly young and a rebound by him would be a big boost to the Indians' lineup. Grady Sizemore's already playing at an MVP-level clip but he's still young enough to have some more growth in him. Cliff Lee's probably not going to be as good as he was in 2008, but he also may not regress as much as the projections expect.

Why they might be worse than projected: Hafner may not rebound at all. They've got Carl Pavano as their #3 starter. They could use a little more power from the infield and OF corners than they project to get.

Team: Detroit

Avg Prj W: 81

2008 Actual W: 74

2008 PythagenPat W: 78

W Diff: 7

PythagenPat W Diff: 3

Avg Prj RF: 784

2008 RF: 821

RF Diff: -37

Avg RA: 775

2008 RA: 857

RA Diff: -82

RF+RA Diff: 45

Division %: 25%
Wild Card %: 1%
Playoff %: 27%
High W: 85 (chone)

Low W: 76 (marcel)

Gap: 9

Avg Div Plc: 2

Why they might be better than projected: Their defense should be better with Inge at third and Adam Everett as short. Miguel Cabrera is still one of the best hitters in baseball. Gary Sheffield looked cooked in 2008, but if healthy he could exceed his projections. Justin Verlander also has the talent to outpitch his projections by a non-trivial amount.

Why they might be worse than projected: Their rotation is still a little iffy with Jeremy Bonderman's health status and Dontrelle Willis's lost talent. Brandon Lyon's penciled in as the closer right now but his health and effectiveness are legitimate concerns.

Team: Kansas City

Avg Prj W: 75

2008 Actual W: 75

2008 PythagenPat W: 72

W Diff: 0

PythagenPat W Diff: 3

Avg Prj RF: 728

2008 RF: 691

RF Diff: 37

Avg RA: 801

2008 RA: 781

RA Diff: 20

RF+RA Diff: 17

Division %: 4%

Wild Card %: 0%
Playoff %: 5%
High W: 77 (chone)
Low W: 70 (cairo)

Gap: 7

Avg Div Plc: 4

Why they might be better than projected: Alex Gordon improved his OBP by 37 points and his SLG by 21 pts in 2008 and could possibly make more improvements in 2009. Billy Butler disappointed in 2008 but he's still really young (23) and still has that prospect sheen. Zack Greinke was very good last year and over his last 11 starts he had a 2.34 ERA and struck out 69 hitters in 69.1 innings. The projections expect him to give some of those gains back, but he may not.

Why they might be worse than projected: Kyle Farnsworth. Right now 2B looks suspect, although Mark Teahan may be able to make the transition.

Team: Minnesota

Avg Prj W: 79

2008 Actual W: 88

2008 PythagenPat W: 89

W Diff: -9

PythagenPat W Diff: -10

Avg Prj RF: 748

2008 RF: 829

RF Diff: -81

Avg RA: 769

2008 RA: 745

RA Diff: 24

RF+RA Diff: -105

Division %: 17%

Wild Card %: 1%

Playoff %: 18%
High W: 85 (chone)
Low W: 78 (chone)

Gap: 7

Avg Div Plc: 3

Why they might be better than projected: Most of their core players are relatively young. Their defense projects to be around 20 runs above average using a combination of zone rating and Fan Graphs' UZR, something that may or not be factored in adequately in the various projection systems.

Why they might be worse than projected: Joe Mauer is probably their most important player, and he's dealing with knee and back issues this spring. Joe Crede's back may not hold up that well playing half his games on turf,

AL West

Team: Los Angeles Angels

Avg Prj W: 85

2008 Actual W: 100

2008 PythagenPat W: 88

W Diff: -15

PythagenPat W Diff: -3

Avg Prj RF: 777

2008 RF: 765

RF Diff: 12

Avg RA: 734

2008 RA: 697

RA Diff: 37

RF+RA Diff: -25

Division %: 56%

Wild Card %: 1%
Playoff %: 57%
High W: 87 (pecota)
Low W: 84 (hbt)

Gap: 3

Avg Div Plc: 1

Why they might be better than projected: Their division isn't particularly strong, which may help them win a few more games than they project to. Howie Kendrick hasn't been able to stay on the field. The ability to stay healthy is a skill, but he may be able to crack the magic 500 PA barrier. They may get more innings from Kelvim Escobar than I have him projected for (around 80 innings).

Why they might be worse than projected: Ervin Santana and John Lackey are likely to open the season on the DL. While I assume that just about every pitcher will miss at least 2-3 starts a season in my depth charts, they could both miss more than that. Vlad Guerrero looks like he may be slowing down a little, and could underperform his projections. I've assumed Bobby Abreu will DH more than play the field, and his glove could hurt them if he sees too much time in the OF.

Team: Oakland

Avg Prj W: 81

2008 Actual W: 75

2008 PythagenPat W: 76

W Diff: 6

PythagenPat W Diff: 5

Avg Prj RF: 768

2008 RF: 646

RF Diff: 122

Avg RA: 755

2008 RA: 690

RA Diff: 65

RF+RA Diff: 57

Division %: 26%

Wild Card %: 1%

Playoff %: 27%
High W: 83 (chone)
Low W: 78 (chone)

Gap: 5

Avg Div Plc: 2

Why they might be better than projected: The projections all generally agree that Matt Holliday's performance will take a fairly significant hit by moving to the AL and from Colorado to Oakland. While I can't speak for the exact park/league factors of all the different systems, I can tell you that in CAIRO, Coors Holliday projected to hit .334/.409/.576 vs. Oakland Holliday hitting .295/.374/.501. If Holliday's game translates better than that, the A's should be able to snag another win or two. Even with Jason Giambi at first base, the A's look to have enough good defenders to have an above average overall defense. They've also got one of the deeper farm systems in baseball, which should help them with both filling in holes from within and acquiring pieces if needed.
Why they might be worse than projected: The health of some of their key players is usually an issue, particulary Eric Chavez. They'll also be relying on some pretty young pitchers who are talented, but notoriously difficult to project.

Team: Seattle

Avg Prj W: 79

2008 Actual W: 61

2008 PythagenPat W: 67

W Diff: 18

PythagenPat W Diff: 12

Avg Prj RF: 712

2008 RF: 671

RF Diff: 41

Avg RA: 725

2008 RA: 811

RA Diff: -86

RF+RA Diff: 127

Division %: 9%

Wild Card %: 4%
Playoff %: 13%
High W: 81 (cairo)
Low W: 78 (hbt)

Gap: 3

Avg Div Plc: 3

Why they might be better than projected: Felix Hernandez is already really good, but it wouldn't surprise anyone if he became the best pitcher in the majors as soon as this season. They've shored up their defense (the projected difference between a full season of Endy Chavez vs. Raul Ibanez is around 20 runs just by itself). Erik Bedard could make more than the 24 starts I have him penciled in for.

Why they might be worse than projected: The Mariners have several veterans in the last year of their contracts who they may decide to trade as part of their rebuilding. Trading any of them may cost them some wins in the short-term. The Mariners still haven't annointed a closer. While the role is generally overrated, it's still nice to have a decent one.

Team: Texas

Avg Prj W: 72

2008 Actual W: 79

2008 PythagenPat W: 75

W Diff: -7

PythagenPat W Diff: -3

Avg Prj RF: 776

2008 RF: 901

RF Diff: -125

Avg RA: 879

2008 RA: 967

RA Diff: -88

RF+RA Diff: -37

Division %: 3%

Wild Card %: 0%

Playoff %: 3%
High W: 75 (marcel)
Low W: 69 (zips)

Gap: 6

Avg Div Plc: 4

Why they might be better than projected: The Rangers probably have the best farm system in baseball. Neftali Feliz and Derek Holland should begin the year in AAA and be available for a boost in the rotation at some point during the season. Ian Kinsler out-OPS+'ed AL MVP Dustin Pedroia by 12 points (134 to 122) and could outperform his projections.
Why they might be worse than projected: Michael Young's transition to 3B may not work out real well. Kinsler hasn't been able to play more than 130 games yet in his MLB career so his health is a potential concern.

Anyone who wants to look at or play around with the raw team level data from the simulations can download this Excel spreadsheet.
And that's your 2009 Diamond Mind Projection Blowout. Like I say every year, results are not guaranteed.

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