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2012 Pythagorean Thread

#1 User is offline  
Lyford 

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Posted 09 April 2012 - 09:01 AM

One of the things that I like to do during the baseball season is compile a weekly report of the AL standings, looking at runs scored and allowed, to see who's better than their records and who's worse.

For those unfamiliar, the Pythagorean report is based on a Bill James discovery regarding the relationship between runs scored, runs allowed and winning percentage. It intuitively makes sense that a teams record will be related to how many runs they score and how many they allow. What James discovered was that, for almost all teams, the winning percentage is very close to a ratio of the square of the runs scored to the sum of the squares of the runs scored and runs allowed. Which was dubbed the "Pythagorean" theorum of baseball.

The report consists of, for each team, their runs/game, runs allowed/game and Pythagorean project winning percentage, along with their rank among the teams in the league for each of those categories. The Pythagorean winning percentage is calculated as (r ^ 1.83) / ( (r ^ 1.83) + (ra ^ 1.83) ). (1.83 has been determined to be a slightly more accurate exponent with the current offensive levels than 2.) Using the Pythagorean winning percentage, the expected wins total is calculated and compared to the actual win total. Finally, any difference is expressed as "luck", with negative numbers representing underperforming teams.

Finally, there's a linear projection of final records, based on current winning percentage, and based on Pythagorean winning percentage.


So, on to week 1.

Season To Date:
[pre]
AL Pythagorean Projection Report - 4/9/2012

Team R/G (rank) RA/G (rank) Pyth (rank) proj w act w luck
Baltimore 5.000 (4) 1.667 (1) 0.882 (1) 3 3 0
Detroit 8.667 (1) 4.667 (9) 0.756 (2) 2 3 1
Texas 3.667 (11) 2.000 (2) 0.752 (3) 2 2 0
Tampa Bay 6.000 (2) 4.000 (6) 0.677 (4) 2 3 1
Toronto 5.667 (3) 4.000 (6) 0.654 (5) 2 2 0
Seattle 4.750 (5) 3.750 (5) 0.606 (6) 2 3 1
Kansas City 4.333 (7) 3.667 (3) 0.576 (7) 2 2 0
Los Angeles 3.667 (11) 4.333 (8) 0.424 (8) 1 1 0
Oakland 3.750 (10) 4.750 (10) 0.394 (9) 2 1 -1
Cleveland 4.000 (8) 5.667 (12) 0.346 (10) 1 1 0
[red]New York 4.000 (8) 6.000 (13) 0.323 (11) 1 0 -1[/red]
Chicago 2.000 (13) 3.667 (3) 0.248 (12) 1 1 0
[blue]Boston 4.667 (6) 8.667 (14) 0.244 (13) 1 0 -1[/blue]
Minnesota 1.667 (14) 5.000 (11) 0.118 (14) 0 0 0


Top 5 projections (using current winning %)
Baltimore 162 0
Detroit 162 0
Tampa Bay 162 0
Seattle 122 40
Texas 108 54

Top 5 projections (starting with today's record, using Pythagorean winning %)
Baltimore 143 19
Detroit 123 39
Texas 122 40
Tampa Bay 111 51
Toronto 106 56
[/pre]


(How does one present a formatted, fixed-width table in this markup code?)


Well, that was a brilliant bloody start, wasn't it?

- As anyone who has read my baseball commentary over the years knows, I tend not to overreact to a short stretch of bad (or good) play. One of the truisms of the game is that anything can happen in a short series, so the fact that the Red Sox have - again - started 0-3 doesn't mean much. And, in fact, it really doesn't mean much.

- In fact, there's much from <a href="http://lyflines.blogspot.com/2011/04/monday-pythagorean-442011.html">last year's first report</a> that's relevant and appropriate.

<blockquote>That all said, this was three games, and three games means...well, not nothing, but in the scope of the baseball season, not much. There were no "fatal flaws" revealed, anyone who says that "they can't beat TexasDetroit" is a moron, and it's just three games. Awful games, true. Disappointing. And magnified in our perception because a) they're the last three we've seen and b) for the 20112012 Red Sox, they're the only three games we've seen. It doesn't matter, it's still a three-game series.

Obviously, all sensible people of proper moral framework loathe the Yankees, but it's worth noting, in this context, that the 1998 Yankees lost their first three games (while being outscored 21-6) and four of their first five. They finished with a record of 114-48, which is not too bad. That doesn't mean that this Red Sox team will win 114 games, of course. It just means that losing the first three isn't always indicative of a disastrous season...
</blockquote>

- The problem is that there are enough significant differences (specifically, the manager and the closer) between this team and the team that we know is really good, the team that played the middle of the 2011 season, to erode confidence, and enough similarities to what happened in September to make this a much worse start - or, at least, to make this feel like a much worse start - than it otherwise would be.

- For those [this may be a strawman, as I haven't had the radio on or been on the bulletin boards, but I suspect there are many who take this position] who think that the absence of Bard and Papelbon from the bullpen cost the team badly this weekend, I'd note that both were in Texas for the 0-3 last start, both pitched badly and that Bard, in particular, was a key component to the 0-3 start of the 2011 team. This bullpen may turn out to be bad, Aceves and Melancon may turn out not to be able to pitch in late innings. But it's far too early to make that judgement right now. All we can say now is, "well, that was not a good performance."

- You can win a game with poor starting pitching. You can win a game with poor relief pitching. You can win a game with poor offense. It's tough to win a game if two of the three are bad, though. And that's what they did in Detroit. Bad offense and relief pitching in game one. Bad offense and starting pitching in game two. Bad starting pitching and relief pitching in game three. That's an excellent recipe for an 0-3 start.

- To repeat what I said after week 1 of the 2011 season, "there will be no Player of the Week awards this week, given the minimal length and maximal putrescence of what we witnessed over the weekend."

But Jon Lester pitched very well.
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RedSoxAnni 

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Posted 09 April 2012 - 09:05 AM

Wonderful! Thank you so much!
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FishCake 

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Posted 09 April 2012 - 10:36 AM

Look forward to reading these! And if you have anything to add to the B vs C thread, the guys would really appreciate it.
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Kid T 

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Posted 09 April 2012 - 04:08 PM

What is the margin of error for PT over the course of a season? I find PT to be a useful tool for determining a rough estimate of W/L, but find that the win totals often vary by 3-10 wins from the PT.
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roidrage 

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Posted 09 April 2012 - 04:37 PM

The root mean squared error is about 4 wins.
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Mike LansWho 

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Posted 10 April 2012 - 07:24 AM

This is great. Can't wait to see who makes it to the Pythagorean Series.
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Hail Cesar 

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Posted 10 April 2012 - 07:45 AM

View PostFishCake, on 09 April 2012 - 10:36 AM, said:

Look forward to reading these! And if you have anything to add to the B vs C thread, the guys would really appreciate it.


Yes, yes you should. I can't wait to see naked pictures of Pi.
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Lyford 

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Posted 16 April 2012 - 07:10 PM

Season To Date:
[pre]
AL Pythagorean Projection Report - 4/16/2012

Team R/G (rank) RA/G (rank) Pyth (rank) proj w act w luck
Texas 4.500 (7) 2.400 (1) 0.760 (1) 8 8 0
Detroit 5.333 (3) 3.778 (4) 0.653 (2) 6 6 0
Toronto 5.222 (4) 3.889 (6) 0.632 (3) 6 5 -1
Chicago 4.000 (11) 3.375 (2) 0.577 (4) 5 5 0
[red]New York 5.111 (5) 4.444 (7) 0.564 (5) 5 5 0[/red]
[blue]Boston 5.889 (2) 5.444 (11) 0.536 (6) 5 4 -1[/blue]
Cleveland 6.500 (1) 6.250 (13) 0.518 (7) 4 4 0
Baltimore 4.444 (8) 4.444 (7) 0.500 (8) 5 5 0
Seattle 3.636 (12) 3.818 (5) 0.478 (9) 5 6 1
Los Angeles 4.667 (6) 5.222 (9) 0.449 (10) 4 3 -1
Oakland 2.800 (14) 3.500 (3) 0.399 (11) 4 4 0
Kansas City 4.333 (9) 5.444 (11) 0.397 (12) 4 3 -1
Tampa Bay 4.111 (10) 6.333 (14) 0.312 (13) 3 4 1
Minnesota 3.111 (13) 5.333 (10) 0.272 (14) 2 2 0


Top 5 projections (using current winning %)
Texas 130 32
Detroit 108 54
Chicago 101 61
Toronto 90 72
[red]New York 90 72 [/red]

Top 5 projections (starting with today's record, using Pythagorean winning %)
Texas 123 39
Detroit 106 56
Toronto 102 60
Chicago 94 68
[red]New York 91 71 [/red]
[/pre]
.


Past Week:
[pre]
AL Pythagorean Projection Report - 4/16/2012

Team R/G (rank) RA/G (rank) Pyth (rank) proj w act w luck
Texas 4.857 (7) 2.571 (1) 0.762 (1) 5 6 1
[blue]Boston 6.500 (2) 3.833 (6) 0.724 (2) 4 4 0[/blue]
Chicago 5.200 (4) 3.200 (3) 0.709 (3) 4 4 0
[red]New York 5.667 (3) 3.667 (5) 0.689 (4) 4 5 1[/red]
Toronto 5.000 (6) 3.833 (6) 0.619 (5) 4 3 -1
Cleveland 8.000 (1) 6.600 (13) 0.587 (6) 3 3 0
Detroit 3.667 (11) 3.333 (4) 0.543 (7) 3 3 0
Los Angeles 5.167 (5) 5.667 (10) 0.458 (8) 3 2 -1
Oakland 2.167 (14) 2.667 (2) 0.406 (9) 2 3 1
Seattle 3.000 (13) 3.857 (8) 0.387 (10) 3 3 0
Baltimore 4.167 (9) 5.833 (11) 0.351 (11) 2 2 0
Minnesota 3.833 (10) 5.500 (9) 0.341 (12) 2 2 0
Kansas City 4.333 (8) 6.333 (12) 0.333 (13) 2 1 -1
Tampa Bay 3.167 (12) 7.500 (14) 0.171 (14) 1 1 0
[/pre]
.


Well. Week 2 was a bit more successful than week 1. Or, as Dorothy Gale would put it, "there's no place like home. There's no place like home..."

- The good news included the very successful rotation debut of Felix Doubront, another good start from Jon Lester and, perhaps most importantly on the starting front, the dominant performance from Josh Beckett in the home opener.

- It was also good to see Buchholz respond to a bad first performance and a bad 1st inning in the second to put up six excellent innings.

- Can we take a deep breath and relax, at least a little, about the bullpen? As I said last week, Alfredo Aceves is a very good pitcher and there's no reason whatsover to think that he won't be able to successfully pitch 9th innings.

- Obviously, it was a week of silver linings that was not without its dark cloud. The biggest and darkest of which was the loss of Jacoby Ellsbury for some yet-to-be-determined (and, no doubt, much-to-be-argued-about) time with a separated shoulder in a bit of a fluke play at 2nd base in the home opener. The good news is that it didn't have much effect on their performance in the Tampa series. But he's not a fungible talent; the likes of Cody Ross and Jason Repko and Che-Hsuan Lin won't replace him.

- Red Sox Player of the Week - The Red Sox offense came alive in the presence of home cooking, and nobody more than David Ortiz, who hit .692/.714/1.231/1.945 over the weekend to put up a .458/.519/.750/1.269 week with 1 HR, which tied the Sunday game, 4 doubles and 3 walks.

- Red Sox Pitcher of the Week - Jon Lester was very good again. They got good work from Scott Atchison and Franklin Morales out of the 'pen. Alfredo Aceves' performances at the end of three games was enough to significantly calm the initial "oh my God, our closer's hurt!" panic. But the performance of the week, all things considered - his September, his first start, his thumb, the 1-5 record, the division opponent - was Josh Beckett's domination of Tampa in the home opener.
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ghostoffoxx 

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Posted 16 April 2012 - 07:20 PM

This is great stuff, Lyford. Thanks for posting it.
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BigSlick 

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Posted 16 April 2012 - 09:13 PM

View Postghostoffoxx, on 16 April 2012 - 07:20 PM, said:

This is great stuff, Lyford. Thanks for posting it.


I know that posts like "Me too" and "+1" are frowned upon on the interwebs (and with good reason), but I feel this is the exception.

Lyford, I really appreciate the time and effort you put in to these posts and I really hope you continue to post them all season.
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Lyford 

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Posted 17 April 2012 - 05:23 AM

Thanks. I'm just glad that people like them...
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Posted 17 April 2012 - 07:13 AM

4 posts and he's added more to the board than I have in 8 years. Thanks a lot, jerk.
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Hail Cesar 

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Posted 17 April 2012 - 07:22 AM

View PostManny, on 17 April 2012 - 07:13 AM, said:

4 posts and he's added more to the board than I have in 8 years. Thanks a lot, jerk.


That's inaccurate. Your insights into midget and nugget porn have helped this board progress in ways that you wouldn't imagine.
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Mike LansWho 

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Posted 17 April 2012 - 07:22 AM

Now if he could only figure out the table markup coding...
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Lyford 

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Posted 17 April 2012 - 08:21 AM

View PostMike LansWho, on 17 April 2012 - 07:22 AM, said:

Now if he could only figure out the table markup coding...


Exactly. Hopefully, he's still working on it...

;-)
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Mike LansWho 

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Posted 17 April 2012 - 08:29 AM

View PostLyford, on 16 April 2012 - 07:10 PM, said:

Team                  R/G   (rank) RA/G  (rank) Pyth  (rank) proj w act w luck
Texas                 4.500 (7)    2.400 (1)    0.760 (1)       8      8     0
Detroit               5.333 (3)    3.778 (4)    0.653 (2)       6      6     0
Toronto               5.222 (4)    3.889 (6)    0.632 (3)       6      5     -1
Chicago               4.000 (11)   3.375 (2)    0.577 (4)       5      5     0
New York              5.111 (5)    4.444 (7)    0.564 (5)       5      5     0
Boston                5.889 (2)    5.444 (11)   0.536 (6)       5      4     -1
Cleveland             6.500 (1)    6.250 (13)   0.518 (7)       4      4     0
Baltimore             4.444 (8)    4.444 (7)    0.500 (8)       5      5     0
Seattle               3.636 (12)   3.818 (5)    0.478 (9)       5      6     1
Los Angeles           4.667 (6)    5.222 (9)    0.449 (10)      4      3     -1
Oakland               2.800 (14)   3.500 (3)    0.399 (11)      4      4     0
Kansas City           4.333 (9)    5.444 (11)   0.397 (12)      4      3     -1
Tampa Bay             4.111 (10)   6.333 (14)   0.312 (13)      3      4     1
Minnesota             3.111 (13)   5.333 (10)   0.272 (14)      2      2     0



Something like that. Still working on the color part.

This post has been edited by Mike LansWho: 17 April 2012 - 08:43 AM

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Lyford 

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Posted 17 April 2012 - 08:39 AM

OK. Here's this week's report with the correct alignment, anyway...

Season To Date:

AL Pythagorean Projection Report - 4/16/2012

Team                  R/G   (rank) RA/G  (rank) Pyth  (rank) proj w act w luck
Texas                 4.500 (7)    2.400 (1)    0.760 (1)       8      8     0
Detroit               5.333 (3)    3.778 (4)    0.653 (2)       6      6     0
Toronto               5.222 (4)    3.889 (6)    0.632 (3)       6      5     -1
Chicago               4.000 (11)   3.375 (2)    0.577 (4)       5      5     0
New York              5.111 (5)    4.444 (7)    0.564 (5)       5      5     0
Boston                5.889 (2)    5.444 (11)   0.536 (6)       5      4     -1
Cleveland             6.500 (1)    6.250 (13)   0.518 (7)       4      4     0
Baltimore             4.444 (8)    4.444 (7)    0.500 (8)       5      5     0
Seattle               3.636 (12)   3.818 (5)    0.478 (9)       5      6     1
Los Angeles           4.667 (6)    5.222 (9)    0.449 (10)      4      3     -1
Oakland               2.800 (14)   3.500 (3)    0.399 (11)      4      4     0
Kansas City           4.333 (9)    5.444 (11)   0.397 (12)      4      3     -1
Tampa Bay             4.111 (10)   6.333 (14)   0.312 (13)      3      4     1
Minnesota             3.111 (13)   5.333 (10)   0.272 (14)      2      2     0


Top 5 projections (using current winning %)
Texas                   130  32   
Detroit                 108  54   
Chicago                 101  61   
Toronto                 90   72   
New York                90   72   

Top 5 projections (starting with today's record, using Pythagorean winning %)
Texas                   123  39   
Detroit                 106  56   
Toronto                 102  60   
Chicago                 94   68   
New York                91   71   



Past Week:

AL Pythagorean Projection Report - 4/16/2012

Team                  R/G   (rank) RA/G  (rank) Pyth  (rank) proj w act w luck
Texas                 4.857 (7)    2.571 (1)    0.762 (1)       5      6     1
Boston                6.500 (2)    3.833 (6)    0.724 (2)       4      4     0
Chicago               5.200 (4)    3.200 (3)    0.709 (3)       4      4     0
New York              5.667 (3)    3.667 (5)    0.689 (4)       4      5     1
Toronto               5.000 (6)    3.833 (6)    0.619 (5)       4      3     -1
Cleveland             8.000 (1)    6.600 (13)   0.587 (6)       3      3     0
Detroit               3.667 (11)   3.333 (4)    0.543 (7)       3      3     0
Los Angeles           5.167 (5)    5.667 (10)   0.458 (8)       3      2     -1
Oakland               2.167 (14)   2.667 (2)    0.406 (9)       2      3     1
Seattle               3.000 (13)   3.857 (8)    0.387 (10)      3      3     0
Baltimore             4.167 (9)    5.833 (11)   0.351 (11)      2      2     0
Minnesota             3.833 (10)   5.500 (9)    0.341 (12)      2      2     0
Kansas City           4.333 (8)    6.333 (12)   0.333 (13)      2      1     -1
Tampa Bay             3.167 (12)   7.500 (14)   0.171 (14)      1      1     0

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Mike LansWho 

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Posted 17 April 2012 - 08:44 AM

Nicely done, looks great. I'm guessing that you can't use the font, color, bold, etc formats in addition to using the code tags.
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Lyford 

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Posted 17 April 2012 - 08:59 AM

View PostMike LansWho, on 17 April 2012 - 08:44 AM, said:

Nicely done, looks great. I'm guessing that you can't use the font, color, bold, etc formats in addition to using the code tags.


Not embedded, apparently. I'm still playing with it, but that may be it.
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Bozzs 

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Posted 17 April 2012 - 10:32 AM

View PostLyford, on 17 April 2012 - 08:59 AM, said:

Not embedded, apparently. I'm still playing with it, but that may be it.


Welcome Lyford !
This is great !!
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