Effects of Blowouts and 1-run Games on Pythag record

Question: Can one-run games and blowout wins and losses explain why a team's Pythagorean record is different from their official record?

Note: The formula to get the expected Pythagorean winning percentage :

Win% = (Runs Scored^2)/( Runs Scored^2+Runs Allowed^2)

Why I asked the question: Last season there was much discussion about how the Diamondbacks were overachieving by winning more games than their Pythagorean record said they would.

In the 2007 season the Diamondbacks went 90-72, but according to the Pythagorean formula (712 runs scored and 732 runs allowed), they should have been 79-83, a difference of 11 games. I read many an article on this, and what I found even more interesting was that two years before, this same team did the same thing when they went 77-85 with 696 runs scored and 856 runs allowed. These runs scored resulted in a Pythagorean record of 64-98. In the over 100 year history of baseball the Bob Melvin coached Diamondbacks hold the second (2007) and 7th (2005) best percentage of games won compare to the number of games that they were supposed to achieve. Most teams average a difference of 0 to 4 game difference.

Searching the Internet, I found quite a few articles on the subject. Many of the authors were not able to put their exact finger on what was going on. A couple of people did make pretty compelling arguments. First Dan Rosenheck of the New York Times (http://www.nytimes.com/2007/09/23/sports/baseball/23score.html?_r=4&ref=sports&oref=slogin&oref=slogin&oref=slogin&oref=slogin) showed that Arizona’s relievers either had the duty of come in when it was close or mop duty. Chris Jaffee of the Hardball Times (http://www.hardballtimes.com/main/article/no-mirage-in-arizona/) stated the same thing. A common observation from several articles was that Arizona was really good in 1 run games and really bad in blowouts (games decided by 5 runs or more) as seen in Table 1. I decided to isolated those two factors and see if they really did matter in the difference in the records.

Analysis:

From 2002 to 2007 there were 180 season of baseball played and during that time21 teams (10% of the teams) over/under achieved by 7 games or more.

Table 1

 Team Year Actual Record RS RA Pythag. Record Difference (actual – pythag.) Record in 1 run games Record in Blowouts Cleveland 2006 78-84 870 782 90-72 -12 18-26 33-20 Toronto 2005 80-82 775 705 89-73 -9 16-31 25-14 Boston 2002 93-69 859 665 101-61 -8 13-23 34-19 Chicago Cubs 2002 67-95 706 759 75-87 -8 18-36 16-18 Houston 2003 87-75 805 677 95-67 -8 19-21 28-14 Detroit 2004 72-90 827 844 79-83 -7 12-27 23-22 Boston 2007 96-66 867 657 103-59 -7 22-28 36-17 NY Mets 2005 83-79 722 648 90-72 -7 21-24 25-17 Chicago Sox 2005 99-63 741 645 92-70 +7 35-19 21-16 Minnesota 2002 94-67 768 712 87-75 +7 29-16 23-20 Oakland 2006 93-69 771 727 86-76 +7 32-22 21-22 Cincinnati 2003 69-93 694 885 62-100 +7 30-21 9-29 St. Louis 2007 78-84 725 829 70-92 +8 16-20 25-38 Seattle 2007 88-74 794 813 79-83 +9 28-20 24-29 Cincinnati 2004 76-86 750 907 66-96 +10 25-20 11-35 Arizona 2007 90-72 712 732 79-83 +11 32-20 20-26 NY Yankees 2004 101-61 897 808 89-73 +12 24-16 27-28 Arizona 2005 77-85 696 856 64-98 +13 28-18 18-35

With the list of teams, their W/L records needed to be estimated for the 1 run games and the blowouts in order to see if they could help explain the difference.

1 run games - I adjusted these W/L records to be the percentage averaged the actual and Pythagorean winning percentages. I figured the teams idea winning percentage was some where in between the actual and Pythagorean values and average gave me that value. For example the 2007 Diamondbacks went 32-20 in 1 run games so here is the formula to get the estimated wining percentage.

(90/162)+(79/162)

Estimated Winning Percentage = --------------------------- = 52.16%

2

52.16% of 52 is 27, so their estimated record would be 27-25.

So over the 2007 season the Diamondbacks won 5 more games 1 runs than they should have won. This change in wins was subtracted or added to the teams W/L total.

Blowouts - The winning percentage was needed also to estimate the number of games the team should have been blown out. The actual W/L total was not adjusted, instead, the runs allowed (for teams being blown out too often) or runs scored (teams administering the blowout) were adjusted. Taking an average of all the blowout games, the average run difference was 7.5 runs. Since 4 runs was not considered a blowout, 3.5 runs per game would be added or subtracted from Runs Scored or Runs Allowed.

For example using the 2007 Diamondbacks again, they should have had a record in blowouts of 24-22. They were probably blown out 4 too many times, so their Runs Allowed was decreased by 14 runs (4 games * 3.5 runs/game).

The following shows what the teams Actual and Pythagorean records would be after being adjusted for a more normalized record in 1 run games and blowouts.

Table 2

 Team Year Actual Record (adjusted) RS (adjusted) RA (adjusted) Pythag. Record (adjusted) Difference (actual – pythag.) (adjusted) Cleveland 2006 83-79 850 782 88-74 -5 Toronto 2005 88-74 759 705 87-75 1 Boston 2002 101-61 850 665 100-62 1 Chicago Cubs 2002 72-90 702 759 75-87 -3 Houston 2003 90-72 789 677 93-69 -3 Detroit 2004 78-84 819 844 79-83 -1 Boston 2007 105-57 855 657 102-60 3 NY Mets 2005 86-76 713 648 89-73 -3 Chicago Sox 2005 96-66 744 645 92-70 4 Minnesota 2002 91-71 772 712 87-75 4 Oakland 2006 91-71 781 727 87-75 4 Cincinnati 2003 59-103 716 885 64-98 -5 St. Louis 2007 78-84 738 829 72-90 6 Seattle 2007 85-77 806 813 80-82 5 Cincinnati 2004 71-91 782 907 69-93 2 Arizona 2007 85-77 782 907 80-82 5 NY Yankees 2004 100-62 913 808 91-71 9 Arizona 2005 69-93 714 856 66-96 3

Initially the average difference in wins of the actual to Pythagorean records were off by 8.72 wins. After being adjusted they were off by only 3.72 wins (average difference for all 180 was 3.29 wins). There was one case where a team maintained a difference of of greater than 7 games. The 2004 Yankees only changed from winning more 11 games than they were supposed to winning 9 more. With all this information, one run games and blowouts, in most cases, can explain why a team's actual and Pythagorean records don't match.

There were several reasons I read about for reasons some teams might be better than other in the 1-runs games and blowouts. Besides the articles by Dan Rosenheck and Chris Jaffe, not many gave good explanations, but here are some of their theories (and the reasons I do or don't believe them).

Good in one run games.

• Good bullpens allowing team to win close games. The bullpens of the overachieving teams had an ERA of 4.11, while the ERA of the underachievers was 4.18. This idea didn't hold much water

• Clutch hitting. People have been trying to determine clutching hitting for years and if you Google "clutch hitting statistics", 768,000 articles will be available for reading, but I am not going to begin to tackle the subject.

• Bad bullpens. I actually looked to see if Blown Saves and the record in 1-run games was correlated. They weren't significantly correlated (teams that overachieved averaged 18.8 blown saves, while the underachievers averaged 20.0). There was some teams that this could definitely be the case with though, such as Detroit in 2004 blew 28 saves

More blowouts wins

• Really good offensive team. These teams would jump out to an early lead and the other team throws out the dreg pitchers for the high power offense to tee of on. There is some truth to this in that of the underachievers scored about 50 runs per season less than the overachievers (804 runs vice 754 runs per season).

More blowout losses

• Bi-polar starting and/or relief staffs (pitching staffs that have pitchers that are really good or really bad, no middle of the road pitchers). The bullpen aspect was looked at in the two previous articles by Rosenheck and Jaffe. This could also be the case with a team's starting rotation. A team could have 3 aces and the other starters are horrible, thereby increasing the number of blowouts..

I might look into expanding this topic in the future, for now my question has been answered.

Other articles on difference in Pythagorean record and actual record:

Pondering Pythagoras

by David Gassko

http://www.hardballtimes.com/main/article/pondering-pythagoras/

Managers and the Pythagorean Theorem

By Pizza Cutter

http://mvn.com/mlb-stats/2007/12/15/managers-and-the-pythagorean-theorem/

Pythagoras solved?: An R-squared of 97.8 percent

By Pizza Cutter

http://mvn.com/mlb-stats/2007/11/05/pythagoras-solved-an-r-squared-of-978-percent/

Update for 2008 season: Again 10% of the teams (3) had a difference of more than 7 games between their actual and Pythagorean records and their records when adjusting for 1 run games and blowouts:

 Team Actual Record RS RA Pythag. Record Difference (actual – pythag.) Record in 1 run games Record in Blowouts Toronto 86-76 714 610 94-68 -8 24-32 24-10 Houston 86-75 765 697 77-84 9 21-21 18-24 LA Angels 100-62 765 697 92-70 11 31-21 20-20

 Team Wins Losses RS (adjusted) RA (adjusted) Wins (Pythag adjusted) Losses (Pythag adjusted) Difference (actual – adjusted pythag) Toronto 86 76 696 610 92 70 1 Houston 86 75 723 743 78 83 7 LA Angels 100 62 808 697 93 69 7