## Friday, October 31, 2008

### What effect on a teams run total does the ½ inning a home team doesn't play if it is ahead going into the bottom of the last inning?

Question: What effect on a teams run total does the ½ inning a home team doesn't play if it is ahead going into the bottom of the last inning?

Why I asked the question: I have wondered where why teams were off on their Pythagorean record and wondered if the ½ inning that wasn't played made any difference.

I explain the Pythagorean theorem with respect to baseball records under the article:

http://jeffsqanda.blogspot.com/2008/10/can-1-run-games-and-blowout-wins-and.html

Analysis: The number of innings that a team pitched vice the number innings that a team batted were researched and compared. The innings pitched was easy to find as it is used in every pitching statistic under the sun, but I was not able to locate the innings batted or outs record. After trying to find a list of total outs, innings batted, etc., I had to go with the following formula to determine innings batted (basically Innings = Outs/3):

Innings batted =(TPA+DP+CS-H-BB-HBP-CI)/3 + 5.3

TPA = Total plate appearances

DP = Double play (out after getting on base)

CS = Caught Stealing (again out after getting on base)

H = Hit

BB = Base on Balls

HBP = Hit by pitch

CI = Catcher interference

5.3 = When I initially took the total innings pitched minus the innings batted there was an average discrepancy of 5 1/3 innings worth of outs not accounted for. These were cases when a runner was on base but was picked off the base pitcher, thrown out stretching a single to a double, etc.

Innings pitched minus innings batted were used to get the difference from one team to the next. The number show what I expected, teams with a winning record did not have as many innings batted compared to those that didn't win as often. For example the Cubs had 18 more innings pitched than batted while the Nationals hit in 31 more innings than they pitched.

After those calculations, the runs these innings would have created was calculated. The league average of 4.5 runs per games was used. Here is the formula:

Runs difference if extra inning played = Innings/9*4.5

The positive or negative runs were added to the team's total in runs scored for the season. The teams initial Pythagorean W-L record was calculated. Then the total number of games wons that the Pythagorean was off was added together. For the non adjusted values, it was off by a total of 103 games. Finally, I took the Pythagorean value using the new runs scored value, got the sum of the difference of the new Pythagorean wins and the actual number (98) and then compared the two sums. Here is the data:

 MLB W L RS RA W – Orig Py L – Orig Py Diff – Orig Py Washington 59 102 641 825 61 100 2 Seattle 61 101 671 811 66 96 5 San Diego 63 99 637 764 66 96 3 Pittsburgh 67 95 735 884 66 96 1 Baltimore 68 93 782 869 72 89 4 San Francisco 72 90 640 759 67 95 5 Atlanta 72 90 753 778 78 84 6 Cincinnati 74 88 704 800 71 91 3 Detroit 74 88 821 857 78 84 4 Colorado 74 88 747 822 73 89 1 Oakland 75 86 646 690 75 86 0 Kansas City 75 87 691 781 71 91 4 Texas 79 83 901 967 75 87 4 Cleveland 81 81 805 761 86 76 5 Arizona 82 80 720 706 83 79 1 LA Dodgers 84 78 700 648 87 75 3 Florida 84 77 770 767 81 80 3 Toronto 86 76 714 610 94 68 8 Houston 86 75 712 743 77 84 9 St. Louis 86 76 779 725 87 75 1 Chicago Sox 88 74 810 729 90 72 2 Minnesota 88 74 829 744 90 72 2 NY Mets 89 73 799 715 90 72 1 NY Yankees 89 73 789 727 88 74 1 Milwaukee 90 72 750 689 88 74 2 Philadelphia 92 70 799 680 94 68 2 Boston 95 67 845 694 97 65 2 Tampa Bay 97 65 774 671 92 70 5 Chicago Cubs 97 64 855 671 100 61 3 LA Angels 100 62 765 697 89 73 11 Original Difference 103

 MLB Innings Pitched – Innings Batted Additional runs New RS W – Py Adjust L- Py Adjust Diff – Py Adjust Team change Washington -31 -15.5 626 59 102 0 2 Seattle -23 -11.5 660 64 98 3 2 San Diego -13 -6.5 631 66 96 3 0 Pittsburgh -13 -6.5 729 66 96 1 0 Baltimore -5 -2.5 780 72 89 4 0 San Francisco -12 -6 634 67 95 5 0 Atlanta -8 -4 749 78 84 6 0 Cincinnati -11 -5.5 699 70 92 4 -1 Detroit -3 -1.5 820 77 85 3 1 Colorado -8 -4 743 73 89 1 0 Oakland -8 -4 642 75 86 0 0 Kansas City 1 0.5 692 71 91 4 0 Texas 0 0 901 75 87 4 0 Cleveland -2 -1 804 85 77 4 1 Arizona 9 4.5 725 83 79 1 0 LA Dodgers 3 1.5 702 87 75 3 0 Florida 0 0 770 81 80 3 0 Toronto 8 4 718 94 68 8 0 Houston 2 1 713 77 84 9 0 St. Louis 10 5 784 87 75 1 0 Chicago Sox 9 4.5 815 90 72 2 0 Minnesota 5 2.5 832 90 72 2 0 NY Mets 2 1 800 90 72 1 0 NY Yankees 8 4 793 88 74 1 0 Milwaukee 5 2.5 753 88 74 2 0 Philadelphia 6 3 802 94 68 2 0 Boston 17 8.5 854 98 64 3 -1 Tampa Bay 18 9 783 93 69 4 1 Chicago Cubs 18 9 864 100 61 3 0 LA Angels 15 7.5 773 89 73 11 0 Adjusted Difference 98
The difference is 5 games, not a lot of games, but does bring a better understanding of the difference in records a little more in focus. The lost half inning, along with my explanation on Blowout and 1 runs games, help to explain the difference in Pythagorean records.