June 17, 2004  

In-season Report Card: The First Half

Once again, it's time to break out the slide rules and do some sabermetric number crunching on the league standings and take a look at the league's under- and over-achievers over the first 80-some games of the 2004 season.

Pythagorean Baseball

The Pythagorean Theorem isn't just for triangles. Initially developed by Bill James, it can be used to determine what a team's record "should" be, based on how many runs they score and how many runs they allow. Over the course of a few thousand games, a team's won-loss record will almost always correspond to its Pythagorean Winning Percentage, which is determined by the square of a team's runs for divided by the square of a team's runs against plus the square of runs for: RF^2/(RA^2+RF^2).

However, the smaller sample size of just 80 or so games played means most teams will perform a couple games better or worse than their Pythagorean Winning Percentage. Old-school baseball watchers say the difference between the expected and actual winning percentages can be explained by intangibles like team chemistry, clutch hitting or plain ol' hustle. But the sabermetricians chalk the difference up to luck -- which usually evens out over the course of a long season. In theory, a team that is one or two wins ahead of its Pythagorean Performance over the first quarter can expect to give those games back sometime before the end of the year; the same goes for teams that are "owed" wins.

Pythagorean Performance				Expected			Actual
2004	RF	RA	Diff	PCT	W	L	PCT	W	L	+/-
Arkansas	469	361	+108	0.628	50	30	0.638	51	29	+1
Stanhope	495	390	+105	0.617	50	31	0.593	48	33	- 2
Newark	489	391	+ 98	0.610	50	32	0.634	52	30	+2
Carolina	415	350	+ 65	0.584	47	34	0.617	50	31	+3
Columbia	375	351	+ 24	0.533	45	39	0.548	46	38	+1
Vancouver	423	401	+ 22	0.527	43	39	0.524	43	39	0
Philly	435	427	+  8	0.509	41	40	0.469	38	43	- 3
Tijuana	402	408	-  6	0.493	40	42	0.488	40	42	0
Honolulu	321	365	- 44	0.436	35	46	0.469	38	43	+3
Phoenix	421	472	- 51	0.443	36	46	0.439	36	46	0
Westwood	320	373	- 53	0.424	34	47	0.383	31	50	- 3
Harrison	389	467	- 78	0.410	34	49	0.422	35	48	+1
Hillsboro	362	459	- 97	0.383	31	50	0.370	30	51	-1
Hoboken	335	436	-101	0.371	32	53	0.412	35	50	+3

According to the theorem, the unluckiest teams over the first quarter were the Philadelphia Endzone Animals and the Westwood Deductions, who are both three wins worse than their run differential suggests they should be. It wouldn't make much of a difference for the Ducks, who finished the first-half with the second-to-worst record in baseball: if they'd played up to their run differential, they'd instead have the fourth-worst. But if Philly had three more wins, they'd be 1 game over .500 and just 1½ games out of the sixth and final playoff berth. The Endzone Animals also were one of the unluckiest teams over the first quarter of the season, playing about two games worse than their differential, so they are certainly owed a couple lucky breaks over the second half. The Stanhope Mighty Men, who finished the first half with the third-best record in baseball, also had some bad luck: Their second-best +105 run differential suggests a 50-31 record, two games better than their actual performance. If the Mites did have two more wins, they'd be sitting atop the Hanover Division and just a half-game out of 1st place overall. The only other team to finish worse than its theorem projection were the last-place Hillsborough Destroyers, who "should" be a game better than their 30-51 record. Even with an extra win, however, they'd still have the worst record in baseball.

Three teams played better than theorem expected. We hate to kick 'em while they're down, but the Hoboken Cutters, who had the league's third-worst record, "should" be even worse. Their league-worst -101 run differential suggests a 32-53 record, three wins less than what they actually have, which would tie them with Hillsborough for the DMBL's worst record. (And, if we credit Hillsborough with the win the theorem says they're owed, the Cutters are actually in dead last.) Another first-half overachiever were the Carolina Mudcats, who finished the first half in 3rd place overall at 50-31, just 1½ games out of the league's best record. But the Mudcats' +65 run differential predicts a 47-34 record, which would drop them into 4th place, 3 games out of 1st place. The Honolulu Sharks were also three games better than their run-differential; without those three wins, they'd drop from an 8th place tie into 10th place. The Newark Sugar Bears, tied for the league's best record at 52-30, are two games ahead of the theorem; a little less luck and they'd be a game back for the league's top mark. (And if Stanhope's record also matched the theorem, Newark would be a half-game behind them in the Hanover Division, instead of 3½ games ahead.) The Arkansas Golden Falcons,  Columbia Rattlesnakes and Harrison Rats were all one win better than the theorem predicted, but it wouldn't have much of an effect on the standings.

Three teams played right where the formula said they would: The Phoenix Dragons, the Tijuana Banditos and the Vancouver Ironfist.

One Is the Loneliest Number

Don't like looking to the ancient Greeks for baseball analysis? No problem! Another way to look at a team's performance is how they do in one-run games. In addition to his pioneering work in applying the Pythagorean Theorem to predicting a team's winning percentage, Bill James also has another theory that a team's winning percentage in one-run games should roughly correspond to its Pythagorean Winning Percentage -- a team that has a Pythagorean winning percentage of .600 should win about 60 percent of its one-run games. But, of course, it doesn't always work that way. The difference between a team's expected and actual one-run records could be explained by managerial tactics, clutch hitting, tough pitching, a deeper bench or bullpen, a blown call by an umpire... or just dumb luck.

We looked at how many one-run games each team had been in over the first quarter, then multiplied those games by the team's Pythagorean Winning Percentage to come up with the team's expected performance in one-run games. Then we compared it to their actual performance in those contests. Because a team can't get half a win, we rounded the results to the closest whole number.

1-Run Games	Expected			Actual
2004	W	L	Pct.	W	L	Pct.	+/-
Hoboken	8	13	0.371	13	8	0.619	+5
Carolina	14	10	0.584	14	10	0.583	0
Columbia	16	15	0.533	18	13	0.581	+2
Honolulu	10	13	0.436	13	10	0.565	+3
Phoenix	8	10	0.443	10	8	0.556	+2
Newark	13	9	0.610	12	10	0.545	-1
Stanhope	8	5	0.617	7	6	0.538	-1
Tijuana	11	11	0.493	11	11	0.500	0
Harrison	7	9	0.410	8	8	0.500	+1
Arkansas	11	6	0.628	8	9	0.471	-3
Vancouver	9	8	0.527	8	9	0.471	-1
Hillsboro	8	13	0.383	8	13	0.381	0
Westwood	10	13	0.424	8	15	0.348	-2
Philly	11	11	0.509	7	15	0.318	-4

Once again, the Hoboken Cutters rank as one of the league's luckiest teams. The Cutters have the DMBL's third-worst record, but they have the league's best record in one-run games -- 13-8 (.619). That's a whopping five games better than predicted! The Honolulu Sharks are three games better, the Columbia Rattlesnakes and Phoenix Dragons are two games better, and the Harrison Rats are one game better than the numbers suggest.

Just as the Cutters were "luckiest" for both Pythagorean Theorem and One-Run Game analysis, the Philadelphia Endzone Animals get the fuzzy end of the lollipop on both counts. The Animals "should" be right around .500 when it comes to one-run games, but in actuality they're a woeful 7-15 -- the worst record in baseball. That's four games worse than the numbers suggest. The Arkansas Golden Falcons are right behind them, three games worse than their one-run record should be; the Westwood Deductions are two games worse; and the Newark Sugar Bears, Stanhope Mighty Men and Vancouver Ironfist are one win worse.

The Carolina Mudcats, Hillsborough Destroyers and Tijuana Banditos are in line with their predicted performance in one-run games.

So What Does It Mean?

Looking at Pythagorean Winning Percentage and One-Run Winning Percentage from the first-quarter, we can make some predictions about how the rest of the season will go, assuming luck evens out over the course of 162 games.

The unluckiest team over the first quarter: The Philadelphia Endzone Animals, who are seven games worse than the numbers predict. Other underachievers: Westwood Deductions (-5), Stanhope Mighty Men (-3), Arkansas Golden Falcons (-2), Hillsborough Destroyers (-1) and Vancouver Ironfist (-1).

The luckiest team were the Hoboken Cutters, who were five games better in the One-Run Formula and three games up according to the Pythagorean Theorem. That's a whopping eight-game swing, which would drop them to 27-58 (.318 W%), which would be  the worst record in baseball by a wide margin. The Honolulu Sharks were almost as lucky, playing six games ahead of what the numbers suggest; the Carolina Mudcats (+3), Columbia Rattlesnakes (+3), Phoenix Dragons (+2), Harrison Rats (+2) and Newark Sugar Bears (+1) also have been playing over their heads, in theory, over the first half.

Breaking even: The only team to be where the numbers say they should be are the Tijuana Banditos. Interestingly enough, the Banditos were a perfect "0" -- dead on with estimates from both the Pythagorean Winning Percentage and One-Run Winning Percentage formulas -- for both the first quarter and the first half of the season.

Cecil Fielder was the first selection in the DMBL's inaugural draft in 1991. Since then he's enjoyed a solid career as a member of seven DMBL teams. He is now retired and serves as the color man for the Columbia Rattlesnakes radio team. Click Here for past articles.