June 13, 2003  

Midseason Report Card Part 1: Pythagorean Baseball

Once again, it's time to apply the Pythagorean Theorem and see who was lucky and who was good over the first half of the '03 season.

Remember, in baseball, the Pythagorean Theorem -- initially developed by Bill James -- is a method of determining what a team's record "should" be, based on how many runs they score and how many runs they allow. Some teams will win more games than their run differential would suggest because of hustle, clutch performers, managerial genius or just dumb luck.

The simplest way of determining a team's Pythagorean Winning Percentage is by adding the runs for, squared, and then dividing it by runs against, squared, plus runs for, squared: RF^2/(RA^2+RF^2).

 ExpectedActual 
2001RFRADiffPCTWLPCTWL+/-
ARK476350+1650.64955300.6355431-1
NWK507378+1290.64353290.6715527+2
STP435395+ 400.54847380.5885035+3
PHI318310 +80.51341390.4753842-3
VAN357351 +60.50842400.5244339+1
HON406400 +60.50743410.5244440+1
HIL356355 +10.50140390.4683742-3
BRK373395 -220.47138420.5134139+3
HBK397433 -360.45738450.4703944+1
CAR307341 -340.44836440.4753842+2
COL326368 -420.44037460.4223548-2
HAR335378 -430.44037470.4173549-2
PHX370417 -470.44035450.4503644+1
TIJ357449 -920.38731500.3582952-2

According to the Pythagorean Theorem, the luckiest team over the first half of the season was the Brooklyn Bean Counters, a team that can appreciate statistical analysis. But this time the numbers don't add up for the Beanies, who are three wins better than they "should" be. If a calculator determined the standings, Brooklyn would flip from a sixth-place team, two games above .500, to an eighth- place team, four games under .500 -- the biggest drop of any team. Another Hanover squad, the Stanhope Mighty Men, also have overachieved by three wins, but it wouldn't matter: Their adjusted record would make them the third-best team in baseball, which is how they finished the first half anyway.

Pythagoras also tells us that the DMBL's best team, the Newark Sugar Bears, aren't as quite good as their gaudy record. The numbers say the Bears' have lucked into two extra wins, which would drop them from the league's best record back to where they spent almost the entire first half, as the No. 2 seed. The Carolina Mudcats also are in reality two wins better than the Pythagorean suggests, which would drop them from a seventh-place tie into ninth. The Vancouver Iron Fist, Honolulu Sharks, Hoboken Cutters and Columbia Rattlesnakes are all one win ahead of the formula.

The unluckiest teams over the first half should both be above .500 and right in the thick of the playoff hunt, according to the formula. The Philadelphia Endzone Animals, four games under .500 and in a tie for seventh place, should have expected three extra wins based on their run differential. Those three wins would have propelled them into fourth place overall, two games above .500. An equally big jump would go to the 10th-place Hillsborough Destroyers, who also were three wins better than their 37-42 record, according to the theorem. The numbers say the Destroyers could just as easily be one game above .500 and sitting in seventh place, a half-game out of a playoff berth. Three other teams that were two wins worse than expected -- the Phoenix Dragons, Harrison Rats and Tijuana Banditos -- wouldn't have seen a significant change in the standings anyway. Finally, the Arkansas Golden Falcons are just one win worse than their league-best +165 run-differential would predict -- but that one win, coupled with Newark's -2 win adjustment, would have left them with the best record in baseball after the first half, albeit by just a half-game.

One Is Enough

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 Theorem winning percentage -- that is, a team that has a Pythagorean winning percentage of .600 should win about 60 percent of its one-run games. Of course, it doesn't always work that way, because of luck, strategy, timely hitting or magic pixie dust.

The Sugar Bears have the best record in one-run games (14-6, .700), followed by the Mighty Men (13-7, .650) and Bean Counters (12-8, .600). The worst teams are Tijuana (7-14, .333), Hillsborough (8-13, .381) and Harrison (10-14, .417). Three of the league's best teams at the top of the list; three of the league's worst teams at the bottom. But it is a little surprising to see the 11th-place Rattlesnakes posting the fourth-best record (.538), or the 2nd-place Golden Falcons posting the five-worst (.455) in one-run contests.

So which team has been the luckiest in one-run games? That would be the Bean Counters, who "should" have gone 9-11, not 12-8, in one-run games. That three-game swing would drop them below .500. The Mighty Men and Rattlesnakes are each about two wins better than expected in close contests.

As if they needed a break, the Golden Falcons have been the unluckiest team when it comes to winning one-run games; their 10-12 record should be more like 14-8, according to the formula. The Destroyers and Endzone Animals are also "owed" about two wins.

Interestingly enough, both formulas agree that the Bean Counters and Mighty Men were two of the luckiest teams over the first half, while the Destroyers and Endzone Animals were the two unluckiest. Will the numbers even out over the second half, or is it a sign that the Mighty Men or the Bean Counters are a team of destiny this season? One thing is certain: It will be a great second-half of DMBL Baseball!

Be sure to tune in next time for Part 2 of the series as we take a look at run-differentials, home-road splits and team vs. team match-ups!

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.