The baseball postseason is the most exciting time to be a fan of our great national pastime. Every pitch and every swing of the bat can potentially bring glory or ruin to an entire team of hard working ballplayers, to say nothing of the cardiac damage done to the hearts of the millions of fans that live or die with their every base knock, or with their every out. Tension and drama envelopes all, and as a consequence of the emotions running high, we must deal with the inevitable bouts of hyperbole.

While the Indians and Red Sox engaged themselves in an oddly anti-dramatic battle to see which team could pile up the most blowout wins in a ten day period, the hyperbole came forth faster than a highly viscous fluid in a cylindrical pipe flowing under high Reynolds Number conditions. According to these shrill hyperbolists, the venerable Sawks began the series as the clear class of the league, beating up on a naive young Indians squad that looked confused and overwhelmed by Big Game Beckett and his loyal mates. A few days later, even their most spirited fans had turned against them, all but congratulating the Indians on a series well-played and bemoaned the unquantifiable lack of “spirit” entrenched in the 2007 Red Sox in comparison to the 2004 version. And yet, only a few days later, once this same Boston club had soundly vanquished their opponents, they were once again toasted as the class of the league, in possession of an unflappable will to win. Unfortunately, unlike the aforementioned fluid dynamics model of critical turbulent flow in pipes, it is not possible to design a rigorous model to explain the source of such fantastical hyperbole. Its explanation will therefore go unsolved for yet another postseason.

The same cannot be said for the recent on-field performance of the Colorado Rockies. Their spectacular hot streak has seen them win 21 of 22 games, vaulting themselves from an afterthought in the NL Wild Card race to the cusp of scaling the mountain and being crowned world baseball champions. Their streak has been described as “astounding”, “improbable”, and “historic”, so far beyond the realm of rational comprehension that it practically defies physics. This is where I, dear reader, must step in. Outcomes in baseball are governed by nothing more than gravity and Newton’s Laws of Motion. Nothing, not even Jessica Alba’s breasts, can defy gravity (the proof is left as an exercise for the reader … hint: Serway’s elementary text “Physics for Scientists and Engineers”, plus a wisely worded GIS should suffice as reference material). It is certain that the Colorado Rockies, thin air or not, cannot defy physics either.

Let us begin with a simple, intuitive model. Consider a game between two baseball teams X and Y. If they are perfectly evenly matched in terms of talent and ability, then the chances of victory for either club is 50%. We can trivially state that

lim n->inf., P_{v} ^{X} (n/2) = P_{v} ^{Y} (n/2) = 0.5.       (1)

For the more linguistically inclined, this means that if X and Y play each other many, many, many, many, many, many, many, many, many, many, many, many, many, many times in a row, then chances are that each club wins half of the games. However, what are the chances that X beats Y in 21 out of 22 games? The chances of winning two straight games is (0.5)^2 = 0.25, and the chances of winning three straight games is (0.5)^3 = 0.125, etc. The chances of winning 21 of 22 games is in the neighborhood of (0.5)^21 = 4.77E(-7), so if X represents the Rockies and Y represents their opponents, then the chances of reeling off such a streak, P(S), are 1 in 2 097 000.

This is obviously absurd. Einstein famously stated that God does not play dice, and while the Rockies may be playing like Gods, and play in a stadium that is situated closer to God than the stadia of other baseball clubs, they are most certainly not gods. The chances of Matt Holliday and company making good on a one in two million dice roll is even less than the chances that I will win the grand prize on a future season of “Dancing With the Stars”, that is to say, the chances of this happening are virtually zero.

Therefore, this simple, but illogical model needs refining. The Rockies enjoyed a sizable home field advantage this year. They played .622 ball at Coors Field, but just .481 on the road. We can approximate 0.481 ~ 0.500 with less than 4% uncertainty, but the Rockies deserve credit for their greater win probability in their home field. Taking half of their games to be home games during the streak, we recalculate

P(S) = (0.5)^10 * (0.622)^11 = 5.26E(-6),       (2)

or a 1 in 190 000 chance. This is still no better than the chances of turning on your TV and seeing me performing the tango with laser-like precision, but it is an improvement over the previous calculation.

But fear not, physics enthusiasts, for there is more! According to the Denver-area humidor equation, we have

B = [E^(2)]*R,       (3)

where B is the correction factor, R, is the height of Coors field above sea level, and E is the relative mass index of the humidor baseballs compared to non-humidor ones. Stated as such, B represents an extra win probability factor for the Rockies due to their familiarity (relative to the rest of the National League) in hitting the specially treated baseballs in their home park, as well as the the regular baseball in other parks. Taking care to use the Czochralski system of units in the calculations, we obtain B = 1.55, and thus, via substitution of Equation (3) into Equation (2), we find

P(S) = (0.5)^10 * (0.622)^11 * B^21 = 0.052.       (4)

Then there is the matter of the Arizona Diamondbacks, who are, simply put, a poor approximation for an evenly matched team Y in the model. This is a team that was outscored by its opponents this season. Their best hitter is cannot prevent himself from performing somersaults on throws to home plate, and their second-best hitter is a pitcher. A Rockies sweep was all but assured from the outset. We may neglect the season-ending series between the two, but it is reasonable to assign the Rockies a unity probability of winning the NLCS games. This removes two home games and two road games from the equation for P(S), and replaces them with a win probability ~ 1. Finally, amending Equation (4) gives us

P(S) = (0.5)^8 * (0.622)^9 * B^21 *(1)^4 = 0.54.       (5)

This final result in Equation (5) conclusively demonstrates that the chances of the Rockies winning 21 of 22 games were actually fairly reasonable, around 54%. Their run was not improbable at all, but was in fact quite probable. Once again, the scientific method has directed us toward the underlying physics behind the problem, and has shown us how to filter out the crap spewed at us by the sports media, beer-chugging lunatics at your local pub, and Tim McCarver. As for the World Series, I will refrain from making predictions. I prefer not to ponder my equations during the next week and will enjoy the games just like the common fan would. Please continue rooting for your favorite team, be they the Red Sox or the Rockies, and for goodness sake please join me, your humble professor, in rooting for the still-sultry Jane Seymour on season five of “Dancing With the Stars”. Homina homina!