After two Senior Circuit blowouts, the St. Louis Cardinals and Los Angeles Dodgers are making the best case for an NLCS showdown. By defeating the Pittsburgh Pirates in Game 1, the Cards surpassed the idle Boston Red Sox for the lead in World Series victory probability. Meanwhile, Clayton Kershaw & Co. made the hometown Atlanta Braves look hapless at the plate.
With their victory, the Cardinals increased their championship probability by 6%; the Dodgers increased theirs by 3%. On the flip side, the Pirates saw their hopes dwindle from 8% to 4%, the Braves' from 9% to 5%.*
*Future posts will include a graphic demonstrating the shifting World Series championship probabilities.
Beyond the jump, I look at individual series and explain a bit more about my team rating and projection systems.
The opening-game loss may prove a death blow for the Pittsburgh Pirates. They now face 3:1 odds to beat the Cardinals (the Cardinals face similar odds... to win the World Series). The disparity in the estimated talent levels of the Cardinals and Bucs, the Game 1 result and home field advantage mean that the most likely single outcome is now a St. Louis sweep.
In the other ALDS, the most likely outcome is now a Dodgers win in four, followed by a Dodgers' sweep. Even so, the Braves loss wasn't nearly so devastating: Atlanta still has a 30% chance of winning the series. Unlike the Pirates, the Braves enjoy home field advantage. If the series makes its way back to Atlanta for a Game 5, the generic probability favors the Braves.*
*It's worth noting that the generic probability doesn't fully account for Clayton Kershaw starting twice in five games.
Since I'm working with my own rating system this fall, you and I can see how the individual game results affect estimated team talent levels. St. Louis moved up the #2 spot, while Pittsburgh sinks all the way down to #11. Three teams that are no longer playing now have a better rating than the Pirates.
As I noted in yesterday's post, two-thirds of the power rating is based on the Elo rating system. Elo ratings are most commonly associated with chess, but are also used in international football (soccer). Baseball nerds might recognize Elo ratings from Baseball Reference's crowdsourced player rater, while movie aficionados might remember it as the formula the fictional Mark Zuckerberg used to estimate physical attractiveness of the women in his dorm at the beginning of The Social Network.
Those who are familiar with the system will note that Elo ratings are typically expressed on a four digit scale, where 1000 is an average score, less than 1000 is a below-average score and, well, you get the idea. This is true, but Elo scores are easily converted into a power score between 0.000 and 1.000 using the formula P = 1 / (1+10^((1000 - E) / 400)) where E is the Elo rating and P is your estimated talent level (represented in the table above as eAVG).*
*The conversion breaks down at the extremes, but baseball teams never perform at such a high or low level for this flaw to effect eAVG of individual teams. This is true at such a small sample size that the numbers will be accurate well before May 1 of any given season. In baseball, there are no grandmasters.
Once you have the eAVG for two teams, you need only to plug it into the Log5 formula, adjust for home field advantage, and you'll have a generic probability of each team's victory in a single game match-up. Calculate those probabilities for every possible game and you end up with probability distributions for each series. If you want, you can take it a step further and convert the percentages to odds ratios, as I have below.
These are the odds predicted by the system before the games of October 3 as compared to the Vegas betting line. You'll note some key discrepancies. Vegas likes the Dodgers and the Tigers far more than my system does. In fact, it likes a lot of teams more than my system does.
In fact, it likes too many teams more than my system does.
If you convert the odds ratios of the Vegas lines to percentages, they add up to 118%. But how can the combined probabilities of all possible outcomes equal more than 100%? It's important to remember that Vegas lines are set to encourage bettors to put their money on less likely outcomes, ensuring that the bookmakers turn a profit in the long run. They're interested in profit margin, not mathematical purity.
If you scale the Vegas odds down so that they sum up to 100%, you'll note that they don't look so different from Rational Pastime's expectations. While Vegas is still more optimistic about the Dodgers than my system is (and last night's performance largely explains why), we reach very similar conclusions about the Red Sox, Rays, Cardinals, Braves and Pirates.
Stop by tomorrow to see how our teams are faring after the first full slate of playoff games in the 2013 MLB postseason.