September 15, 2010
Checking the Numbers
Say Goodbye to the Triple Crown
Over the last two weeks I have utilized a neat simulation I built in order to assess the likelihood that a Triple Crown occurs this year. Simulations are the best way to make such a determination, as the three stats involved—batting average, home runs, and RBI—are intertwined. They might not always be connected, but it is more accurate to operate under this assumption than it is to multiply together the probabilities that a player leads the league in each category. When I ran through the rest of the season 10,000 times back on September 1, the feat was only achieved 777 times even though Albert Pujols and Joey Votto ranked either first or second in all three categories. Pujols won the Triple Crown in a whopping 663 of those 777 seasons, suggesting that the feat was unlikely to be achieved, but that Prince Albert was the heavy favorite.
Now, the rate that the Triple Crown occurred was going to be lower than it may have seemed because even though Votto and Pujols led in the categories, the simulation considered it very likely that someone would win one category while the other player took the remaining two. Another reason laid in the hands of Omar Infante, who didn’t have enough plate appearances to show up on the batting average leaderboard but had such a big lead that he was likely to win the batting title even with phantom at-bats added to his seasonal total. Overall, it was exceedingly likely that Infante would win the batting title while Pujols and Votto split the homer and RBI crowns.
Between September 1-7, much had changed across the statistical spectrum. Carlos Gonzalez, who was a dark-horse candidate at the beginning of the month, put up monster numbers and emerged as the most likely player to achieve the Triple Crown. His numbers were so good, in fact, that he legitimately overtook Infante in the batting average department. Of the 10,000 simulations, a Triple Crown occurred 503 times, with CarGo winning all three legs in 338 of those seasons. His 3.38 percent was over twice the rate that Votto won (1.57 percent), and Pujols’s 0.08 percent was but an afterthought. A week later, everything has once again changed. The first table below shows the statistics and rankings as of September 7, while the second shows updated numbers through September 13:
And a mere six days later:
So what has changed? Well, Pujols went on a home-run rampage, upping his total to 39 and retaking the RBI lead. Ryan Howard has gone on an RBI spree, coming within four of the league-leading Pujols even though he had a stint on the disabled list in August. Troy Tulowitzki came from out of nowhere to the third spot on the batting leaderboard, though it will definitely be difficult to make up 14-18 points with so few games remaining on the schedule. Put together, the three categories are no longer shared as much as they were over the last two weeks. Pujols could win the home run and RBI titles, but he is over 30 points behind the batting average leader. Gonzalez could win the batting average and RBI titles, but is he really going to out-homer Pujols down the stretch? Votto is close in all three categories, but he has significant ground to cover in the BA and HR departments.
Because of everything that has transpired over the six days between my last update and this one, the Triple Crown is now a very far-fetched idea. In 10,000 simulations, it was only achieved 46 times in total, marking by far the lowest rate of occurrence since I started using the tool. Of those 46 times, Gonzalez overtook Pujols in home runs while winning the other two legs in 24 seasons; Votto led in all three on 20 occasions; and Pujols achieved the feat twice. The non-CarGo seasons saw him absolutely crater down the stretch, while Votto or Pujols looked as hot as he did as the beginning of the month. Essentially, the simulation views Gonzalez as equally likely to have a supreme power burst down the stretch as it does Votto to start accumulating hits while CarGo slumps. Regardless of its views, 46 out of 10,000 are not good odds at all, leaving me convinced that the feat will not be achieved this year.
Then again, Gonzalez was a dark-horse candidate who, in 12 days, became the ultimate contender, so I will still monitor the results. It just seems, however, that the odds the Triple Crown occurs this season are about as low as the Dodgers or Marlins making the playoffs.