MLB Triple Crown Race: Probabilities and Projections With One Month To Go
As the final month of the 2010 baseball season gets under way, the imaginations of baseball fans everywhere are alive with the possibility of a triple crown winner in the National League. With statistics and probability we can put hard projections to that amazing possibility.
Albert Pujols, Joey Votto and Carlos Gonzalez all have an opportunity to win the first National League triple crown since Joe Medwich of St. Louis did it 1937 (interesting note - three of the four NL Triple Crown winners since 1900 have played for St. Louis).
What this article will attempt to do is examine the probability of each player winning the triple crown. Using past performance as an indicator of future performance, we’ll examine what Pujols, Votto and Gonzalez have done in past Septembers and see if we can project what they will do this September.
We’ll also weight that historical data against their performances this season to give us a better estimate of where they’ll finish the season.
We begin with showing where each player stands on September 1st.
Albert Pujols 35 HR, 95 RBI, .316 AVG
Joey Votto 32 HR, 97 RBI, .327 AVG
Carlos Gonzalez 29 HR, 91 RBI, .326 AVG
After a slow start to the season, for Pujols standards, the great Albert has been on fire since the All-Star break. In the second half he has slammed 12 home runs, driven in 28 base runners and hit .342.
Pujols is first in HR, second in RBI and fourth in batting average.
Pujols is in the midst of his 10th major league season. As a result we have a lot of data showing how he has performed in the month of September.
Here are his last four years, all of them occurring since he and the Cardinals moved into new Busch Stadium.
2009: 30, games, 134 PA (17 walks), 6 HR, 25 RBI, .357 AVG
2008: 25 games, 103 PA (17 walks), 8 HR, 27 RBI, .321 AVG
2007: 28 games, 109 PA (18 walks), 2 HR, 19 RBI, .386 AVG
2006: 29 games, 129 PA (19 walks), 10 HR, 28 RBI, .373 AVG
The average is the most important because it’s the category Pujols has to make up the most in. He can certainly do it. In four of the last six seasons Pujols has hit over .350 in September. For his career he is a .343 hitter in the season’s final month. That’s 10 points higher than his career mark of .333.
Here are his total stats in September and October.
1055 PA 884 AB 51 HR 192 RBI .343 AVG
Now just because Pujols has performed at a certain level in the past doesn’t mean he’ll do the same this year. It’s important to consider how he’s been doing recently in 2010. Since he has 32 games left in 2010, we’ll look at this last 32 games played.
143 PA 129 AB 13 HR 26 RBI .364 BA
If we add in his recent performance with his average performance over the last nine years (giving a little bit more weight towards his recent performance), we get the following projections for the rest of the season:
7.5 HR(+/- 1) 24 RBI(+/- 2) .344 AVG
Which added to his totals as of September 1st, give him a final projection of:
43 HR, 119 RBI, .323 AVG
As indicated above there is a margin of error. However the projections should be 95 percent certain within the margin of error.
Votto has only been a full-time baseball player for his three years. In 2007 he was a September call-up for Cincinnati. He made his major league debut on September 4th of that year.
Here are his performances in September since 2007:
2009: 30 games, 126 PA (22 walks), 5 HR, 19 RBI, .385 AVG
2008: 25 games, 110 PA (15 walks), 9 HR, 20 RBI, .309 AVG
2007: 24 games, 89 PA (5 walks) 4 HR, 17 RBI, .360 AVG
For Votto we get totals of 325 plate appearances and 298 at-bats. This gives him an AB per HR of 15.6, an PA per RBI of 5.8 and an average of .340. If he can duplicate that line this year, he’ll win the batting title and have an excellent shot at the triple crown.
Votto and the Reds have 30 games left this year.
Based on his history, weighted with his recent performance, Votto is projected to hit seven or eight home runs, produce 24 to 26 RBI and hit around .345. I have weighted his 2009 and 2008 seasons more than his 2007 season in this calculation.
For Votto I have also factored in the increase in walk rate, which could reduce his home run and RBI potential, but help his batting average (as it did in 2009).
This gives him a final line of:
40 HR, 123 RBI, .333 AVG
Like Pujols, Votto’s projection is based on him starting all of the Reds remaining games. Also like Pujols, this is a safe assumption considering the Reds pursuit of a playoff spot. The only difference with Votto is that the Reds have a better chance of wrapping up a playoff spot with a few games remaining. If this happens, Votto might receive some days off before the playoffs.
Gonzalez is the hardest to predict. Since he only has one season in Colorado, and the National League, there is a large margin of error in estimating his performance over Colorado’s final 31 games.
Here is Gonzalez’s performance over the last month of the season (almost all of this was compiled in 2009):
136 PA 121 AB 5 HR 13 RBI .273 AVG
And more importantly his performance over his last 31 games of 2010:
135 PA 121 AB 12 HR 29 RBI .388 AVG
Gonzalez really wore down in September and October last year. Like this year he had been scorching hot in August (.317, 6 HR, 13 RBI).
To get an accurate projection for Gonzalez we’ll weight his performance this year more than his performance last year. This gives us a projection for September 2010 of:
8 HR (+/- 3), 19 RBI (+/- 7) and a .342 AVG
Gonzalez’s margin of error is huge because we have so little data to go on. If he sticks to the data in the middle he’ll finish with a line of:
37 HR, 110 RBI, .326 BA
Other Players to Consider
We have to give attention to Adam Dunn’s chances of leading the NL in home runs. Dunn is second in home runs with 33, that's two behind Pujols.
Here are Adam Dunn’s September homerun totals over the past six years:
2009: 27 games, 3 HR in 99 AB - Played for the Washington Nationals
2008: 26 games, 6 HR in 88 AB - Played for the Arizona Diamondbacks
2007: 20 games, 4 HR in 62 AB
2006: 28 games, 2 HR in 87 AB
2005: 30 games, 5 HR in 104 AB
2004: 31 games, 6 HR in 110 AB - Played for the Cincinnati Reds through 2007
That’s 26 home runs in 550 at-bats or about 21 at-bats per home run. The evidence suggests that Dunn fades as the season wanes. This probably explains why he has never lead the NL in home runs but has finished second twice and third once.
History suggests we can discard Dunn as a threat to overtake the home run lead by season’s end.
The Atlanta Braves have two hitters which could spoil the triple crown pursuit, Martin Prado and Omar Infante. Prado is hitting .317 and Infante is hitting .341.
Infante only has 370 plate appearances this year. He needs 502 to qualify for the batting title. Since being inserted into the Braves everyday staring lineup on July 29th, he has averaged 4.6 PA per game, most of them from the lead-off spot.
The Braves have 31 games left. If he starts everyone of them and maintains this pace, he’ll finish with around 512 PA.
It’s going to be close with Infante. He’ll have to play everyday and keep hitting. Infante is only a .275 career hitter, so how he’s doing it this year is a complicated mystery for another article. It’s hard to predict if he’ll keep it up and stay ahead of Votto and his projected final average of .333
Prado is a career .311 hitter with an career average of .276 in September. There’s little chance he wins the batting title, unless he significantly outperforms his past history.
Based on this projection system the final lines for these three players are:
Pujols 43 HR (+/- 1), 119 RBI (+/- 2), .323 AVG
Votto 40 HR (+/- 0.5) 123 RBI (+/- 1) , .333 AVG
Gonzalez 37 HR (+/- 3) , 110 RBI (+/- 7) , .326 AVG
Joey Votto has the best chance to win the NL triple crown. He has a 95 percent chance to win the batting title and the RBI title. He has a 22% chance to win the HR title.
Albert Pujols has a 68 percent chance to win the HR title, about a 40 percent chance to win the RBI title and only a 22.5 percent chance to win the batting crown.
Gonzalez's chances are lower than 34 percent in each category. His total chances of winning are about 0.5%. Albert Pujols has a 13 percent chance of winning the National League Triple Crown.
Remember that all of these are a projections based on past performances in the season’s final month and recent performances in 2010. Many other factors will come into play in September (injuries, home/road splits, lineup strength, days of rest or another hitter emerging in one of the three categories).
If the past and present hold true though, Joey Votto has an excellent chance to win the NL Triple Crown.
I’d put Votto's chances at about 18 percent as of September 1st.
For a look at the data and methodology used in this study click here.
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