Red Sox: Calculating the odds J.D. Martinez wins the triple crown
Batting Average
Now for the category that I had to put, by far, the most thought into. Mookie Betts currently leads baseball with a .338 batting average, followed by Altuve at .329, and then Martinez at .323.
What I ended up doing to estimate Martinez’s chances at a batting title is a good bit more complicated than above. Let’s start with the following tables. The categories monitored will be the league leaders in batting average in both leagues on July 31 and at the end of the season, the number of players who had batting averages within 10 points, 20 points, and 30 points of the league leader on July 31, and whether or not a player from that batting average group won the batting title.
| Year | League | League Leader 7/31 | League Leader (end of season) | # of players within 10 points | Winner from that group? | # of players 10-20 points below league leader | Winner between 10-20? | # of players 20-30 points below league leader | Winner? | Winner from group >30 points below league leader? |
| 2017 | NL | Justin Turner | Charlie Blackmon | 0 | No | 0 | No | 4 | Yes | No |
| 2016 | NL | Daniel Murphy | D.J. Lemahieu | 0 | No | 1 | No | 4 | Yes | No |
| 2015 | NL | Paul Goldschmidt | Dee Gordon | 0 | No | 3 | Yes | 2 | No | No |
| 2014 | NL | Troy Tulowitzki | Justin Morneau | 0 | No | 0 | No | 1 | Yes | No |
| 2013 | NL | Chris Johnson | Michael Cuddyer | 1 | Yes | 2 | No | 5 | No | No |
| 2012 | NL | Andrew McCutchen | Melky Cabrera | 0 | No | 1 | Yes | 2 | No | No |
| 2011 | NL | Jose Reyes | Jose Reyes | 0 | No | 1 | No | 6 | No | No |
| 2010 | NL | Joey Votto | Carlos Gonzalez | 1 | No | 6 | Yes | 4 | No | No |
| 2009 | NL | Hanley Ramirez | Hanley Ramirez | 0 | No | 3 | No | 6 | No | No |
| 2008 | NL | Chipper Jones | Chipper Jones | 0 | No | 1 | No | 2 | No | No |
| 2007 | NL | Hanley Ramirez | Matt Holliday | 5 | Yes | 4 | No | 2 | No | No |
| 2006 | NL | Freddy Sanchez | Freddy Sanchez | 0 | No | 5 | No | 9 | No | No |
| 2005 | NL | Derek Lee | Derek Lee | 1 | No | 1 | No | 0 | No | No |
| 2004 | NL | Barry Bonds | Barry Bonds | 0 | No | 0 | No | 5 | No | No |
| 2003 | NL | Albert Pujols | Albert Pujols | 0 | No | 0 | No | 1 | No | No |
| 2002 | NL | Larry Walker | Barry Bonds | 0 | No | 1 | Yes | 1 | No | No |
| Year | League | League Leader 7/31 | League Leader (end of season) | # of players within 10 points | winner from that group? | # of players 10-20 points below league leader | winner between 10-20? | # of players 20-30 points below league leader | winner? | winner from group >30 points below league leader? |
| 2017 | AL | Jose Altuve | Jose Altuve | 0 | No | 0 | No | 0 | No | No |
| 2016 | AL | Jose Altuve | Jose Altuve | 0 | No | 0 | No | 1 | No | No |
| 2015 | AL | Miguel Cabrera | Miguel Cabrera | 0 | No | 2 | No | 0 | No | No |
| 2014 | AL | Jose Altuve | Jose Altuve | 0 | No | 4 | No | 4 | No | No |
| 2013 | AL | Miguel Cabrera | Miguel Cabrera | 0 | No | 0 | No | 1 | No | No |
| 2012 | AL | Mike Trout | Miguel Cabrera | 0 | No | 1 | No | 2 | Yes | No |
| 2011 | AL | Adrian Gonzalez | Miguel Cabrera | 0 | No | 0 | No | 1 | No | Yes |
| 2010 | AL | Josh Hamilton | Josh Hamilton | 0 | No | 2 | No | 2 | No | No |
| 2009 | AL | Ichiro | Joe Mauer | 1 | Yes | 0 | No | 1 | No | No |
| 2008 | AL | Alex Rodriguez | Joe Mauer | 4 | No | 7 | Yes | 8 | No | No |
| 2007 | AL | Magglio Ordonez | Magglio Ordonez | 2 | No | 4 | No | 1 | No | No |
| 2006 | AL | Joe Mauer | Joe Mauer | 0 | No | 2 | No | 1 | No | No |
| 2005 | AL | Johnny Damon | Michael Young | 0 | No | 3 | Yes | 6 | No | No |
| 2004 | AL | Ivan Rodriguez | Ichiro | 1 | Yes | 2 | No | 6 | No | No |
| 2003 | AL | Ichiro | Bill Mueller | 0 | No | 7 | Yes | 5 | No | No |
| 2002 | AL | Mike Sweeney | Manny Ramirez | 1 | No | 0 | No | 1 | No | Yes |
So, now to do some thinking. Let’s start by looking at how often the league leader on July 31 won the batting title. This happened 18 out of 32 times. So we will say the league leader will win about 56.25% of the time.
Now let’s talk about the group of players within 10 points of the league leader on July 31. It turns out that this category was non-empty only nine times. This year, Jose Altuve is in that category so it makes sense to see how often a player in that category wins the title. In four of those seasons, one player from that group led the league in hitting, but sometimes there was more than one player in that group. If we add up all the players who trailed in batting average by 10 points or less on July 31 of a given season and divide by the nine non-empty buckets, we find that, on average, the size of this group when not empty was about 1.89.
What does that mean? Well, the league leader emerged from this group four seasons out of a possible nine. However, we must divide by the average size of the group to approximate the odds a single player from this group has at the batting title. Therefore, a player within ten points of the crown on July 31 has approximately a 23.5% chance at the title.
Doing this exact same operation for each of the groups above we find the results below.
| Avg # of players within 10 points of league leader | Percent winner emerged from group | Percent chance of individual | Avg # of players 10-20 points below league leader | Percent winner emerged from group | Percent chance of individual | Avg # of players 20-30 points below league leader | Percent winner emerged from group | Percent chance of individual | Avg # of field (rest of league) | Percent winner emerged from group | Percent chance of individual |
| 1.89 | 44.4% | 23.5% | 2.86 | 31.8% | 11.1% | 3.24 | 13.8% | 4.3% | N/A | 6.3% | ~0 |
Just for a sanity check, let’s make sure these percentages sum to somewhere close to 100. There is only one individual within ten points of the league leader (Altuve), one player ten to twenty points below the league leader (Martinez), and three players twenty to thirty points off the pace for the title.
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Multiplying the individual odds by the number of players in each group (except for the field which will just get the flat 6.3% contribution) we get the following odds each group produces the league leader:
League leader: 56.3%
<10 points off the pace: 23.5%
10-20 points off the pace: 11.1%
20-30 points off the pace: 12.9%
Field: 6.3%
So that sums to about 110% which is close enough to 100%. So using that back of the envelope style of math we can conclude that Martinez has about an 11.1% of winning the batting title.