Red Sox: Calculating the odds J.D. Martinez wins the triple crown

RBIs

Let’s start with the easiest one to place: RBIs.

This one is easiest to predict only because Martinez has a solid lead over the rest of the league in this category. Martinez’s 89 RBIs top his closest competitor’s total, Khris Davis‘ 84 ribbies, by five.

So here’s what we are going to do. We are going to look at the AL and NL RBI leader on July 31 each year since 2002 (FanGraphs splits leaderboards only goes back that far). We will take note of the margin the player is leading his league by and whether or not he won the RBI crown. To avoid opening a can of worms we will throw out all years that involved a tie at the top of the leaderboards at the trade deadline.

So of the 28 data points not invalidated by ties, the league leader in RBIs finished first 15 times. Further, if we want a closer picture to our current leaderboard we can consider only seasons when a player led his league by five or more RBIs (again, Martinez currently leads by five). In these cases, the league leader at the trade deadline went on to win six out of twelve times.

We could go in further depth, but the numbers seem to be pointing to about an even split for Martinez.

Odds of leading the league in RBIs: ~50%

Home Runs

This one is more complicated only because Martinez is tied at the top of the American League with Jose Ramirez at 32 dingers a piece. So we will use the same methodology as above, ignoring the fact that Ramirez exists, and then divide the resulting odds by two to account for the Indian’s slugger.

In 16 of the 28 non-void data points, the league leader in homers on July 31 went on to lead his respective league in home runs. We could be more cynical and look at years where the league leader was above his closest competitor by three homers or less (Martinez and Ramirez sit three homers above Mike Trout). In these cases, the player went on to lead his league in homers nine times out of twenty (again, throwing away voided data points).

Going with that number, there is at least a 45% chance Ramirez or Martinez will lead the league in round-trippers. Cutting that in half, we get a 22.5% chance Martinez leads the AL in homers.

Odds of leading the league in home runs: ~22.5%

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.

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.

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.

Triple Crown Odds

To put these all together we simply multiply the percentages to calculate the odds of Martinez leading the league in each category.

.50 x .225 x .111 = .0124875

So we have found the lower bound for J.D. Martinez’s triple crown odds to be approximately 1.25%.

That’s not particularly likely of course, but stranger things have happened and this is still just a lower bound. When adjusting for the lack of independence of these categories my gut tells me it’s closer to 3-5% (which is not, by any means, a scientific estimate).

But if there’s any conclusion from this piece it’s that winning the triple crown is really, really hard no matter how great of a season you’re having and everything has to break just right. Let’s hope it does.