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

BOSTON, MA - MAY 02: J.D. Martinez #28 of the Boston Red Sox celebrates after hitting a two-run home run during the fourth inning against the Kansas City Royals at Fenway Park on May 2, 2018 in Boston, Massachusetts. (Photo by Tim Bradbury/Getty Images)
BOSTON, MA - MAY 02: J.D. Martinez #28 of the Boston Red Sox celebrates after hitting a two-run home run during the fourth inning against the Kansas City Royals at Fenway Park on May 2, 2018 in Boston, Massachusetts. (Photo by Tim Bradbury/Getty Images)
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BOSTON, MA – MAY 02: J.D. Martinez #28 of the Boston Red Sox celebrates after hitting a two-run home run during the fourth inning against the Kansas City Royals at Fenway Park on May 2, 2018 in Boston, Massachusetts. (Photo by Tim Bradbury/Getty Images)
BOSTON, MA – MAY 02: J.D. Martinez #28 of the Boston Red Sox celebrates after hitting a two-run home run during the fourth inning against the Kansas City Royals at Fenway Park on May 2, 2018 in Boston, Massachusetts. (Photo by Tim Bradbury/Getty Images) /

J.D. Martinez has been phenomenal for the Boston Red Sox, leading the league in homers and RBIs. Does he have a legit shot at the triple crown?

Boston Red Sox slugger J.D. Martinez has been one of the best hitters in baseball in 2018. He’s slashed .323/.391/.638 with 32 home runs and 89 RBI.

Martinez is leading the American League in both homers and RBIs. Considering that Martinez is also in third place in the AL in batting average, one begins to wonder if the triple crown award is in play.

Only Miguel Cabrera has won a triple crown award since Carl Yastrzemski achieved that honor while leading the “Impossible Dream” Red Sox to the 1967 World Series. In the rest of this post, I am going to try to calculate the odds that Martinez ends 2018 with a triple crown of his own.

So here is the way we are going to do this: I am going to try to calculate the odds Martinez wins each of these three categories and then multiply the probabilities. Because leading the league in these three categories are not independent events (every home run Martinez hits, for example, lifts all three boats) this methodology will yield a lower bound on his triple crown odds. We know that leading the league in home runs and RBIs are tied especially close together so the actual probability will be somewhat higher than our final mark, but a conservative estimate here should prove enlightening.

BOSTON, MA – APRIL 14: J.D. Martinez #28 of the Boston Red Sox hits a solo home run in the third inning of a game against the Baltimore Orioles at Fenway Park on April 14, 2018 in Boston, Massachusetts. (Photo by Adam Glanzman/Getty Images)
BOSTON, MA – APRIL 14: J.D. Martinez #28 of the Boston Red Sox hits a solo home run in the third inning of a game against the Baltimore Orioles at Fenway Park on April 14, 2018 in Boston, Massachusetts. (Photo by Adam Glanzman/Getty Images) /

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.

YearLeagueLeader on 7/31MarginDid he win?LeagueLeader on 7/31MarginDid he win?
2017ALNelson Cruz3YesNLNolan Arenado10No
2016ALEdwin Encarnacion4YesNLTieTieVoid
2015ALKendrys Morales1NoNLNolan Arenado1Yes
2014ALJose Abreu2NoNLGiancarlo Stanton2No
2013ALTieTieVoidNLPaul Goldschmidt4Yes
2012ALTieTieVoidNLCarlos Beltran1No
2011ALAdrian Gonzalez10NoNLMatt Kemp1Yes
2010ALMiguel Cabrera4YesNLRyan Howard7No
2009ALJustin Morneau5NoNLAlbert Pujols3No
2008ALJosh Hamilton17YesNLRyan Howard7Yes
2007ALAlex Rodriguez14YesNLTieTieVoid
2006ALDavid Ortiz8YesNLCarlos Beltran1No
2005ALManny Ramirez5NoNLCarlos Lee1No
2004ALMiguel Tejada1YesNLScott Rolen7No
2003ALCarlos Delgado12YesNLPreston Wilson4Yes
2002ALAlex Rodriguez3YesNLLance Berkman8Yes

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%

BOSTON, MA – APRIL 11: J.D. Martinez #28 of the Boston Red Sox hits a grand slam during the fifth inning against the New York Yankees at Fenway Park on April 11, 2018 in Boston, Massachusetts. (Photo by Maddie Meyer/Getty Images)
BOSTON, MA – APRIL 11: J.D. Martinez #28 of the Boston Red Sox hits a grand slam during the fifth inning against the New York Yankees at Fenway Park on April 11, 2018 in Boston, Massachusetts. (Photo by Maddie Meyer/Getty Images) /

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.

YearLeagueLeader on 7/31MarginDid he win?LeagueLeader on 7/31MarginDid he win?
2017ALAaron Judge3YesNLGiancarlo Stanton5Yes
2016ALMark Trumbo1YesNLTrevor Story1No
2015ALMike Trout1NoNLNolan Arenado2Yes
2014ALJose Abreu2NoNLAnthony Rizzo1No
2013ALChris Davis6YesNLPedro Alvarez1Yes
2012ALAdam Dunn2NoNLRyan Bruan5Yes
2011ALJose Bautista2YesNLLance Berkman1No
2010ALJose Bautista6YesNLJoey Votto3No
2009ALTieTieVoidNLAlbert Pujols6Yes
2008ALCarlos Quentin2NoNLAdam Dunn2No
2007ALAlex Rodriguez7YesNLPrince Fielder1Yes
2006ALDavid Ortiz2YesNLRyan Howard2Yes
2005ALTieTieVoidNLTieTieVoid
2004ALTieTieVoidNLJim Thome2No
2003ALCarlos Delgado1NoNLBarry Bonds4No
2002ALAlex Rodriguez4YesNLSammy Sosa1Yes

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%

ST. PETERSBURG, FL – APRIL 1: J.D. Martinez #28 of the Boston Red Sox hits an RBI single in front of catcher Wilson Ramos #40 of the Tampa Bay Rays to score Mookie Betts during the fifth inning of a game on April 1, 2018 at Tropicana Field in St. Petersburg, Florida. (Photo by Brian Blanco/Getty Images)
ST. PETERSBURG, FL – APRIL 1: J.D. Martinez #28 of the Boston Red Sox hits an RBI single in front of catcher Wilson Ramos #40 of the Tampa Bay Rays to score Mookie Betts during the fifth inning of a game on April 1, 2018 at Tropicana Field in St. Petersburg, Florida. (Photo by Brian Blanco/Getty Images) /

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.

YearLeagueLeague Leader 7/31League Leader (end of season)# of players within 10 pointsWinner from that group?# of players 10-20 points below league leaderWinner between 10-20?# of players 20-30 points below league leaderWinner?Winner from group >30 points below league leader?
2017NLJustin TurnerCharlie Blackmon0No0No4YesNo
2016NLDaniel MurphyD.J. Lemahieu0No1No4YesNo
2015NLPaul GoldschmidtDee Gordon0No3Yes2NoNo
2014NLTroy TulowitzkiJustin Morneau0No0No1YesNo
2013NLChris JohnsonMichael Cuddyer1Yes2No5NoNo
2012NLAndrew McCutchenMelky Cabrera0No1Yes2NoNo
2011NLJose ReyesJose Reyes0No1No6NoNo
2010NLJoey VottoCarlos Gonzalez1No6Yes4NoNo
2009NLHanley RamirezHanley Ramirez0No3No6NoNo
2008NLChipper JonesChipper Jones0No1No2NoNo
2007NLHanley RamirezMatt Holliday5Yes4No2NoNo
2006NLFreddy SanchezFreddy Sanchez0No5No9NoNo
2005NLDerek LeeDerek Lee1No1No0NoNo
2004NLBarry BondsBarry Bonds0No0No5NoNo
2003NLAlbert PujolsAlbert Pujols0No0No1NoNo
2002NLLarry WalkerBarry Bonds0No1Yes1NoNo
YearLeagueLeague Leader 7/31League Leader (end of season)# of players within 10 pointswinner from that group?# of players 10-20 points below league leaderwinner between 10-20?# of players 20-30 points below league leaderwinner?winner from group >30 points below league leader?
2017ALJose AltuveJose Altuve0No0No0NoNo
2016ALJose AltuveJose Altuve0No0No1NoNo
2015ALMiguel CabreraMiguel Cabrera0No2No0NoNo
2014ALJose AltuveJose Altuve0No4No4NoNo
2013ALMiguel CabreraMiguel Cabrera0No0No1NoNo
2012ALMike TroutMiguel Cabrera0No1No2YesNo
2011ALAdrian GonzalezMiguel Cabrera0No0No1NoYes
2010ALJosh HamiltonJosh Hamilton0No2No2NoNo
2009ALIchiroJoe Mauer1Yes0No1NoNo
2008ALAlex RodriguezJoe Mauer4No7Yes8NoNo
2007ALMagglio OrdonezMagglio Ordonez2No4No1NoNo
2006ALJoe MauerJoe Mauer0No2No1NoNo
2005ALJohnny DamonMichael Young0No3Yes6NoNo
2004ALIvan RodriguezIchiro1Yes2No6NoNo
2003ALIchiroBill Mueller0No7Yes5NoNo
2002ALMike SweeneyManny Ramirez1No0No1NoYes

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 leaderPercent winner emerged from groupPercent chance of individualAvg # of players 10-20 points below league leaderPercent winner emerged from groupPercent chance of individualAvg # of players 20-30 points below league leaderPercent winner emerged from groupPercent chance of individualAvg # of field (rest of league)Percent winner emerged from groupPercent chance of individual
1.8944.4%23.5%2.8631.8%11.1%3.2413.8%4.3%N/A6.3%~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.

BOSTON, MA – JUNE 27: J.D. Martinez #28 hugs Brock Holt #12 of the Boston Red Sox after hitting a three-run home run in the second inning of a game against the Los Angeles Angels at Fenway Park on June 27, 2018 in Boston, Massachusetts. (Photo by Adam Glanzman/Getty Images)
BOSTON, MA – JUNE 27: J.D. Martinez #28 hugs Brock Holt #12 of the Boston Red Sox after hitting a three-run home run in the second inning of a game against the Los Angeles Angels at Fenway Park on June 27, 2018 in Boston, Massachusetts. (Photo by Adam Glanzman/Getty Images) /

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).

Next. MLB trade deadline recap. dark

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.

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