Haney's Handle: Odds of Josh Hamilton winning the Triple Crown
Some baseball fans have been proclaiming that the middle of May is way too early to be talking about any batter making a run for the MLB Triple Crown.
I could not disagree more, for a couple of reasons.
First, any news item that serves to reintroduce Ducky Medwick, Dick Allen and Dante Bichette into the public discourse is OK with me.
Those venerable names, usually heard only in trivia contests, have been ringing out in the wake of Josh Hamilton’s splendid season for the Texas Rangers.
Hamilton leads the American League in batting average, home runs and RBIs - all by a sizeable margin – generating speculation that he could become baseball’s first Triple Crown winner since Carl Yastrzemski in 1967.
That means we get to hear about Medwick, the last National Leaguer to win the Triple Crown (1937); Allen, who won two of the three categories in 1972; and Bichette, who came close in 1995.
Second, this kind of speculation – premature or not – dovetails nicely with sports oddsmaking.
A proposition posted on the betting board forces the chattering masses to put up or shut up, in the strictest, most literal sense of that expression. When a sports book hangs a Triple Crown prop with an opportunity to bet either the “yes” side or the “no” side, assuming a fair and equitable amount of “juice,” or vigorish, it serves as the ultimate argument settler.
Have an opinion? Big deal, so does everyone else. Back it up with cash. You can take a pass, which means you implicitly agree with the line on the board. That’s fine, too. At least it’s clear where you stand.
No sports book has posted odds on Hamilton winning the Triple Crown yet, but you can be sure bettors are busy creating their own odds.
My calculations, for example, give Hamilton approximately a 20 percent chance of winning the AL Triple Crown.
A no-vigorish line at that price would read -400 on “no,” Hamilton will not win the Triple Crown, and +400 that he will.
A line in a sports book would read something like -475 on the “no,” +325 on the “yes,” assuming a theoretical hold rate of 5.8 percent.
If I had the opportunity, I would gladly bet “yes,” Hamilton will win the Triple Crown, at a price of +500 or better today.
By the way, I would not bother wording the prop any differently, taking into account a long shot emerging as a Triple Crown contender. At this point, it’s all about Hamilton. I don’t think any other player has even a 1 percent chance of winning a Triple Crown this year.
I was surprised my projection came out as high as 20 percent, considering the magnitude of the achievement and the fact that it is indeed only May.
I won’t get into all the gritty details of how I arrived at that figure.
For one thing, my editor would probably board the next airplane to Las Vegas and personally punch me in the face if I tried to use the term “joint distribution of outcomes of two binomial distributions” in a sports column. He’d be well within his rights to do so.
Suffice it to say, though, a familiarity with the basic binomial distribution function in Excel can come in handy in estimating Triple Crown odds.
Let’s take a look at the AL home run race, which I see as the most hotly contested of the three Triple Crown categories.
My seat-of-the-pants projection has Hamilton playing in about 111 of the Rangers’ remaining 125 games, coming to the plate perhaps 480 more times and belting about 23 more home runs to finish with 41 homers. For what it’s worth, I also have Hamilton finishing with 121 RBIs and a .326 batting average.
There’s an element of subjectivity in estimating his, or any player’s, plate appearances-to-home run ratio the rest of the way. You don’t want to simply extrapolate his current numbers over 162 games, though. That would yield something like 80 homers and 200 RBIs. Not even Ducky Medwick could maintain that pace.
Next, estimate the odds of his rivals overtaking Hamilton in the three key categories. Hint: Excel is your friend. For example, I consider Curtis Granderson the biggest threat to Hamilton’s Triple Crown run, with about a 30 percent chance of beating Hamilton for the home run title.
Some final considerations:
- Hypothetically, if you give Hamilton a 50 percent chance of winning each Triple Crown category, don’t just multiply .5 * .5 * .5 and figure he has a 12.5 percent change of winning it. Home runs and RBIs are extremely correlated with each other, and both are somewhat correlated with batting average as well. They’re not independent outcomes.
- Much has been made of Hamilton’s propensity to spend time on the disabled list. Unless he’s channeling the ghost of Pistol Pete Reiser, I don’t consider Hamilton significantly more likely to get injured than Granderson, Adam Dunn or Edwin Encarnacion.
- Ties count as a win in the Triple Crown. Yaz shared the ’67 home run title with Harmon Killebrew.
- Betting lines are organic. Obviously, if someone like Miguel Cabrera goes off for five homers in two days while his competitors remain homerless, the odds could change substantially.