The actor penned a heartfelt letter addressed to Kendra and Alexa, the oldest two of Stabler's three daughters. Hanks' letter begins with him telling the women that the reason behind why people choose a certain athlete as their favorite is all but a mystery, describing it as "a personal attraction."
As the letter goes on, the Forrest Gump star explains what triggered his attraction to Stabler, describing how he would tune into the games on his "busted" kids TV, using pliers to change the channel.
"Your father with his left-handedness and those two bad knees, displayed a permanent smile of bemusement that said – win or lose – 'ain't this fun'?" Hanks wrote. "I really did see in him the honor to be found in playing the game, of using one's god given talent, of taking pleasure in the effort."
He continued, saying that Stabler, who hailed from Alabama and attended the University of Alabama but played for the Oakland Raiders, made him realize the different types of people found across the United States.
"That Ken Stabler came from the likes of Alabama yet played right there in my own home town helped me understand the variety found in the USA," he added. "I would tune in San Diego to see your Dad play, or Shea Stadium to see him take on the Jets – learning that if you were good enough you could do your thing anywhere you wanted."
The letter was a response to Kendra, the former quarterback's oldest daughter, sending Hanks some memorabilia from her father after his death from complications of colon cancer in July.
Hanks took to twitter after Stable died to pay tribute to his favorite player, writing, "Goodbye Kenny Stabler, QB for the Oakland Raiders, who showed how cool it was to be cool under pressure. Go deep, baby. Hanx'"
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In his current letter, thanking the family for his gifts, he says that he can don the "stablerwear" that they sent, saying that when anyone asks how he got where he is today, he gives them a little reference to the NFL player.
"I'm honored to wear the fine bit of Stablerwear you sent along and will continue to offer up to anyone who comes my way, and maybe ask how I ended up where I am, that you just have to throw deep, baby…," Hanks wrote.
Kendra shared the moment on Twitter, posting a photo of the letter along with a tweet reading; "It's not every day you get a letter from Tom Hanks. What a stud! So cool of him to reach out. #respect #throwdeep."