Dom Brown’s Monte Hall Paradox – Phillies Nation

Dom Brown’s Monte Hall Paradox

As regular readers of Phillies Nation may have deduced, I am an avid fan of professional wrestling. While I attempt to limit my references to hide my fandom, every once-in-a-while, it rears its ugly head. In addition to baseball, and pro wrestling, I am also an avid game show enthusiast. I have spent more hours than I care to admit watching Richard Dawson’s Family Feud and analyzing Michael Larson‘s record breaking 1984 Press Your Luck win. One of my favorite game shows of all time, however, is Let’s Make a Deal.

Baseball is viewed in a lot of ways; one of the ways the game is interpreted is as a game of chance and probability positively or negatively impacted by the skill of those who are playing it. In this regard, Let’s Make a Deal does not appear to be very close to baseball; it appears to be solely a game of chance. Contestant is selected, is given a few choices, and either wins big or gets zonked. But in my opinion, Let’s Make a Deal and baseball can be summed up in the same way. Particularly in the case of the Monte Hall Paradox and the number of pitches seen.

The Monte Hall Paradox has been explored by many mathematicians, scientists, and even Mythbusters. It goes like this: A contestant is offered a choice of three doors. Host Monte Hall, or now Wayne Brady, removes one of the choices that does not have the grand prize, leaving the prize between the contestant’s original choice and a new door. The host offers the contestant the opportunity to switch. Since their were three original choices, the contestant, in theory, has the same odds of wining the grand prize if he or she maintains his first selection or if they choose the other option, correct? Wrong. And in a way, Domonic Brown, sporting a career low strike-out rate of 9.2% in 76 PA since being called up, is caught in his own Monte Hall paradox and, in some cases, defying it.

Why the Monte Hall problem is a paradox is simple: the instinctive answer is that the choice when there is two items is an even 50/50 split, the same odds assigned to either. But in Monte Hall’s problem, this is not true: because you are given the choice of switching your door, by switching your door, you now have 2 to 3 odds of winning the grand prize because you now have both the new door and the removed door. The answer is not immediately apparent but has been proved by mathematician after mathematician and becomes clearly when expanding the sample size.

domonic brown catching a flyballBrown’s paradox isn’t as cut and dry and, like the Monte Hall paradox, may not even seem like it is a problem. However, Brown is doing something relatively difficult and is due for some sort of change, either positive or negative, according to historic trends. At 3.96 pitches seen per plate appearance, Brown has shown high-level plate discipline since being called up. If Brown had enough plate appearances to qualify for the batting title, he would be tied for 21st in most pitches seen per plate appearance. Yet, the other 20 batters in front of Brown read like a “Who’s Who” of most-likely to strike out. In fact, of those 20, eight also appear in the list of players whose K-rates are in the top 30, with 4 of the top 5 K-raters appearing on both lists.

This is nothing new to baseball. As Bill James explains, seeing more pitches is both a blessing and a curse for hitters, meaning both more walks and strikeouts, and is usually accompanied by power. Those 4 of the top 5 for K-rate who find themselves in the top 20 for pitches seen (Adam Dunn, Chris DavisCarlos Pena, and Curtis Granderson) also rank highly among the MLB leaders in isolated power (Dunn ranks highest at 6th in the MLB). Despite seeing 3.96 pitches per at-bat, Brown is not striking out as much as anticipated, particularly when factoring in his 18.5% career rate.

So what does this mean? The sample is still incredibly small but the lowered strike-out rate, which for arguments sake, would rank 6th in the MLB if Brown had enough PA to qualify for the batting title, is promising. It is incredibly unlikely Brown maintains this pace throughout the end of the season but the number of pitches Brown is seeing suggests the improvement in discipline is real. For the hitters in the top 20 of most pitches seen per PA, the entire top 11 also appears in the top 30 of the BB% rate. Brown’s MLB career BB% rate of 10.7% has been solid, and at 10.5% this year, would put him firmly at 27th in the MLB in walk rate, above likely-MVP Andrew McCutchen and on-base aficionado Alex Gordon.

So where is the paradox? Brown has hit for almost no power this year, unlike most who occupy both lists, defying both the lists and Bill James’ assertions. His .060 ISO would rank third-worst in the MLB, above only Ben Revere and Jamey Carroll. Caroll, who ranks 13th in pitches seen per plate appearance, is only one of six players in MLB who walks greater than 10% of the time and strikes out less than 15% of the time. Despite this feat, Carroll’s career ISO of .067 limits him, in his twilight, to a ceiling of around 1.8-2.0 fWAR a year. Thus Brown’s paradox is this: does Brown modify his approach to become more aggressive, in an attempt to hit for more power or does Brown keep on keeping on and continue to make productive outs and continue to walk?

Thus, Brown’s three doors are something like this:

1.) GRAND PRIZE: Walks remain high, strikeouts low, power develops

2.) Parting Gift: Plate discipline is good, Brown has doubles power

3.) ZONK!: Brown attempts to adjust his swing again, walks go down, Ks up, and no power develops.

The answer? Brown may have turned the corner and may be entering the beginning stages of accepting the Grand Prize. Brown’s approach will lead him to see many more pitches, and nearly by default, a higher number of pitches seen means the selection of pitches, in a normal sample, should improve. Instead of Monte Hall or Wayne Brady offering Brown the opportunity to switch his selection, Brown has the opportunity to walk away with both the grand prize and the runner-up prize, all while avoiding the Zonk.

If you should end up on Let’s Make a Deal, however, you probably will not be so lucky. Unless, you want a YUGO full of goats, always switch once the empty door is taken away.

Click to comment


  1. TheDipsy

    August 20, 2012 at 3:23 pm

    Couldn’t read it all. But I’m liking Dom Brown a little (dropped ball notwithstanding).

    The Dipsy

    • Ian Riccaboni

      August 20, 2012 at 4:11 pm

      Executive summary:

      If Dom Brown had enough PAs to qualify for the batting title, he’d be one of seven players to have >15% BBs and <10% Ks. The other six are Jamey Carroll, Joe Mauer, Mark Texeira, Ben Zobrist, David Ortiz, and Prince Fielder, all quality players.

      Paradox lies in whether or not his solid plate discipline peripherals are real and they will help him develop power (Door 1), if it will level out (Door 2), or if the Phillies will have him try to adjust his swing/approach again and he'll get Zonked (Door 3).

      In the Monte Hall paradox, it's believed you have equal odds once one choice is removed and you're offered to switch. In this, Brown has likely eliminated the Zonk and the question is whether he wins the grand prize or becomes a good, but not great, player.

  2. Cory

    August 20, 2012 at 4:04 pm

    Domonic has hit nearly as many doubles this year as his best year in 2010, in 100 less at bats. He has seemed to develop a line drive/gapper swing mindset. He is still young, and I believe he has 30/30 potential a la Granderson, but defensively, not even close.

    I believe Domonic will stick around for a while and will be an above average player, but whether he becomes a star remains to be seen.

    • Ryan H.

      August 20, 2012 at 4:18 pm

      dom’s got speed. there’s no reason why his defense can’t become and asset. they used to say the same thing about chase utley. defense is all about how much you want to improve. if he’s willing to take the time to get good mechanics, he can be a top notch outfielder.

  3. Ken Bland

    August 20, 2012 at 4:05 pm

    Monty Hall did a fine job. He wasn’t any Richard Dawson on Da Feud, but I go back to the days of before television when “To Tell the Truth (Bill Cullen?) was the best game in town.

    And that show went something like this….

    Guest number 1, what is your name please?

    My name is Domonic Brown, and I’m an outfielder in the Philadelphia Phillies farm system. For about 4 years now, I have led the trasactions list with record frequent flier miles since the day that George Steinbrenner had a thing for the Columbus shuffle. Give me time, and I will find my niche.

    Thank you, Guest number 1, guest number 2, what is your name please.

    My name is Domonic Brown, and I’m an outfielder in the Philadelphia Phillies system. For about 4 years now, I have been a highly scrutinized talent, based on being the most untouchable trade commodity since Santa Claus tried to trade Rudolph for Peter Pan. Pete could fly, so Santa figured he’d save time on his 24 hour crunch day.

    Thank you, Guest number 2, and Guest number 3, what is your name, please.

    My name is Domonic Brown, and I am an outfielder in the Philadelphia Phillies system. Everyone has a twin in this world, and although we’re years apart, most people think I am more of an original Darryl Strawberry than that particular Strawman his damned self. People expected me to hit 500 homers in the majors before I saw my first minor league pitch. I just try to relax about the pressure without crossing the Jimmy Loafline to realize my talent and ask peaople’s patience.

    Time to fins the real Domonic Brown, our questioning begins with Tom Posten.

    • Ian Riccaboni

      August 20, 2012 at 4:12 pm

      I like it, Ken! I’m guessing he’ll land somewhere between your guest 1 and guest 3. Any chance of a series of standing dekes to fool the audience?

  4. Ryan H.

    August 20, 2012 at 4:17 pm

    dom brown does not have a big enough sample size to accurately say he is defying anything. we need to see him play every day for at least a year (and uninterrupted by injuries) before we can draw conclusions.

  5. Jeff Dowder

    August 20, 2012 at 4:55 pm

    I hope Brown becomes a valuable player, but I always wonder how he was ever labeled as a “5 tool player”. Isn’t defense one of those “tools”?

  6. Jaron B

    August 20, 2012 at 5:11 pm

    Too long… I had to skip to the end. I would like to know what’s gonna become of his defense… what do you think, Ian?

  7. Bob in Bucks

    August 20, 2012 at 5:20 pm

    Ian -Small sample size means DO NOT ANALYZE!

    • George

      August 20, 2012 at 7:31 pm

      Your comment and the one above by Ryan H are the only sensible responses. Analyzing Brown at this point in the season is like flipping a coin twice, and when it comes up “heads” both times, believing that it will always come up “heads.”

  8. TheDipsy

    August 20, 2012 at 6:14 pm

    Does anybody realize that this team is in danger of not having one player draw 50 walks this year. I wonder if thats ever happened before. Its pathetic.

    The Dipsy

    • Ryne Duren

      August 20, 2012 at 11:25 pm

      i do believe dipsey j-bag will eclipse way more walks than are on the stat sheet! number 1 there’s the regular recorded walk. then number two you hit the ball to an infielder on the ground and you walk to first! or you hit a pop up to any designated infielder and gently walk towards first! see dipsey hell probably amass about 150- 175 of the three combined.

      • schmenkman

        August 20, 2012 at 11:30 pm

        While that is hee-larious, Rollins already has 42 and will likely end up in the low-to-mid 50s.

  9. Lefty

    August 20, 2012 at 7:10 pm

    Charlie Manuel found a goat behind every door when looking for a relief pitcher this season.

    Creative posting Ian, thanks.

  10. JohnMatrix

    August 20, 2012 at 11:20 pm

    Just becaus you have a friend who has a website and can post whatever you want, doesnt mean you should

  11. Ryne Duren

    August 20, 2012 at 11:20 pm

    good fun article ian! and so was your comment ken! kudos to both of ya. after the game i was watching comcast post game show and m barkan reported that phillipe aumont was called up from LHV to the phils. yayyyyy. he said he’ll be replacing j. horst who’s out on maternity leave.
    i never knew men can have babies! does this mean horst will be out for three months? lol

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