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Mon Jun 02, 2008 12:26 pm EDT

No, Andruw will not hit .360-something after the break

By Andy Behrens

Earlier this season we mentioned "the gambler's fallacy", which is basically the notion that chance events* are influenced by prior results. They aren't. But there were a few dissenting opinions in the comments.

This is not just some fool idea we came up with, however. (We have lots of those, but the gambler's fallacy isn't one of them). Credible people have been writing about it for years.

Last week over at The Hardball Times, Derek Carty wrote an excellent piece discussing what he called "The myth of the 'law of averages'":

In fantasy baseball terms, let's say that David Ortiz is absolutely a true .300 hitter, that his batting average skill level is exactly .300, and that he has simply been unlucky so far this year. A person using the the law of averages may say that because Ortiz is a true .300 hitter and/or because he had him projected to hit .300 at the beginning of the year, his current .247 batting average is simply bad luck ... This person will then conclude that Ortiz should hit .318 over the final three-quarters of the season because, while he is only a .300 hitter, he has to hit that .318 to even out the bad luck early on. That way, he will finish at .300, his true skill level.

Even if Ortiz is truly an exact .300 hitter, it is ridiculous to think he'll hit better than that simply because he's had bad luck. Luck doesn't work this way.

The full piece deserves a read. You have to appreciate Derek's cut-throatedness, too, when he recommends that you use the flawed (but somehow totally believable) math of the law of averages in trade negotiations.

Independent events are...well, they're independent. If a true .300 hitter bats .250 over the first three months of the season, you should not expect him to magically become a .350 hitter from July through September, simply because the law of averages compels him.

You'd like to think that Jonathan Papelbon eventually got around to explaining the gambler's fallacy to Hideki Okajima during this animated tutorial:

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(* No, baseball is not exactly a chance event in the way that, say, a coin flip is a chance event. Still, you shouldn't underestimate the influence of randomness).

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109 Comments

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  1. a-mak15
    1. Posted by a-mak15 Thu Sep 03, 2009 2:51 pm EDT

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    If Howard is batting just over .200 at the end of May, I'm targeting him in every league. It's FUTURE at-bats which count*. And he's got a decent track record. Same w. Cano, for example. You buy-low to extract value. And it doesn't hurt that he's hit .343 in 07, .365 in 06 and .303 in 05 post-break.
    * Meaning that .208 AVG means nothing. When you get him, his value is the production he delivers at that point in time. Some people shy away from sluggers who aren't hitting their weight.
    Oh, and if Derrick R and birdie get this, msg me (amak2k1 or amak_15) and I'll send the invite pronto.
  2. Peter
    2. Posted by Peter Thu Sep 03, 2009 4:02 pm EDT

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    Hey Andy, can we see your fantasy profile? Do any of you experts plan on writing about strategy throughout a whole season to win a league? a-mak and I have been discussing over on Evans blog about you guys giving up your secrets.
  3. nycwiseman
    3. Posted by nycwiseman Thu Sep 03, 2009 7:42 pm EDT

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    Im banking on the law of averages, yeah im talkin to u vladdy and miguel carbrera
    Not Lance in my pants tho
  4. Mr. Pink
    4. Posted by Mr. Pink Thu Sep 03, 2009 8:12 pm EDT

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    really? Is this worthy of a post? I consider this common sense.
  5. Max Muscles
    5. Posted by Max Muscles Thu Sep 03, 2009 3:46 pm EDT

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    do you think we are playing with retards or something? i'd love to see you try the law of averages trick on some of the guys im playing with. thanks for the mathematical breakthrough
  6. QuinnArm
    6. Posted by QuinnArm Thu Sep 03, 2009 3:09 pm EDT

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    I believe that video is of papelbon teaching them how to play Craps
  7. man
    7. Posted by man Thu Sep 03, 2009 7:05 pm EDT

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    those are all probabilities. Ortiz might hit 318 for the rest or may not. it is all probability. i just had a question regardin to Ortiz"s 0.300 definition. if he is a life-time .300 hitter, .hitting 318 for the rest of this season might be less. he might hit .280 in 2008 and .320 in 2009. take into his age, all players getting older, his average will go down. the definition of .300 hitter may change year by year to .275 batting average. never know. anyway, Ortiz is still a good ball player and has a big name value. hard to trade him unless you are offerd a great deal. ps. Jacob D.... E-Gagne is uderpaid? he should be retired a few years ago. peace out all. hope your team is doing good in your fantasy league.
  8. zschaffran
    8. Posted by zschaffran Thu Sep 03, 2009 11:02 pm EDT

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    This is a ridiculous point to make... If I were to trade for Ortiz I don't care what his total #'s are at the end of the season, I care what they are from this point on. And I wouldn't expect him to finish the season at .300, but I'd expect him to .300 from today until the end of the season. I don't think there is a single fantasy baseball player in America who expects Andruw Jones to hit .360 the rest of the way. Write stuff worth reading please.
  9. John C
    9. Posted by John C Thu Sep 03, 2009 8:16 pm EDT

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    This article misses the point. The reason people like Ortiz, Cano, etc. are targeted in trades is because smart owners understand that players with a track record will generally play at that level. These owners aren't banking on a .300 hitter to hit .350 over the 2nd half of the season. Instead, they figure that the player will hit .300 but will only have to give up someone hitting in the .265-.270 range to get a deal done.
  10. Pisco
    10. Posted by Pisco Thu Sep 03, 2009 8:13 pm EDT

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    Take Nick Swisher . . . please!
  11. Big Daddy
    11. Posted by Big Daddy Thu Sep 03, 2009 4:51 pm EDT

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    I have been targeting Cano, Howard, Ortiz, Prince, and Vlad. I just picked up Cano off waivers, traded dan Uggla (who I picked up off waivers at the begining of April) for Vlad Guerrero. I look at it this way Uggla Hit .360 for me and gave me 1/2 the home runs he is gonna hit this year. His post all-star avg is .250 and he has never hit more than 31 Hrs. One league I got Howard for E. Volquez straight up and I have a pending trade for Prince, Saito and Cano giving up Cliff Lee (Let The Shelling Begin), Clayton Kershaw and Kaz Matsui. People are panicing and thats cool with me
  12. Christmas
    12. Posted by Christmas Thu Sep 03, 2009 10:14 pm EDT

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    That definitely looks like some sort of make shift craps table. I guess that is what Papelbon learned to do at Mississippi State. They don't call Starkville, MS StarkVegas for nothing.
  13. Lee Majors
    13. Posted by Lee Majors Thu Sep 03, 2009 2:44 pm EDT

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    #3, Here's a quick cut-and-paste...
    Overall Performance: 67% (64 eligible teams)
    Player Since: 2001
    Teams Managed: 67 League Commish: 10% (7 of 67 leagues)
    Played Most: Baseball
    22 trophies
    In recent years, I've mostly been involved in fairly competitive custom leagues. That obviously doesn't represent my full fantasy history, nor the years of off-line leagues.
  14. Normdude
    14. Posted by Normdude Thu Sep 03, 2009 7:17 pm EDT

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    I trade Sabbathia straight up for Ryan Howard 4 weeks ago. So far so good.
  15. Evan L
    15. Posted by Evan L Thu Sep 03, 2009 3:56 pm EDT

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    i agree with 9, 10, 11 here. if we want to look at ortiz, you cant expect him to hit .320 the rest of the year. the only thing you can and should expect from him is .300 for the rest of the year if he is a true .300 hitter regardless of what has already happened this season. it would give him about a .275 average. but last year he had a .332, and a .287 the year before that. it all averages out to a .300 hitter but that doesnt mean he can do it every year. there are a numerous players every year who underperform so i think this way of looking at players doesnt make sense. players also dont look to the past, they try and play well in the current season. anything can happen regardless of what has ever happened earlier in their career.
  16. parklife420
    16. Posted by parklife420 Thu Sep 03, 2009 7:59 pm EDT

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    The gambler's fallacy argument is based on events that are cut and dry mathematics. Even if a coin lands on heads ten times in a row, the eleventh time the chances are still fifty-fifty no matter how counter intuitive it may seem. Baseball, however, is a game filled with a virtually infinite amount of variables. If Ortiz made ten outs in a row, damn right I would bet on him to get a hit in that eleventh at bat. Even though the gambler's fallacy argument would state that Ortiz' chance of getting a hit would be the same probability as his other ten oh-fers, the years of his being a .300 hitter say that he is due. Being a .300 hitter over a long period of time is in large part skill, not luck.
  17. Knowname
    17. Posted by Knowname Thu Sep 03, 2009 4:58 pm EDT

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    but why is furcal pictured at the top?? and can he pls get off the dl?? my fantasy team depends on him lol basically. their both in first though, but both are waiting on furcal and it was alot easier to win with him.
  18. daniel g
    18. Posted by daniel g Thu Sep 03, 2009 3:35 pm EDT

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    I couldn't disagree more with that theory. If a proven player like Ortiz is slumping, you know he's going to pick it up. Then there are players who are not proven yet, but still somewhat predictable, like Nick Markakis, who is known for picking it up in the second half.
  19. slywolf666
    19. Posted by slywolf666 Thu Sep 03, 2009 9:28 pm EDT

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    It's not that stupid of an argument... the laws of probability do not AFFECT outcomes, they can only PREDICT. For instance, if you were to flip a coin 10 times, chances are of course very slight that you'd get heads 10 times in a row. But if you've flipped it 9 times and it's been heads every time, the original probabilty does not apply from the original event. The individual flip at the end is 50-50. The event that includes all 10 flips is MUCH lower than 50-50. Likewise, a hitter whose decided skill is .300 could play a whole season and not get a single hit, theoretically. But in his last at-bat of the season, even though the chances of him not getting a hit the entire season is astronomically unlikely, his chances of getting a hit in his last is still 30%. It's a clash of 2 perceptions: reality and probability.
  20. Max Muscles
    20. Posted by Max Muscles Thu Sep 03, 2009 3:46 pm EDT

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    hey behrens, what are the odds of heads coming up when i flip a coin?
  21. V
    21. Posted by V Thu Sep 03, 2009 9:24 pm EDT

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    Too bad I can't take advantage of my opponents' lack of stats knowledge... (private league, all players work in the same statistics related profession ;-)).
  22. Heynow
    22. Posted by Heynow Thu Sep 03, 2009 7:40 pm EDT

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    David Ortiz isn't going to pick it up. This is what happens when somebody plays half the season with a torn up knee and relies on pills and shots instead of rest. I hope the Red Sox think crippling their best player was worth another championship. Its going to be so funny when all the poor choices finally add up and the Sox are right back out of contention in a couple years. Where are all the fair-weather fans going to turn to: the Rays? HAHAHAA.
  23. Derrick R
    23. Posted by Derrick R Thu Sep 03, 2009 10:54 pm EDT

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    A-MAK! I'm still interested in the league. Those Id's you listed were yahoo email addresses? You can email me at yankeessuckas@yahoo.com if you did not get my email...
    Oh and I don't know why but I think Vlad is gonna be hottest 2nd half player this year. I'm targeting him heavily. Tejada gonna fade without the juice...
  24. kevin
    24. Posted by kevin Thu Sep 03, 2009 6:54 pm EDT

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    so what bout the reverse side of this...say lance berkman and utley for instance? should i assume that they will both come back to earth and average out to say last years stats? and if so, wouldnt i benifet from trading for someone like ortiz thats expected to do the opposite? im not, berkman is my keeper, but just asking...

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