Pascal’s Wager as Applied to Brandon Beachy

Back in the seventeenth century, French philosopher-mathematician Blaise Pascal contributed to the foundations of calculus, probability theory, physics, the scientific method, and the mullet. He also left a lot of stray papers an stray ideas around after he died, one of which has become known as Pascal’s Wager. His idea, which is the first recorded modern example of game theory, can be paraphrased as follows:

Suppose there are two states, there being a god and there not being one. Also suppose that you have two choices: believe in Him or don’t. You have to choose. There are four possible results.

  • You believe in God, and he exists: eternity in heaven, worth infinite points.
  • You believe in God, and he doesn’t exist: you waste time praying. Worth a small, finite number of negative points.
  • You don’t believe in God, and he doesn’t exist: you get a few extra hours each week to watch football. Worth a small, finite number of positive points.
  • You don’t believe in God, and he does exist: brimstone.
  • Having laid all these out, Pascal’s premise is pretty simple: negative infinity is pretty lame, and positive infinity is pretty good, so you may as well choose the side that leans toward the positive side, whether it turns out right or not. Thus, God.

    Pascal’s Wager has had its critics over the years, but it still stands as a solid theory for pragmatism – given the choices beyond your control, do what works best – as well as a rousing endorsement for drafting Brandon Beachy in your head-to-head fantasy league this year.

    Considering the depth of starting pitching, there are a surprising number of quality starters who will spend a good chunk of the early part of the season on the disabled list. Beyond Beachy, there’s Cory Luebke, Michael Pineda, Daniel Hudson, and Colby Lewis, all at least above-average pitchers when healthy, all due to miss enough time to fall on draft boards. Weathering April is fine, but having to waste a roster spot for ten weeks on a starter can be intimidating.

    Pascal says otherwise. His posthumous argument: the purpose of playing fantasy baseball is to win your championship. And when it comes to head-to-head leagues, games played in September are much more important than games played in April. Thus, you should draft as if you believe your team will be in the championship, whether it will be or not, and field the best team for the big weeks at the end.

    Of course, there are considerations; the existence of DL slots will make Beachy and his comrades more expensive, while a shallow bench will make them costlier. But especially in keeper leagues, picking an injured player is a good idea, because they have a strong probability of earning value over the season. You pay the discount price, wait out your time, and as the player gets closer to their return date and regular productivity, they become more valuable to you and as a trade piece. Even if you find yourself in last place come July, there should be teams in the stretch run willing to provide you some future value for the chance to win now. And even if they don’t, there are plenty of keeper formats where guys like Beachy, Luebke and Pineda are going to help your team in 2014.

    Drafting injured pitchers is always going to involve some risk, especially with Pineda. Shoulder injuries are scary things. But to win fantasy baseball, you’re going to need to take some risk. And as Pascal would wager, you may as well take the risk that maximizes your chance of fielding the best team in September, whether you need to or not.




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    Patrick Dubuque writes for NotGraphs and The Hardball Times, and he served as former Bill Spaceman Lee Visiting Professor for Baseball Exploration at Pitchers & Poets. Follow him on Twitter @euqubud.

    22 Responses to “Pascal’s Wager as Applied to Brandon Beachy”

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    1. SteveL says:

      Tho not as valuable, in deeper leagues consider Felipe Paulino and Danny Duffy as well.

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    2. Ryan B says:

      Couldn’t a similar argument be applied for guys like Billingsley (pitching, but likely to be injured)? Again, especially in keeper leagues.

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      • You could, especially if there’s a discount because the injury is assumed on draft day. But the problem with Billingsley’s ilk is that we don’t know when they’ll be hurt – and thus don’t know if they’ll be back for the stretch run. There’s value, but more risk.

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        • Blue says:

          But surely it is more likely that a player who is injured NOW will be a higher injury risk in the future than a player who has an injury history but is healthy at the moment?

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      • Dave Silvy says:

        Except Billingsley is not good

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    3. David Wiers says:

      I’m a big fan of both Beachy and Luebke this year. Thanks for letting the cat out the of bag, jerk.

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      • Joe says:

        What kind of a league would you be playing in where people DON’T know about Beachy and Luebke?! If they read FanGraphs, chances are they know a thing or two… and if they didn’t know about them until reading this, then you shouldn’t have too much to worry about from them. PS I realize you were likely joking around… just sayin :)

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    4. Larry says:

      It’s one thing to get a DL stashie after the draft or with a late pick but if you have to draft the guy at a spot you can get a healthy guy with upside why take the risk? Pineda in a keeper league, fine. But luebke, no thanks. Think of all the owners who drafted victor Martinez with a decent rd pick last yr thinking they’d have a top cheap catcher this yr. that didn’t work out. I’m not so sure Beachy is worth anything but a last rd pick.

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    5. kdm628496 says:

      “the existence of DL slots will make Beachy and his comrades more expensive, while a shallow bench will make them costlier.”

      the use of ‘more expensive’ and ‘costlier’ as opposites hurt my head.

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    6. harpago17 says:

      Although I agree with the theory, particularly as it applies to Beachy, I do think that the author is downplaying the “risk” a bit much in this case.

      While I understand “draft as if you will be in the championship”, depending on how much Beachy costs an owner he could be the reason you AREN’T in the championship, if another player is passed over that would have had more value over the early course of the season.

      In this case I’d say that risk is pretty low, so drafting Beachy makes sense. And I guess that was really the point of the article….i just wish the “risk” side had been a little better defined. Still enjoyed the article.

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      • True. Obviously Beachy’s not a first-round pick, or even close to where you would have drafted him last year. And if I were a better analyst, I could tell you exactly which two pitchers I’d slot him between. But I’ve only done about five informal rankings, and they’ve all come out different, as will the sixth one. So instead, the moral: as always, trust your gut, and just make sure you don’t forget about him.

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      • Dave Silvy says:

        Ya, how many of the players that you draft between the 8-18th rounds do you end up dropping anyways? There’s always a few. I don’t think the risk is too high here.

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      • Blue says:

        Exactly. Let’s say you choose Beachy over a rising star like Cobb or a bounceback guy like Garcia and that pick hits.

        You’ve got to compare the potential value of the pick AND its alternatives.

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    7. Matt Bertelli says:

      One of the greatest intro’s into a fantasy baseball article. Big fan of game theory. Also pretty big fan of Beachy. I asked Jeff Sulivan in his chat yesterday to rate in order of the best DL stasher among Beachy, Lewis, Leubke, and Pineda.

      I believe he said: Lewis, Beachy, Luebke, Pineda.

      I think it is close between Beachy and Lewis but I would favor Beachy.

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    8. dacure says:

      I 100% endorse this strategy. Mid season last year I was sitting in a nice position and made moves to acquire Evan Longoria, Joey Votto, and Giancarlo Stanton massively discounted due to injury. It was a struggle remaining in the playoff race, but when they got healthy it was a fairly easy post season en route to a championship. The risk paid off and I plan to manage the same way this season.

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      • Wade8813 says:

        It seems example might illustrate the potential dangers of “too much of a good thing.” Even if every single injury-reduced player you bid for produces as expected when they come back, if you trade away too much, you might end up with a team that would have won the championship but lost the regular season.

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      • fredricks says:

        I initially thought the same thing, but I have since learned otherwise. Last year I was way out in first place in my H2H league by the ASB, so that I was pretty much guaranteed to make the playoffs. I started making moves on injured players and acquired Votto, Longoria, Bautista, Ortiz, Ellsbury, Tulowitzki. Of those players, only Longoria ended up being better than what I gave up – despite me getting all the players at huge discounts. I lost my championship due to Bautista, Ortiz, and Tulowitzki never coming back, while Votto and Ellsbury were only average and below average respectively.

        Granted, if the discount is big enough and the payout is big enough you still go for it – like I drafted Ortiz this year and that payed off big. But for somebody like Beachy I think it’s better to have the extra bench spot to work with unless your benches are really deep. By being an active manager you could have picked up guys that are as good as Beachy on the waiver wire. A good manager doesn’t win his league through the draft – they win it through in-season managing. And plugging up a bench spot for half the season is a good way to make your team worse off.

        I drafted Chris Carpenter and held onto him for half a season last year. Didn’t help too much. We don’t even have any idea how Beachy will be when he comes back – so although it’s okay to think about grabbing him pretty soon now, it would have been a waste to draft him except in the deepest of leagues as a late round pick.

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    9. Blue says:

      The winning game for any of these injured players is not to acquire them–it is to acquire them at a cost that provides for surplus value.

      Here’s the problems with that:
      1) Calculating their expected value is tough. Any of us who have played fantasy sports for any length of time have a story of the player who was supposed to be back early in the season and ended up contributing very little over the course of the entire season;

      2) The likelihood that at least one of your other league partners will miscalculate that expected value on the high side.

      For the player to be worth drafting, your expected value calculation must be correct AND the rest of your league must have made an error in their assessment AND the effect all of those errors must be to underestimate the expected value of the player.

      It is FAR more likely, when you are considering drafting an injured player, that YOU are the sucker who is drafting him too soon!

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    10. pascha says:

      I’m applying this theory to Brian McCann. IMHO he is going extremely late/very cheap in drafts. Sure, shoulder injuries are scary, but he was a 5 WAR player in 2008 and 2010 and a 4 WAR player in 2006, 2009 and 2011.

      If he’s well, he could easily return those type of numbers in his age 29 season.

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