So I’m fairly lame and really love reading about brain teasers, paradoxes, and space. One of the more popular brain teasers, the Monty Hall problem, is one I found really interesting when I first read about it in college. I also think it’s really useful – not only with DFS but all areas of your life – to try to combine ideas and think about things through different lenses. Call it “idea sex” (credit to James Altucher on that) or whatever you prefer – the point is to constantly make yourself reevaluate the way you approach a problem. You never know what inspiration you may find that could lead to huge revelations.
Anyway, the Monty Hall problem goes like this:
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
The answer is one that is pretty counterintuitive – you increase your odds by one-third just by switching to a different door. When it was first debated, tons of people screamed that switching doesn’t do anything for the contestant – if you had a one-third chance of picking the car, why would switching affect that? Or even further, once you’re down to two doors, isn’t it just a 50-50 chance of picking the car?
However, mathematicians have shown that your odds increase from one-thirds to two-thirds if you switch after the host reveals one door with a goat. And the reason that is true despite the apparent mathematical paradox is this: the host always knew where the car was.
British mathematician Keith Devlin explains it in a nice way: “By opening his door, Monty is saying to the contestant, ‘There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I’ll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.'”
Or probably my favorite way of visualizing the problem is to think of it with 1,000 doors instead of just three. If you picked door No. 478 and then the host proceeded to open every single door – all containing goats – except for No. 478 and No. 211 and asked you if you wanted to switch, well, it seems pretty intuitive at that point, right? The odds you picked the car with your first guess (1 in 1,000) are now much smaller than switching doors.
The DFS application of this fun brain teaser (I know, you’re probably making fun of me saying fun here) is one of the sentences from Devlin: “You can now take advantage of this additional information.”
I believe there are two very direct applications to DFS here. Let’s touch on them.
- Always use incoming data to adjust your models and views.
New data – and thus, large sample sizes – are imperative in DFS. And the biggest thing here to remember is to allow new data to affect your thinking. If I’m really high on a player, say D’Angelo Russell, coming into the NBA and believe he’s going to be a superstar (I still do), I need to use new data constantly in my evaluation of him. Are his first 20 games a perfect indicator of his future stardom? Of course not. In fact, they might not be an indicator at all. However, at a point, I need to open up the possibility that I could be wrong about a player. That point might not be 20 games, but as I keep on getting data on Russell, I should be willing to change my opinion on him if it is warranted.
The latter part of that statement is always tougher than the former – models do a much better job of adjusting their view of a player than our biases. Renee Miller is one of my favorite DFS people and I had the pleasure of having her on the Fantasy Labs podcast a couple months ago. We talked about primacy bias and other biases that affect our thinking – it is a huge issue and as we learn from the Monty Hall problem, we should be willing to adjust to new information.
- Use ownership data to adjust players during contests.
I often use late swap on DraftKings probably just like everyone else does – to change out players in my lineup who get scratched after contests start. However, I don’t use it near enough to take advantage of new data – specifically, ownership levels of already started players. Let me give you an example.
Say we’re in a large NBA slate with 12 games. Obviously, it is hard in that circumstance to really accurately predict ownership levels. If you play on a daily basis you probably have an idea, but again, adjusting to new data is always good. If this slate had the top-five salaried PGs of Stephen Curry, Russell Westbrook, Damian Lillard, John Wall, and Chris Paul, ownership is really important in GPPs since all of those players possess high ceilings. If three of these players started at 7pm, one at 8pm, and the other at 10:30pm, we could use the ownership levels of the first three to better gauge the ownership of the last two.
Of course, this is hard because the site that has late swap, DraftKings, also has positional options of a Guard and FLEX – thus, you can have multiples of these five PGs. However, in large GPPs you can conceivably know that if the ownership on the first three are very high, the ownership on the last two are going to be lower. As such, if I had a lower-priced PG in my FLEX spot during one of the later games, it would be advantageous for me to look at ownership percentages of those first three high-priced PGs and possibly re-arrange my lineup to get in one of the under-owned high-priced PGs about to start, if it’s a +EV move.
The Monty Hall problem shows us that our brains naturally have biases that we have to shed in order to grow in our thinking. It’s counterintuitive, which is the big problem – we really on our first intuitions way too much in decision making. DFS is certainly a game of skill, but I think that a large portion of that skill isn’t developing better models than our competition; instead, I believe a large portion of that skill is having the ability to adapt and change when the opportunity presents itself.
