# How to Benefit from Randomness

About a year ago, I was chatting with Cal Spears about GrindersU and he asked why I play daily fantasy football and baseball, but not basketball. I’ve since started dabbling in NBA, but I’m just testing things out and it’s certainly not to the degree that I play the other sports.

My answer to him was that football and baseball are far more random than basketball on a nightly basis. It might sound pretty freaking dumb to purposely seek out randomness. We’re trying to make money predicting outcomes better than other players on DraftKings, so wouldn’t we want it to be as predictable as possible?

No, at least not in many situations.

Here’s the thing: almost all events that transpire in a fantasy sports league are zero-sum. You win, I lose. We don’t actually want to seek out the most predictability at all costs, but rather the *greatest potential advantage over our competitors*. When something is relatively easy to predict, such as NBA fantasy scoring, it becomes harder to create an advantage over others.

I’m not saying NBA isn’t beatable, because lots of players much smarter than myself are crushing it, but when something is more challenging to predict due to greater short-term volatility, such as MLB results from night to night, there’s potentially a larger advantage there.

## How Randomness is Paradoxically Predictable

The idea here is that randomness is predictable. Naturally the very definition of ‘randomness’ makes that statement a bit paradoxical, but I’m talking more about the accrual of many random events. A baseball player’s batting average, for example, is highly volatile from day to day; it’s going to be next to impossible to predict how a player hits on a nightly basis. He could go 0-for-4 for 4-for-5; we just don’t know.

Over the course of an entire season, though, that player’s batting average – the result of the accumulation of many individual events (at-bats) that are filled with randomness – will come very close to stabilizing near his long-term average. Maybe he’ll hit .310 or maybe he’ll hit .290, but he’s not going to hit .500. At-bats aren’t random, but when dealing with the MLB player universe (as opposed to a professional vs. me or you), the individual performances are *mostly* random with bits of skill sprinkled in; the difference between a Hall-of-Fame player and a lifetime Triple-A player in terms of getting a hit is maybe four percentage points.

So we’re basically just dealing with a coin-flipping situation, except the coin is messed up and lands on heads roughly 30 percent of the time. Bad coin flippers can get heads 25 percent of the time and great ones 33 percent of the time. To determine the difference between good and bad coin flippers, we need a pretty high number of coin flips, right? Same for at-bats, same for passing efficiency, same for red zone touchdown percentage, etc.

## How Randomness Is Exploitable

The primary way to exploit randomness is to understand that outlying performances are eventually going to regress toward the mean. If I flip heads 9 out of 10 times, you can bet your ass I’m going to see a lower rate of heads over my next 10 flips.

In that way, you can start to see how randomness can be very predictable. If we know the baseline, we know 1) where the randomness will eventually take us and 2) how quickly we are to get there. Compare coin-flipping to a highly skilled endeavor. Instead of understanding a generic baseline rate we can apply to everyone, we have to try to figure out each person’s lifetime average. So if coin-flipping were actually a skill, it would become *more difficult* to predict each flipper because we would need a large sample of coin flips to determine how skilled he might be.

Let’s take a football example. A highly touted rookie running back averages 3.8 YPC in his first season, dropping him in fantasy drafts. His team adds two big upgrades along the line, though, and we can now get the running back at a much cheaper price than we could when he was a rookie getting a ton of press. This is a situation in which we should be bullish on the running back because research suggests YPC is 1) extremely dependent on offensive line play and 2) very random. It fluctuates a lot from year to year, so we know it’s likely to regress toward the league mean of 4.2 YPC (or above it), especially since we’ve deemed the back a talented one.

So what we’re doing is searching for randomness, looking for outliers in either direction, and then either targeting/fading those outliers based on which direction they’re likely to regress.

One of the interesting things about football is that, unlike other major sports, it’s pretty random not only on the individual game level, but also the season level. With only 16 games, we often see talented players fail to live up to expectations and bums like Tim Hightower tear it up over the course of an entire year.

The second reason that randomness is exploitable is because fantasy football is a marketplace. It’s a game of competing minds, so you can capitalize off of the mistakes of others. Most owners – most people in general – are extremely susceptible to getting fooled by randomness and mistaking it for a signal.

Basically, they’re betting on coin flips as if each individual coin-flipper’s past coin flips were the result of his own skill and not chance. Fantasy football results aren’t completely random, of course, but they’re sure a lot more random than most want to believe. Most will act as though that running back with 4.65 speed who averaged 4.9 YPC in his rookie year will keep up that pace, or that the kicker who connected on 95 percent of his field goals will continue his accuracy, or that the small tight end who scored on 50 percent of his red zone targets will keep killing it to that extent in the red zone.

Sometimes people ask why I analyze big-picture stuff like red zone touchdown rate by size as opposed to looking at each individual player’s past success, and this is one of the major reasons; if you can figure out the overarching baseline rate at which we should expect certain stats from particular players, you can put yourself in the best position to 1) identify randomness, 2) (paradoxically) predict how “random” events will unfold, and 3) create the biggest potential edge over the field.

## Comments

Awesome article!

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Hey. I write about poker. I love your premise and intend on piggybacking the idea to poker. Your logic is flawed however when you propose that 10 coin flips yielding 9 tails means that there will be more heads in the next set of 10. This is called due theory and is false. Your second example, however, capitalizes on the point of conditional probability, something that is not transitive to a static event like a con flip. That runner ran below the mean due to circumstances that you identified, not due to running bad, and is expected to perform above the mean now due to the reversal of the same circumstances.

Polish this article up a bit eliminating that random fallacy and then stick it in your portfolio because it is really close to superb.

@MaverickUSC I think that Jon is trying to say that ‘you can bet your ass off’ that the next set of 10 coin flips will have a lower rate of tails to heads,

becausethe probability of 9/10 tails is so low, that any other outcome below that (8/10, 7/10, 6/10, 5/5, 4/5, etc.) is much more likely.I understand your comment about due theory, I just feel it was interpreted incorrectly (admittedly I read it in the same context as you did the first time).

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I also do not think the “due theory” is an appropriate way to describe Jon’s static event. While the static event would not be deemed a conditional probability, the logic of static probability (i.e., basic probability—> .5 chance of either heads or tails) is a great way to illustrate his point about regression to the mean. I actually use similar examples in the Statistics course I teach. Like @takkyonn said, I think Jon was just stating that the odds of getting >=9 tails on the next or any set of 10 coin flips would be extremely low; thus, “you can bet your ass off” that there would be a lower rate of tails to heads in the next or any subsequent set of flips.

However, I think there is a great chance to write an article about due theory as well as how many DFS players (myself included, especially when emotions overtake logic) mistakenly fall into the due theory trap/fallacy when they really think it is benefiting from regression to the mean.

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Maverick – To build upon what these guys are saying, I don’t think I committed a due theory fallacy because I’m not saying that NINE heads are due since we saw nine tails in the first 10 flips. I’m saying that, due to natural regression (and not some sort of “catching up”), we are very likely to see an increase in heads.

The most likely outcome is that tails will still be “winning” after 20 flips because an even distribution is always the most likely, regardless of the prior flips. If the “score” were 9-1 in favor of tails after 10 flips, the most likely score after 20 flips would be 14-6, which would be a much higher percentage of heads.

Heads isn’t “due” at all; it’s just that we were witnessing an outlier outcome to start, so we can bet strongly on more heads in the future solely because seeing 9/10 tails is unlikely at any point in time (regardless of past coin flips).

I think this is right, though there is one other consideration. The “mean” to which that player’s performances should be expected to regress is the mean based on his talent level (relative to that of his opponents). That isn’t static. It’s always changing. Some guys play with weighted coins, and in looking at an outlying performance, it’s not always easy to tell how big an outlier that performance is.

Are they flipping the same coin, or did they trade their coin in for one that flips heads more often than tails?

With all due respect Jon, the point the others are trying to make in a truly random event like a coin flip, is that there are no dependencies on past coin flips. if 100 flips in a row came up heads, the probability that the next flip is tails, is 50%.

In fact, in the scenario where 9 out of 10 came up heads, or 100 in a row were heads, it may be worth evaluating whether or not the event is actually as random as you think.

DFS players can benefit from regression towards the mean. But the coin flip example you gave is flawed.

“Your logic is flawed however when you propose that 10 coin flips yielding 9 tails means that there will be more heads in the next set of 10. This is called due theory and is false”

this^^ This is why casino make rake on black/red of the roulette wheel. people walk up, see red has hit 10 times in a row and figure black is a “lock” when it is really still the 48/49% (w/e it really is) chance.

past performance of even odds do not change the odds going forward. if 9 heads are flipped in a row it is still 50/50 that tails will be flipped next time.

yup^^ point of the article was correct…example was very much not

I think that the two sides are talking past each other to some degree.

Jon is not saying that, if you flip heads 9x, then 10th is likely to be tails. He’s saying that it’s highly unlikely that the next 10 flips will yield a 90% rate of heads (since we know the baseline is 50%). He is simply saying that everything will, over time, regress to the baseline. i.e. don’t make your DFS picks based on the 90% heads rate since that’s a drastic outlier.

What you, and others, are pointing out (correctly) is that the baseline isn’t particularly clear when it comes to player performance. Sure, we can assess the league mean for various statistics, but an outlying performance might be the “mean level” of performance of an outlying player.

I think the author’s article was fantastic. Without picking apart certain terms, theories or principles… I think he got his point across the way it was intended. It basically means, don’t go chasing last week’s or last game’s points.

Each individual flip just like each individual game have the same general odds of success. What I’ve gathered is that from x number of samples you can use your knowledge of statistical analysis along with past results to predict future trends in the results to follow.

Its just a better way off thinking and more sound reasoning than, “Curry scored 10 last night, he MUST go for 30 tonight”

I think Kennan Allen would be a great example how this theory can be applied.

I Read fantasy dfs for smart people loved it,anything new coming out?NBA of nfl next yr-As for red zone by (size)cld you explain or give example of a player?thanks!

I am not a statistical mind like some of the smarter posts ahead of me, but trying to think of an application for this in hockey…basically are you saying the following?

If a player in the NBA currently has a shooting percentage of 39%, but is historically a 80% shooter, then they should be looked at more closely to figure out what is causing that effect. If everything has remained equal (he didn’t break his arm, etc), then he is due to a regression to the mean, meaning that he should be grabbed as he is under performing. Likewise, if some nobody comes out of the gate with a 100% Shooting percentage, he should be faded. Thus this idea capitalizes on the randomization of clustering.

In the long term, all clusters get ironed out to the mean for that player (or close to it). If a cluster of bad fortune happens to a player, he is going to be dropped in year long leagues and faded in daily leagues. However that player is going to regress to the mean in the long term, so it is figuring out why the bad fortune is happening and when the market corrections will begin to take place.

Or am i way off on this application?

Apply this theory and always win………“heads I win, tails u lose” lol! Good read with valuable insight. The point u make is a critical component in gaining leverage with what we do know rather then guessing or just looking at numbers and match ups. I think Kenny Rodgers said it well too, “You gotta know when to hold them and know when to fold them” Key word is KNOW. I also agree with what jtwfantasy says- “I think Kennan Allen would be a great example how this theory can be applied”

If one stands and watches the shore line then we’ll know when the ebb and flow comes and goes but if we have our backs turned we can only guess even though we know it is coming.

It seems to me that the sample size of games played is what makes predicting football so hard. If there were several hundred games played in a season, then predictable patterns would become identifiable. At least NFL is a little bit easier than college football.. Trying to predict college football is like playing poker with deuces, 3’s, 4’s, and 5’s all wild! I love the piece, but I do believe that you can have a hot player come upon the scene, even if they’re only hot for a few games. So they can be playable for a few games. There are parameters that can come into play that make them hot. Perhaps they are covering for a star player and getting major playing time that they didn’t have before. They’re hot because their price hasn’t caught up with their opportunity, nor have they proved that they’re worth more. Jonas Gray fits your example. He was a one-game wonder, right? How could we have predicted that? If we can figure out how we can pick the one week burning stars, we’re on to something big. I totally agree with your article. The question is, HOW do we know which game Jordy Nelson is going to get the passes over Cobbs or Emmanuel Sanders over Demaryius Thomas? Is the sample big enough to predict, and if so, what criteria do we use? What is it a function of? Is it the person covering them? With million dollar prizes for being the person to best predict a top NFL line-up, I’m interested in learning more about predicting randomness…where do I start? :)

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Awesome insight, brother.

yeah, what JMToWin said.

I tried to have some fun with this but others are just getting a bit overboard here like its quantum physics

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There isn’t regression to the mean in coin flipping. There is always exactly a 50% chance that it will land on heads, and a 50% chance that it will land on tails. There isn’t even a millionth of a millionth percent increase or decrease in the odds at any point no matter how many times it has landed a certain way in the past.

That said, the article is good, and I’ve read one of his books — which was also good. Don’t let the example ruin the point that he’s making. It’s very applicable to DFS.

He’s not talking about that. He’s talking about a results distribution, like Dalton’s probability machine. You expect to see a 50/50 distribution in the end. He should have used a bigger sample like, 900/1000 tails or something, 9/10 is a small sample to start going down the path, but the point he is making is that it all even outs AT SOME POINT. That’s the key takeaway. You have true “unobservable” distribution and then you have sample distribution. We know that heads/tails SHOULD be a 1:1 distribution.

Regression to the mean is trickier to apply to smaller sample sports: soccer, nhl, etc. Work better with more possessions, attempts, scores, events. Ie why basketball is so predictable in aggregate and baseball as well.

Great article, but that example falls into “gamblers fallacy.” Coin flips are not relatable, but I understand the overall premise of the article. Good read.

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Just to be clear, I think the idea that I’m committing the gambler’s fallacy (which seems to be the main critique here) is wrong. The gambler’s fallacy is suggesting that if X occurred less than normal during a specific time period, it will “catch up” to occur more than normal in the future.

I don’t think that at all, nor have I suggested it. I’m saying, “Whether X occurred less than normal or more than normal during a specific time period, the most likely outcome in the future is that it will occur at its normal rate.”

I think the idea that football isn’t random like a coin flip is certainly true, but my point was that it is more random than most believe and we can still treat outliers in the same general way.

Also, there is regression toward the mean in coin-flipping. Again, that is NOT to say that heads is more likely to come up in the future because it hasn’t in the recent past – it is always 50% – but just that with each subsequent flip, the chances of 50% heads over the entire sample are greater and greater. If it has been 60% heads in the past, chances are it will be closer to 50% in the future not because of a catch-up effect, but solely because future flips are likely to be evenly distributed. That’s regression toward the mean.

Again — that’s not a good example. He’s saying that YOU CAN BET YOUR ASS OFF that it’s not going to match 9/10 heads over the next ten rolls. He’s saying exactly what you’re saying — that the randomness/nonrandomness of previous performance does not dictate future performance. Would you bet your ass off that I can’t roll heads 9/10 times? Of course you would. How about you watch me roll heads 9/10 times and then I asking you to bet me that I can’t do it again? You might get thrown off, think I’m some sort of prescient freak, and be skittish. He’s saying you shouldn’t be. Treat random events exactly as they exist — randomly. It’s the same theory as targeting pitchers whose xFIPs are outperforming their ERAs — don;t look at their terrible luck, look at their abilities and the normal progression/regression toward the inevitable mean.