Binomial Distribution and DFS

Binomial Distribution and DFS – What to expect in winning.

I found this article over at wwwDraftManager.com and just wanted to share it with you all here.
All props and credit goes to the guys over at Draft Manger for this great article and insight. Very informative and helpful for DFS Players to really understand what they should expect to gain from DFS.

===============================

In poker, I played somewhere between 5 and 7 million hands.  I don’t exactly remember, but I remember that after a million hands, I had a pretty good idea of what my WR (Winrate) was.  It was easily quantified in bb/100 (bets per 100 hands played).  This was the common standard to measure the game that I played for a living at for over 9 years.

Here are two poker players- and their statistics.  I’m going to make a basic example out of the two of them.

Player A) Jason- Jason has played 500,000 hands of limit holdem and won at .3 bb/100 at 5c / 10c poker.  He was up $1,500 til this point in the story.  One night Ol Jason got into a huge fight with his wife because she left some sharp knives out in the kitchen and decided he was going to drown his sorrows in some Jack Daniels.  Later that night he was looking at a $100/200 LHE game online and decided it was his time to make history.  He hopped in with his entire $1,500 profits and took a shot.  12 hands later he was broke.  His net profit after 500,012 hand was $0.

Player B)Ralph- Ralph enjoys playing limit holdem after work online.  Over the last few years he plays $1/$2 LHE and has played about 20,000 hands.  He doesn’t know it, but his winrate is -5 bb/100.  The money doesn’t matter to Ralph, he has a very well paying Job and win or lose, he likes to compete.  He is currently down $2,000 dollars one night when decides that people at $1/$2 don’t respect his raises and it’s time for him to take his skills to the big time.  He deposits $1,000 and hops right into a $50/100 game where his raises will be respected more.  He plays for a few hours being all in twice, but runs his $1k up to $5k before he signs off.  In those two hours he played 218 hands and left this night up $2,000 in his
online poker career.

Which player has had a better career?  Which player would you rather be?  Which player would I have staked?  If the career was over today, I’d choose Ralph.  Ralph has $2k in his pocket.  If you’re asking me which player is better, the answer isn’t even close.  I’d say that Jason is a very good player, while Ralph is a very poor player.  Give me Jason every day of the week.

So how does this translate to DFS?  Well first- It’s important to note that the guy that wins the biggest tournament in one night, doesn’t mean he’s the best.  How than can you track how good you are, and what you can expect out of DFS.  With poker, you could play 10,000 hands in a single day.  With DFS you can surely play 2 or 3,000 match-ups in a single day, but there are MANY variables that can really go into that.  You could put up a score that’s the same as your friends, and you win and him lose or vice versa.  You could win one day at 55%, another day at 100%.  The problem with looking at overall win and loss records is illustrated in the above poker example.  Imagine day one you put in 100 $1 games on Draftkings and you win all 100.  The next day you put in 50 and lose all 50.  You’re overall record is 100-50 and you’re winning 66% of your matchups!  Was there any skill involved in one day playing 100 and the next day 50?  What if you played ten days in a row of one $50 matchup and won them all.  Then the next day you play all $500 in winnings (less with rake, but easier math) and you lose everything.  You’re now even but you’re a winner 10/11 days.  There are several skills in DFS that help with that.

1. Consistency.  You should try to stick in a similar amount of money and games each day.
2. How you get your money in?  If you have $100 to play do you go to the lobby and pick the first name you see for your entire daily allotted bankroll that day?  Do you put them in ten $10 50/50’s?  Do you find two $50 GPP’s?  How you get your money in is as important as the DFS lineups you play.

What is your winrate?  What % should you play?  Winrate is a very tricky thing to calculate.  DM will be having some tracking software here soon unlike any you’ve seen in DFS that will simplify this equasion, but for now we’ll just keep plugging away.  You need a VERY large sample depending on the sport.  One of the worst things you can do is to win right away for the first 5-6 days, then start going above your bankroll, or chasing losses.  The goal here that this is a marathon, not a sprint.

Binomial distribution and DFS.  This is basically going to help us understand and answer the following questions.  “I win 60% of my h2h matchups.  What are the odds that I’ll go broke playing 20% of my bankroll each night?  What are the odds that I have a losing week, or month?”

First off… What is break even with the rake?  It’s 55%.  Message me if you’d like me to explain that or ask in the forum.

So if we win at 58% (3% above the rake) What are the odds that we’ll have a winning month?

Probability of success on a single trial= .53

Number of trials =60 (assume you play two lineups a day for the sport of Baseball) over 30 days.

Number of Success= 30

Cumulative probability of P(X>30)= 63.2%

Cumulative probability of P(X>30)=72.4%

odds you have a break even or winning month= 72.4%.  This means you could play your best lineups for an entire month, and you have a better than 1/4 chance of having a losing month.  (27.6%)

How about changing it to a week?  Odds of having a winning week?  48%.  Odds of having a break even or winning week= 68.9%.  Short term trials (14 in one week) and a winrate so close to breaking even, breaking even becomes a real possibility.

Let’s change that to a year.  720 Trials over the entire year. Odds you have a winning year?  94.2%.  It’s 95% that you’ll break even or win.  This is why being consistent is so important.  The margins are thin in DFS, but there is definitely an edge to be had.  What do the best pro’s win at?  It’s tough to say.  We have a sample of over 8,000 MLB games against a top known pro where he’s winning at 39%.  Does that mean he’s a loser?  Not at all.  Remember in 8,000 games played with a limit on Fanduel of 750 games per day for MLB- this is just over a 10 day stretch.  It’s important to differentiate between the signal (what’s real) and the noise (what appears to be real).