Math With Jerome

Lotteries are typically really tough to win. Powerball, Mega Millions, and even state lotteries are all damn near impossible claim the jackpot. Even winning anything is pretty unlikely. Getting a Pick 5 (numbers 0-9) exactly right is 1 in 100,000. Getting luck enough to draft the next phenom like LeBron, Anthony Davis, or perhaps Zion Williamson? That's much, much easier than getting a few digits in the right order. NBA Draft System and Protected Picks A quick refresher: The NBA determines the selection order of the first 14 (of 30) teams for an upcoming draft of new players by a lottery system. These are teams that didn't make the playoffs. The rest of the draft order is determined by inverse order of regular season record. The NHL also has a lottery system for non-playoff teams but differs for teams in the post season where order is determined partially by playoff performance and regular season point total. In the NFL, non-playoff teams are ordered purely by regular sea...

So WTF is the NFL's passer rating, really? It's one of those stats announcers and talking heads on TV like to use to make a point when it's mentioned only when it's very high or very low. I knew  only a few things  (and I think is the case for most people)  about passer ratings: Greater values are "better", it ranges from 0 to 158.3, and sometimes a quarterback would be better off throwing all their attempts into the ground, or so the announcer would say.  This prompted several questions. How is this rating calculated? Are greater values always better? Why is the max 158.3? And what is with that weird scenario I hear about where a QB would be better off with all incompletions?  I'll hit on a few of the key concepts and background of passer ratings, but if you want to read more on this the NFL has goes into more detail here . Quick Background of Passer Ratings The point of this passer rating system is to compare passers' performances from season t...

To PPR, or not to PPR: That is the question. Well, at least until the last few years it was a question. It seems more Fantasy Football leagues have some scoring per reception than have the ol' standard format. Before giving points per reception (PPR) became the new standard RBs ruled over all and drafts were so front loaded on the position. To help fix this, giving points for catching passes evened things out some. But now RBs are used differently (not so many "bell-cows", but some grab more receptions) and offenses have changed with tempo and play style that it may be a good idea to take a step back and see how points per reception impacts scoring.  For now, I'm going to look at this impact over the course of an entire season and make a comparison though overall position finishes from 2013 to 2018 -- so we'll see how the top 60 WRs compare to the top 60 RBs each year and what trends/bits of info we can extract. Per usual, the visual below is interactive and y...

Describing something as average is typically innocuous. But sometimes it can be deceiving. Take a look at the definition of average  and you'll see a typical amount , or  common ,  ordinary . When it comes to numbers and data it is also tied to what is called the  arithmetic mean   (sometimes just mean  for short) -- which is adding up a bunch of values and dividing by the number of values you have. Key questions here: When are these ideas in alignment and when does it fail? To help get to the bottom of this, at least from a statistical point of view, is to first talk about resistant statistics  -- which are summarizations of data that are not highly influenced by individual values. Let's also have  a quick reminder of  the  median   or  value that splits the data set into an upper and lower half when the data is ordered. The mean of a data set is not  resistant to extreme values, while the median  is, and w...

I'm back with a bunch of visualizations -- let's go! Time to dive back into more  starter-worthy  analysis.  If you missed my first post from a few weeks ago, I introduced what I call starter-worthy  scores for each individual position. Check out  my first post  to get all caught up. In short, I found point thresholds for each offensive  position that best separates starter-level production from the rest. Let's again dive into this by first looking at how often players are starter-worthy  based off of Average Draft Position,  and how that distribution changes by position.   Ah,  the good ol' ADP.  Play around with the bar graph below to get a better sense of where starter-worthiness  comes from in season-long drafts.  The bar graph shows, across the horizontal axis, the proportion (or percentage)  of games for each season shown (i.e. 16 games for 2015 to 2017, 9 games for 2018)  a player is starter-...

Let's get into what I'm going to call  starter-worthy production. If you're in a 12-team league, with the typical two RB slots to fill, then the top 24 running backs are typically deemed "starters." To get a sense of how things may go for you this week, you visit your favorite rankings site to check out where your guys fall in the top 20 to 30 players at the position. But what point production should you feel good about from those players? Can we find a point threshold that helps identify production worthy of being in your starting lineup? Let's take a look...   I'm defining starter-worthy production for each week as the top 24 scores for RB and WR, and the top 12 scores for QB and TE. The dataset consists of the top scores for each week including 50 for RB/WR, 18 for QB, and 20 for TE. The splits were needed for simplicity and don’t change the analysis. Looking at the visualization below, the blue histogram shows what starter-worthy produ...