Fantasy Playoff Probability

I crunched the numbers for my fantasy football league (methodology details below) and here are the results:

Team (current record) E(Wins) E(Rank) Playoffs 1st Round Bye
Cowboys (8-2) 10.19 1.27 100.0% 93.4%
Jets (7-3) 9.00 2.82 98.7% 61.3%
Vikings (6-4) 8.12 3.21 97.9% 6.1%
Pack (6-4) 7.78 4.34 89.4% 30.6%
Fourth (6-4) 7.39 5.51 74.9% 8.1%
Economists (5-5) 6.77 6.09 59.5% 0.1%
Eiferts (5-5) 6.61 6.08 59.0% 0.4%
Broncos (6-4) 6.59 7.41 17.2% 0.0%
NotGonnaLie (4-6) 4.73 9.64 3.2% 0.0%
Giants (3-7) 3.58 10.60 0.2% 0.0%
Wonders (2-8) 3.82 9.22 0.0% 0.0%
Blue (2-8) 2.54 11.80 0.0% 0.0%

The probability distribution of each team and their rank (grouped by tier) follows:Next week the Economists will play the Eiferts in what will almost be a playoff game. The winner has around a 90% probability of making the playoffs, while the loser has around a 30% probability.Even though the Broncos have a game on both the Economists (me) and the Eiferts, the algorithm is pretty bearish on the Bronco’s chances. Part of that is their 20 points below me (and 120 below the Eiferts) in the tiebreaker, but part of it is their more difficult schedule.Cowboys are definitely in. Jets and Vikings are almost surely in. Blue is almost surely out. The real battle is for those last two spots (5+6).

Top Tier 2017 11 16

Middle Crew 2017 11 16

Bottom Rung 2017 11 16

 

 

P.S. Methodology may follow in an update. Short version: used a version of Pythagorean expected wins to compute win probabilities (exponent of 6) – this seems to be similar to what Yahoo uses in their projections. Had to “guess” at some lineups since some teams have players on byes in future weeks. Then just computed the probabilities for each of the 262,144 possible win / loss outcomes (2^6=64 outcomes per week for three weeks). Also, had to make assumptions about points scored for the tiebreakers (gave the winner the greater of the two expectations).

Olympics 2016 Rio

It’s become a bit of a biannual tradition for me to write an about the Olympics – specifically the distribution of medals between countries.

I don’t have any sport by sport insight into how these games will look, but judging from the last couple years this should be another showdown between the US and China over Olympic supremacy. In three of the last four Olympics the United States has edged out China with China’s lone victory coming as a big win when they hosted in 2008.

Other medal count story lines to watch:

  • Can Britain build on their impressive growth, or was 2012 only about the home country bounce?
  • How will Russia do? Historically they were a powerhouse, but the breakup of the Soviet Union and the struggles of their economy let to a prolonged slump. Their economy has improved and they have seemed determined to reassert themselves on the world stage. Will that show up in their medal count? As a result of a huge doing scandal some of their athletes were banned. How much of a factor will that  be?
  • How will Brazil do? There’s been a lot of press coverage about how Rio want ready to host, but is Brazil ready to compete?
  • Will Japan see a spike add they prepare to host in 2020?

A new type of graph

Introducing the Dan Chart (ok, that name won’t fly. The Dart? Darts fly!), or to name it descriptively, the aligned stacked bar chart. i have had trouble representing data where there are both a lot of categories (series), and a lot of periods (or values). The clustered column stops being useful around 5×5. The typical solution has been to use either the stacked column, or the 100% stacked column. Both of these have serious drawbacks and an easy solution.

First, observe how unintelligible the clustered column chart is:

The stacked bar char shows how the total changes over time, and tries to give you an idea of how the composition of that total changes. Even though changes in an individual category are represented in the chart, ease of interpretation depends on the order of the categories. Changes over time will be very easy to observe for the first/bottom category. You can easily see, for example that for category 1 October is slightly higher than May (0.6 vs 0.53). However, it’s takes a lot more effort to compare Oct to May for category even though the difference is bigger (0.56 to 0.39). If I asked you which category grew more from Oct to May, you’d be pretty hard pressed to answer that (without the numbers).

The 100% stacked bar chart ignores changes over time and only focuses on the change in composition. This is useful for when those changes either don’t matter, or are very small. It gives you a clearer picture for how composition changes. However, it still has the same problem that it is hard to get insights about the changes for those middle categories. It gets unwieldy around 4 or 5 categories. Consider the following example. The total data series is stationary (always sums to 1). You can clearly see that category 10 increased a lot and category 1 decreased. It’s harder to see what is happening to the interior categories, like category 5. It looks like it is staying pretty much the same. Can you notice the consistent decrease from July to Dec (goes monotonically from 8.7% to 5.6%).

These changes are hard to spot because each series is not aligned with itself. What the Dart (ok, fine. the aligned stacked bar chart) does is put white space between each series so that each series is aligned to itself. In the examples I centered aligned them, but they could just as easily chosen to align them to the bottom or the top. With this format you can easily look across the series to see how it changes over time, and make those comparisons. You also can look at a particular time period and see the composition of the total. It works with both with data that changes over time, and data that is stationary. I am not sure why we don’t see this type of graph! I’ve created a hack to make it work in MS excel (contact me if you’re interested) but hopefully this could be adapted into the program to improve chart readability!

Winter Olympics Medals Over Time – Post Olympics Update

The Winter Olympics have now closed. The host nation Russia walked away with both the most medals and the most golds. The increase was pretty dramatic. Russia only managed to pick up 3 gold medals in Vancouver but napped 13 in Sochi. Canada, while lacking the home country bounce they had in 2010, continued to be a top competitor. Norway had another good games reinforcing the fact that their meager haul in Turin 2006 was just an aberration.

A lot of pundits have called this year’s games a huge disappointment for the USA (ESPN: Team USA disappoints in Sochi)However, by historical standards the 2014 games were pretty standard. The USA pulled in the same number of gold medals as 2010, 2006 and only one down from our all time high in 2002 (which we hosted). In both the Summer and Winter Olympics consistency seems to be the name of the game for the United States as I pointed out in my first summer Olympics post. Though, as I mentioned before, the number of events and medals have been increasing so in terms of the percent of gold medals the United States is slipping.

Winter Olympic Gold Medal Counts 1988-2

The total medal counts show pretty much the same story. The United States failed to defend their total medal lead – however, hopefully this time it won’t take us 78 years to be back on top! As with the Summer Olympics it appears that the home-country bounce is more pronounced in the count of gold medals rather than number of total medals. To me this is counter-intuitive and is begging for some good statistical analysis to investigate potential systematic judging bias in favor of the home country. Perhaps if I find myself with some extra time (highly unlikely) I can look into that.

Winter Olympic Total Medal Counts 1988-2

Unlike host country Russia, Germany continued to struggle to regain their passed Winter Olympics glory. They took home the fewest gold medals since 1972 (combining East and West) and fewest total medals since 1968! (See the German/Russian dominance in my original Winter Olympics post)

Probably the most surprising country was the Netherlands. Because historically they were not a big player, I did not even include them in my charts. At one time they led the total medal count and finished with 24 medals and 8 golds. Previously the Netherlands’ highest haul had been 11 medals and 5 golds  (1998) and in 2010 they took home a total of 8 medals.

Winter Olympics Medals Over Time

My Summer Olympics post two years ago was fairly popular, so now that I have a brief respite from graduate school deadlines I put together a couple of charts showing the Winter Olympic Medals over time.

Winter Olympic Gold Medal Counts 1988

There are significantly fewer events, and thus medals in the Winter Olympics – currently 302 to 98. That makes the Gold medal counts a bit more noisy (small sample size), so I’m also including a chart total medal counts (unweighted).

Winter Olympic Total Medal Counts 1988

Both charts show Canada and the United States rising. One thing that these charts are missing is the fact that the total number of events has been climbing significantly as well – from 46 in 1988 to 86 in 2010 and this year’s games features 98 events.

Number of Winter Events 2

Another fact that is not captured by the narrow window of years featured above is how dominant Germany and the Soviet Union were beginning in the early 1970s. From 1972 to 1998 they combined took home 40.5% of the gold medals. The last time the United States led the gold medal counts for the Winter Olympics was 1952 – which makes the lead of this story (The United States has a case of Olympics medal envy) seem a bit odd and ill-informed. The 2010 Winter games was the first time that the United States had led the total medal count since 1932 – a games which were hosted by the United States and only featured 10 other countries. Even then, we only beat out Norway by 2 medals.

Winter Olympic Gold Medal Counts 1952

So congratulations to Canada on becoming a Winter Olympics power house – because let’s be honest, you don’t have all that much else going for you. But that success and growth has been alongside the United States and not at her expense.

Is Congress About to Accidentally End the Shutdown

The House just unanimously passed a bill allowing federal workers to get back pay. The Senate and President are in support so this should soon be law. This measure was not controversial. Even Congress realizes that they, not the Federal workers, are the reason these people are not working and Congress, not the workers, is the problem. While they are getting paid without working (government efficiency?) that workers should miss car payments, house payments, and be unable to pay other crucial expenses while Congress figures stuff out is a hard position to defend.

However, in doing so, they may have un-wittingly removed the legal justification for the shutdown itself. Modern government shutdowns date back to the Carter administration’s interpretation of the, at the time obscure antideficiency act (for an overview of the history see here or here). In short, government cannot enter into a contract without funding – so workers cannot work with the expectation that Congress will fund them (even though  they probably will). Now with the passage of a bill to guarantee backpay (here), workers would no longer be working with a hope that Congress might or expectation that Congress will fund, but instead a legislative guarantee.

A lawyer may need to take a closer look, but from this layman’s eyes it is time for Federal workers to go back to work, and they don’t need a dysfunctional Congress to agree first. Perhaps in this case two wrongs of Congressional dysfunction have made a right?

The Deficit: It’s the Economy, Stupid!

Government-money 46

America’s approaching debt crisis is the topic de jour, both in the news room and in the living room. We have the fiscal cliff, the battle of the debt ceiling (parts I, II and soon to be III), the sequester, fiscal commissions, etc. We are shown scary charts, and told (truthfully) that the federal government is running another trillion dollar deficit and borrows 46 cents of every $1 it spends.

Federal Deficit

However, what we do not see is a careful examination of what is driving these deficits, and what that means for our future and our policy choices. In this, my first series of post, I will drive to do just that with simple charts from freely available data sources.

There are three things that go into the debt to GDP ratio. First, there is the GDP. A fall in GDP will drive up the ratio even if debt does not change. Second, there are the two parts to the debt: revenues, and expenditures. While the economy goes through booms and bust, over the long haul GDP tends to grow at a pretty steady rate. Economist and statistician have a handy, standardized way of removing cyclical components from GDP. It is called potential GDP. A simple view of it is just to say it is what would GDP be if everyone was employed. As you can see below, it correlates pretty closely with the inverse of the unemployment rate:

Unemp and GDP Gap

For reference, here is the long term view of GDP gap, which is just 1 – Potential GDP / GDP:
GDP Gap
It is clear that something happened in the fall 2007. Something very bad! We will return to that. Here is another view that again, shows that something bad happened to GDP in 2007, and we have not recovered:
Nominal GDP
It is only with the background of what was happening in the economy that we can start to look at the deficit. Here are two simple charts of federal government expenditures and revenue:
Federal Government Expenditures

Federal Government Revenue
We see a small spike in expenditures during the recession, but they then go flat. The revenue side is more dynamic. Federal government revenues drop precipitously (17.4% from peak to trough). In fact, in purely nominal terms (not adjusting for inflation or population) they did not pass the pre-recession peak set in Q2 2005 until Q1 2012 – nearly 5 years!

From 1992-2007 government revenues grow about 1.38% per quarter and expenditures grew at 1.18%. If numbers held over the six quarters of the recession we would expect expenditures to grow by 7.3% and revenue to grow by 8.5%. Instead revenue fell by 16.4% (25% below the pre-recession trend!), and expenditures grew by 18.9% (11.6% off of trend).

The point of these charts and data points is to demonstrate that the budget deficit is mainly driven by the very severe recession, from which we still have not fully recovered. But one final chart to drive home this point. Revenues actually vary pretty consistently with drops in unemployment, and along with that potential GDP. When controlling for the GDP gap, the deficit we are facing is not an outlier . What is abnormal is the size, and duration of this drop in employment and GDP. This is what we should be discussing! (And, in future post, hopefully I will).
GDP Gap and Gov Revenue

APPENDIX: Data Sources

All the data was obtained using Federal Reserve Bank of St. Louis’s excellent excel plug-in: http://research.stlouisfed.org/fred-addin/install_windows.html. Here are the exact series and calculations for each chart. In parentheses are the FRED series IDs. Corrections and concerns appreciated!
1: Federal Deficit. This is simply [Federal government total expenditures] (W019RCQ027SBEA) – [Federal Government Current Receipts] (FGRECPT). Both come from the U.S. Department of Commerce: Bureau of Economic Analysis
2a: Unemployment. [Civilian Unemployment Rate] (unrate) From the U.S. Department of Labor: Bureau of Labor Statistics
2b: GDP Gap. 1 – ( [Nominal Gross Domestic Product] (GDP) ) / ( [Nominal Potential Gross Domestic Product] (NGDPPOT) ). Both from the U.S. Department of Commerce: Bureau of Economic Analysis.
3: GDP Gap. 1 – ( [Nominal Gross Domestic Product] (GDP) ) / ( [Nominal Potential Gross Domestic Product] (NGDPPOT) ). Both from the U.S. Department of Commerce: Bureau of Economic Analysis.
4: Nominal GDP. [Nominal Gross Domestic Product] (GDP). From the U.S. Department of Commerce: Bureau of Economic Analysis.
5: Federal Government Expenditures.[Federal government total expenditures] (W019RCQ027SBEA) From the U.S. Department of Commerce: Bureau of Economic Analysis
6: Federal Government Revenues. [Federal Government Current Receipts] (FGRECPT). From the U.S. Department of Commerce: Bureau of Economic Analysis
7a: Government Revenues / Potential GDP. ( [Federal Government Current Receipts] (FGRECPT) ) / ( [Nominal Potential Gross Domestic Product] (NGDPPOT) ). Both from the U.S. Department of Commerce: Bureau of Economic Analysis
7b: GDP Gap. 1 – ( [Nominal Gross Domestic Product] (GDP) ) / ( [Nominal Potential Gross Domestic Product] (NGDPPOT) ). Both from the U.S. Department of Commerce: Bureau of Economic Analysis.