First snow of 2011 - pictures and a car in a ditch

The first snowfall of the year in Delaware puts more than 2 inches of snow on the ground. Here is a measurement showing 2.5 inches. Use the right hand side of the ruler for measuring, this is a measuring square and the left hand side starts at the top of the "L" part of it.


Because it happened at night and into this morning and it wasn't expected to be much there hasn't been any plowing on our street or the streets in the neighborhood around us. That probably led to this person going down the hill on Baynard from Shipley to Marsh too fast and ending up in the ditch just before the Shellpot Creek bridge. There was no one in the car and folks on the scene said the person had gotten out already and was OK.

Shellpot Creek always looks nice after a good snow.




The snow on the driveway might actually need to be shoveled!

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Superbowl winners, Simulations vs the Professionals

I took the odds of a given team winning the superbowl from Yahoo Futures for comparison with my simulation results. My results are in red below.



I match pretty well with 5dimes.com and SBGGlobal, but bodog looks too flat and I don't know what Sportsbook was thinking with the high probability for the New York Jets.

The agreement with some of the professionals lends some credibility to the results of my simulations and the roster decisions I will make based on them. I always say I don't know anything about football so I base my work on those who do and the people who set the odds need to know because they are trying to make money doing this.

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Superbowl simulations - matchups and winners

I am struggling to find the best way to present the data from my simulations of the football playoffs. The key to picking a good roster is to figuring out which teams play multiple games in the playoffs, essentially the ones that make it to the Superbowl. Thus I compiled 10,000 simulations of the playoffs and then determined who the AFC and NFC champions would be that would meet in the Superbowl and who the winner of that game would be. The pie charts below try to capture all of the outcomes from 12.5% chance that NE will beat ATL in the Superbowl to the less than 1 in 10,000 chance that SEA and KC would meet in the Superbowl.


The chart below is a filter of the above data with only NE or PIT as AFC champion, and ATL, CHI or GB as the NFC champion.


The Pareto below shows the top 15 outcomes for matchups in the Superbowl. They represent 78% of the outcomes of the simulations.


The matchups of either NE or PIT vs. either ATL, CHI or GB represent 68% of the outcomes of the simulations. The only wrinkle left there is which team will dominate the game an and so the makeup of the rosters to cover those possibilities. The results are heavily waited to not only a NE appearance in the Superbowl but also to a NE win.

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Better Visualization of the Superbowl Simulation

Rather than the bar charts from earlier I used Tableau to create pie charts showing the fraction of simulations in which a team wins the Superbowl as a function of the home advantage and the standard deviation of the normal distribution dividing the spread. (click the chart for larger).



Does this show better the expectation that New England would win assuming the straight Sagarin ratings determine the winner of each game? The stdev equal to 0.001 assumes that the favored team in the spread wins automatically. The fractions in the pie charts show how NE is dominant even using the normal distribution to more realistically represent teams' chances of winning. A stdev of 1000 is approaching the case where each game is 50/50. Notice the teams without a BYE are more likely to win the Superbowl in this case. That just because they play one fewer game and have one less chance to lose.

Players stats are entered and I am modifying the simulation to let me test 20 rosters at a time in 1000 simulations of the playoffs. More to come.

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Who will win the Superbowl this year? Simulations suggest...

I am currently crunching the numbers for this year's Playoff Fantasy Football Pool. Using the Sagarin ratings and the formula discussed earlier, I have randomly simulated this year's playoffs many times to determine who will win the Superbowl. This year New England seems to be the favorite to win if we just assume wins based on the ratings. Even if we use 13.92 as the standard deviation and the spread and a normal distribution to calculated the probability of a team winning, New England wins about 33% of the time with no home advantage and 39% of the time with a home advantage of 2.11 points as given by the Sagarin ratings. The plot below shows how the winner varies with the standard deviation used in the model for either 2.11 points home advantage on the left or 0 points on the right.


Click on the chart for larger. The X-axis varies from a standard deviation from 0.001 which essentially assumes that the team with the higher spread wins through more reasonable scenarios with higher standard deviations which are more like what has occurred in previous NFL seasons.

Using the home advantage of 2.11 and a standard deviation of 13.92 simulations also show the likely teams to make it to the AFC and NFC championships. The plot below shows those results for 1000 simulations.

The likely matchup is either New England or Pittsburgh as AFC champion vs. either Chicago, Atlanta, or Green Bay as the NFC champion. Other teams have slim chances of appearing as seen down near the x-axis. Notably, New Orleans or Philadelphia have slim but noticeable chances to be the NFC champion, as well as Baltimore, New York Jets or Indianapolis having slim chances to appear as AFC champions.

Next step, collecting player data and simulations to make the perfect roster picks.

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Probability of winning an NFL game - recalculated after thirty years

It's NFL playoff time again. I am in the process of redoing my playoff football model to more accurately reflect the probability of a given team to win a game based on the spread or the Sagarin rating difference.

Stern wrote a paper called "On the Probability of Winning a Football Game" (1991) in which he collected the final scores and the spreads from 1981, 1932, 1984 to determine the relationship between the two. He found that the final score difference between the favorite and the underdog, subtracting the spread could be modeled with a normal distribution with standard deviation of 13.89. The average was 0.07 which is effectively zero for the purposes of the analysis. The probability that a team will win a given game is then the cumulative normal distribution around the spread with a standard deviation of 13.86, or normsdist(spread/13.86) using Excel functions.

I wondered if the analysis had changed in 30 years so I pulled the data for this year through week 16. The plot is below:

The standard deviation is 13.92 with an average -0.17. Hardly any difference found from the earlier analysis for a lot of work to extract the data and get it into a format for the analysis, but at least we now know it hasn't changed. The normsdist function with the spread replaced with the Sagarin difference (home+home advantage-away) divided by 13.92 is what will be used in the game simulation for the playoff fantasy football.

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Happy New Year!

Seems appropriate to point out that the dates for this year have as much scope for binaryness as for last year.

Today is 1/1/11 or 01/01/11 if you like.

In ten days it will be 1/11/11, or 01/11/11.

And, please remind me, our 5th anniversary this year will be on 11/11/11.

I leave the other interesting dates, binaries with zero, for instance, and other numerical coincidences as an exercise for the reader.

Bonus: this year there will be a 9/10/11.

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