In which the author ponders the question, "If you admit that you are a hypocrite, are you really a hypocrite?" He then provides his honest commentary on a number of fascinating topics. He insists, however, that his readers form their own opinions.
There has been a lot of complaint that the weather forecasters missed the call on this recent storm. It started yesterday when we awoke to 4 inches of snow that was twice what anybody expected and was still snowing when we all thought it would turn to rain.
We had in sequence - snow, cloudy skies, rain, ice pellets and lots of snow again. My pictures begin in the middle with the measurement of last night's snow, which was the second wave. About 7.5 inches.
Just trying to see if I can embed the Deldot Traffic Cams pictures in a blog post. It looks successful to me. These will not update automatically, just refresh the browser to see them update. I chose cameras that are roughly on my way to and from work.
After today's unexpected loss of NE to the NYJ a lot of clarity was brought to the RKB playoff fantasy football pool predictions. Firstly the model probabilities for the SB matchup and winners.
The most likely outcome and matchup is PIT playing GB in the superbowl and GB winning.
Because many rosters in the playoff pool had NE players a large number of potential winning rosters (including my own) were wiped out and have no chance of winning. Also, the GB and PIT games this weekend generated a lot of points for rosters which had those players. Finally, not very many people had NYJ and CHI players in their rosters. The combination of these factors means that for the purposes of my simulation model there is not difference in the 1st and 2nd place winners among the several superbowl mathcups and outcomes.
The expected winner of the pool is roster 64, Rich V 3, built on a GB/PIT superbowl matchup with GB kicker, QB and DEF, and filled in with PIT players for the extra RB and WR. The second place winner is roster 9, Bruschi Drink 4, which contains all GB players. The roster just placing out of the money in third place is roster 58, RDK 2, my roster built around GB kicker, QB and DEF, with NE and PIT players filling out the RB and WR positions. There is no graph because these are the results in 2000 simulations no matter the team outcomes. I didn't bother with 10,000 simulations because for this model the results look pretty unequivocal.
The results show a failure in the model in that there is no link between team performance and player performance except for the number of games played. Additionally it doesn't take into account good or bad days for players since it only uses the average number of points per game for the year. There is good and bad news in this. A weird combination of player performance could let me squeak through and win the pool, but that same combination could let a 4th or 5th place through to win. The only way to get better information is to get game by game data to try to get the variation in player performance into the simulation.
The purpose of the fantasy football playoff roster simulation is to search all of the possible combinations of player rosters for the one roster that has the highest chance of beating the other rosters. To do this I have first simulated the expected outcomes of the playoff games using Sagarin ratings. I also collect the expected performance of each player in each given game from available data about their performance this year. Combing the two yields the expected performance of a given roster and then I compare lists of rosters to each other to see which roster beats the other roster the most times.
My goal is to find roster which score a lot of points and which do well in comparison to their competition. Additionally the search is also for rosters which win over the various high probability outcomes of the playoff season. The model is displayed diagrammatically below.
Using the simulations of the NFL playoffs, the average expected points for a given player per game, we can simulate the performance of fantasy football playoff roster against one another. Now that we know the 72 rosters competing in this year's RKB fantasy football playoff pool, the simulations allow us to see what the probability of rosters being in the first two places, those placements are in the money for this playoff pool.
Before the wild card week during creation of my rosters I used a similar technique with 20 roster that I picked to try to choose the best roster. I chose rosters that had players from teams that played the most games and had players with a high average number of points per game. I also tried to cover the different possible superbowl matchups. From the 20 I chose 5 rosters that I felt covered the potential matchups. The chart below shows the performance of those rosters vs. the 72 participants in this years RKB fantasy football playoff pool.
The chart shows the frequency of the first 20 outcomes for first and second place combinations in 10,000 simulations. Green bars are rosters in which I place in the money, red are not. My rosters are 57 (RDK1, NE dominates ATL in SB matchup), 58 (RDK2, GB dominates NE or PIT in SB matchup), 59(RDK3, PIT dominates ATL in SB matchup), 60 (RDK4, NO dominates NE in SB matchup), and for the hometown 61 (RDK5, PHI dominates NE in SB matchup). Rosters are numbered by their alphabetical order on the RKB Fantasy football roster list.
Before the wild card games were played my rosters were in good position to be in the money according to the simulation results. One roster, 57 where NE is in the SB was so popular that two other participants picked exactly the same players for their rosters (2 and 56). Of the 91 different outcomes, 38 of them had my rosters in the money. Those 38 outcomes combined to 75% of the 10,000 simulations with my rosters in the money. But a the wild card week of playoffs has occurred the outcomes have changed.
Now their are only 20 possible outcomes of first and second place combinations according to the simulation. Of these 20 combinations, 8 have my rosters in the money. Those 8 represent 64% of the 10,000 simulations. This is a decrease from the estimate before the wild card games were played, but the most probably outcome, in which I am in a three way tie for first place, has gone from 11% to 22%.
I could still lose the chance to get money if really unusual events like SEA winning or New England losing occur, but the whole point of this was to have the fewest rosters which cover the most probability of being in the money.
Before the NFL Wild Card week the Playoff fantasy football simulations showed the likely matchups were either NE or PIT vs. either ATL, CHI or GB with NO and PHI more distant possibilities on the NFC side and BAL, NYJ and IND as even more distant possibilities on the AFC side. A NE win of the superbowl vs. many different opponents figured high in the probabilities. The chart looked like this (click below for larger):
Now that the wild card games have been played and IND, KC, PHI and surprisingly, NO, have been eliminated, plugging those completed games into the simulation and running under those assumptions yields the following chart:
The earlier conclusion that NE or PIT would likely meet ATL, CHI or GB in the superbowl still holds. The NE vs. GB matchup seems to be the primary beneficiary of the NO and PHI losses. While the probability of SEA in the superbowl is now visible on the chart they are still a distant fourth place in probability vs. the other NFC teams. The balance of probabilities on the AFC side hasn't changed much, NE still leads with PIT a close second. The following chart is a Pareto chart of the likelihood of outcomes for matchups and SB winners with the wild card week results included.
It yields a more detailed view of the outcomes. Still, 79% of the time, NE or PIT meets GB, CHI or ATL in the SB.
My playoff rosters with NO and PHI concentration are eliminated now, but the roster with a GB focus expecting a NE, GB matchup is still very much alive and a contender for first place in the RKB fantasy football playoff pool.
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!
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.
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.
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.
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.
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.