18% Simulated Chance of winning money in the Playoff Fantasy Football pool

This year I have a roster (RDK1) that is currently in fifth place in the RKB Playoff fantasy football and in striking distance of first or second place and winning money in the pool. The goal is to determine the chances of that happening. The focus of this simulation is to answer the question "With only the Superbowl to go, will the RDK1 roster be in the money at the end of the playoffs?" and "What combination of player results does RDK1 need to be in the money and what is the chance that such an outcome will occur?"

Developing the simulation required the following steps and assumptions.

1.) Collect the data for each player or teams games for this season. Turnovers and touchdowns for DEF (and special teams); field goals and extra points for the kickers; passing and rushing touchdowns for the quarterback, wide receivers, tight ends; rushing touchdowns for the running backs. I will randomly select from this history to generate simulations of the Superbowl.
2.) Assume a player's performance in the Superbowl will be identical to their performance in one of the games they played in this season. If a player didn't play they get a zero for that game, except for the kickers for which I only have partial season data. This may decrease the points slightly, and is potentially a bad assumption.
3.) Kickers get their own field goals, but only get extra points equal to the touchdowns their team scores (actually all the rushing and defense touchdowns, but only the QB passing TD's to avoid double counting). Typically a game with field goals has less touchdowns, so decoupling the game history so that a game with a lot of touchdowns for the QB could be paired with a game with a lot of field goals for the kicker could result in a higher than expected points. Possible another poor assumption.
4.) Everybody (RB and QB) gets their rushing touchdowns, but passing touchdowns are awarded only if the quarterback throws at least one. There are instances in the game history of the QB's not throwing any. I really should assign each passing touchdown to a WR, TE, or RB or player not on the list but that is to complicated to program in excel. This may result in excess points, and is an expedient assumption.
5.) The score of the game is the field goals, rushing RD's, and only the quarterback's passing TD's to avoid double counting, and the defense/special teams touchdowns. This is slightly inaccurate since the passing touchdowns for the receivers are not all counted or double counted. The simulation still generates widely varying scores.
6.) Simulate many games by bootstrapping (selecting TD's or outcomes from each particular player's history this season. Add the points for each player to the rosters that have the players on them.
7.) Used the RANK() function to determine the places. Ties get the same rank using this function and the next ranks down are eliminated. For instance 3 first places get rank 1 and the next rank is 4. Rank is important to determine who is "in the money".
8.) As to the money, it is a fraction of the total collected from all of the rosters: 70% for first place, and 30% for second place. However, a tie for first divides the total money (100%) and there is no second, a tie for second with only one first divides the second place money, 30%, among the second place tied rosters. To be in the money RDK1 needs to be alone in first, tie first, or be alone or tied for second with only one first place roster ahead.

The rosters above show RDK1 roster in fifth place, but with enough similarities to other rosters both ahead and behind it that winning money in the pool will require some fine threading of the outcomes.

Remember that the focus of this simulation is to answer the question "With only the Superbowl to go, will the RDK1 roster be in the money at the end of the playoffs?" and "What combination of player results does RDK1 need to be in the money and what is the chance that such an outcome will occur?"

The histogram above (click for larger) shows the rank of the two top RDK rosters, RDK1 and RDK6 after the outcome of 20,000 simulations. The first red bar highlights the fraction of simulations with RDK1 roster in first place and in the money (alone or tied) at 1.4% of 5000 simulations. The green bar highlights the fraction of simulations with RDK1 roster in second place (alone or tied, with no first place tie) and in the money at 16.3% of 5000 simulations. RDK1 is in the money in about 18% of the 5000 simulations. RDK1 starts in fifth place before the Superbowl and can climb to first or slip to 13th place according to the simulations. There was some hope that RDK6 might have the potential to be in the money but from its starting point at 13th place, it never rises above 3rd place and can slip to 30th in the simulations.

Another way to look at this data is go ahead and calculate the winnings for each outcome.



This chart shows that the most likely outcome, 80%, is that RDK1 has no winnings, but the rest of the bars which add up to about 20% are various outcomes with winnings for the RDK1 roster.



This chart expands the Y axis to zoom in on the lower probability outcomes. There is a 10% chance of being alone in second place, a 4% chance of tieing second. There is even a less than 0.2% chance of being alone in first place. The less likely outcomes include situations in which I am tied with several others, up to 5 others, for first or, up to 7 others, for second. I need about 10% of the total collected to break even for the six rosters I entered.

Of course simulation generates outcomes for all of the rosters, otherwise I couldn't perform the comparisons needed to determine what place I am in or whether RDK1 roster will earn money. A less self-centered data reporting approach yields information about all of the outcomes.

The chart above (definitely click for larger) shows the histogram of the frequencies of the final rank after the Superbowl (simulated) of the top twenty rosters as they stand now(actual) before the Superbowl. The top twenty was chosen as a cutoff because it contains the lowest ranked roster that could win money in the simulations. The legend has the roster in their current ranking order (Cara H in 1st through RDK3 in 20th place). Bruschi Drink 3 ends most of the 1000 simulations in first with Tim G5 ending most of the 1000 simulations in second. there is a small but significant fraction of RDK 1 results in second place as we showed earlier. The chart will reward closer examination for the interested.

The information above can be used to determine the fraction of simulations (in this case, 5000) in which any given roster will be "in the money". The chart above shows that Bruschi Drink 3 is more than 80% likely to win some money followed by Tim G 5a at 42%. Almost a third of the time, Cara H in first place is likely to end up with some money. More annoying is that Bruschi Drink 4, a roster currently tied for 20th place, has a small but finite chance of being in the money. The results above do not total to 100% because more than one roster can be in the money (not just 1 and 2 but multiple rosters tieing for first, or one first place with multiple 2nds).

A compilation of the actual outcomes of each of 20,000 simulations can show the most likely particular outcome instead of the probabilistic compilations further above. The outcomes above compile the rosters in first or second place. Recall that in the case of a first place tie there is no second place.

As suggested by the charts further above, but shown directly in this one, the most likely first and second outcome at 22% is that Bruschi Drink 3 will be first with Tim G 5 second. The next most likely is heartening because it has Bruschi Drink 3 in first with RDK1 in second. Even so, these top twenty outcomes represent only 82% of the outcomes generated in 20,000 simulations. There are highly unlikely but predicted outcomes of all sorts, including some interesting ones with 6 tied in first place, or a first place with 8 tied for second, both only 1 time out of 20,000.

The RDK1 roster appears in these outcomes usually as a second place winner in the 2nd, 14th, 15th ,and 18th most likely outcome. You need to go down to the 17th most likely outcome to see RDK1 in first place, though it is tied with the ever successful Bruschi Drink 3.

Thus my final prediction is that Brschi Drink 3 will be in first place with Tim G 5 in second, though I am hoping for the 18% chance of RDK1, my own roster, being "in the money".

Who will win Playoff Fantasy Football Pool?

My clever analysis and modeling of this years football playoffs has yielded a roster (RDK1) that is in fifth place in the RKB Playoff fantasy football results as of the NFC and AFC Championship games. With only the Superbowl to go, the question is, "Will the RDK1 roster be in the money at the end of the playoffs?"

The chart above (click the chart for larger) shows the standings as they are right now, after the conference championship games. The y- axis is total points while the x axis is the name of each of the rosters. The colors represent contributions from each week of games, Red for the wild card week, blue for the divisional week and green for the conference championship week.

Disregarding the two lowest results, the Wild card and Divisional weeks yield anywhere from 65 to 30 points in a roster. A roster can also have a great wild card week and still lose, because your players have to generate points each week and that only happens if their team progresses. Which of these rosters will win, will it be Cara H. in the lead with 119 points?

The above plot is the same data and roster, this time sorted first by the number of players a roster has out, and then by the total points. This chart is very telling because the rosters to the left with no players out or few players out have much more points potential than roster to the left with more players out. The last grouping with all nine players out on their rosters is the most pathological example; they have all the points they are going to get. Tim G 2 with a respectable 101 points is still not in the running. By the way, the RDK1 roster only has 3 players out, and since I still have my quarterback, kicker, and defense.

Taking the starting chart and plotting the contributions from each player position to the total shows the importance of the the positions to a successful roster. The colors in the chart above represent points from a particular position, green for quarterback (QB), yellow for the wide receivers (WR), orange for running backs (RB), red for kicker (K), purple for defense (DEF), and blue for tight end (TE). The greater contribution positions are at the bottom and build up to the total number of points.

QB is the most important, and while RB and WR also contribute as much, realize that there are three WR's and two RB's per roster so the contribution above should be halved for RB or divided by three for the WR's. As an individual player the kicker contributes a fair amount of points, almost always one for each touchdown, and then field goals as well. In this league the DEF gets the special teams points if kickoffs or punts are returned for touchdowns, as well as a point for each turnover after there are three. Finally tight ends rarely receive passes in comparison to wide receivers and their contributions are the smallest.

Above is the leader grid (click for larger) with the top twenty team rosters and with only the players that are left to play in the Superbowl. A grayed out square indicates that that roster doesn't have the player, numbers are the accumulated points for a given player in that roster. The grand total is the total for each roster, and the rank is as of now. The red highlight is first, and green is second, yellow are the rest of the top ten. I included the top twenty because I have evidence that one of them can come in first, though it would be very unlikely (less than one in a thousand)

What combination of player results does RDK1 need to be in the money (70% first or 30% second place, a tie for first divides the money and there is no second, a tie for second with one first divides the second place money), and what is the chance that such an outcome will occur? That is the topic for the next analysis.

Cartoon about taxes by Rube Goldberg

This cartoon is on display at the Brandywine River Museum. Rube Goldberg's cartoon on taxes is probably still as relevant today as it was when he drew it.

I would like to say I don't mind paying taxes, but I would be lying. I do try to realize that a certain level are necessary to run the government and to provide services for those who may need it. Still sometimes feels like a wack on the head.

More information about Rube Goldberg is in the picture of the description.

Cajuns in PA? GEAUKRT license plate.

I do love a clever personalized license plate, and if you can throw in a Louisiana Cajun reference while referring to your Mini as a go cart, more power to you. This GEAUKRT PA license plate embodies the best spirit of license plate personalization.

What military aircraft are you? Quiz.

Have you always wanted to know which type of military aircraft best exemplifies you and your personality. This military aircraft personality quiz can provide you with that answer.



As a bonus the quiz comes with questions for which you will not like any answer. Those are the best type of these silly quizzes.

(via The Presurfer)

University of Delaware auctions off former Chrysler plant assets - robot arm anyone

For the discerning mad scientist: the list of items up for auction by the University of Delaware from the former Chrysler plant in Newark, Delaware. The university is holding an auction Feb 25 and can be inspected Feb 22-24. The university bought the plant after it closed, and apparently got the contents as well. The coolest items are probably the 6 axis robot arms, some still in line along assembly lines. There appears to be all kinds of milling equipment as well as other mysterious devices of unsure provenance. I am sure a machine expert would be able to make sense of all of it. The place is acres large, so I bet there are plenty of robot arms to go around.

Oh to be an independently wealthy mad scientist with a large laboratory, perhaps under an extinct volcano, for this stuff.




Anybody want a robot arms?


Assembly lines?



Some forklifts and cushman carts?



Various mysterious pieces of equipment (the bottom one is a lathe, I think)?


I need some blueprint/map drawers.


These vacuums and sweepers would make house cleaning go fast!

Any financial backers out there want to go halfsies? By halfsies I mean that you get to pay for the robot arms and I get to play with the robot arms.

Playoff Fantasy football arises again

It's time again for playoff fantasy football. Since you don't have to maintain your concentration for 17 weeks, it is a good way for non-football fanatics to play without a huge commitment of time. My sister runs a points-only league so the rules are straightforward: Pick a kicker, quarterback, two running backs, a tight end, three wide receivers and a team defense from the list of players and teams in the playoffs. You get the sum of the points these players or defense, special teams included, scored during the playoffs (the detailed, but simple rules are here).

Having developed a model last year, I simply had to enter this year's teams and Sagarin ratings and the simulation was already to run in last year's format. My process for hopefully picking the winning roster has several steps.

1.) Data collection: Collect the Sagarin data on team ranking and performance and the data (I used Yahoo) on player and defense touchdowns, field goals, turnovers.

2.) Playoff game simulation: Simulate the playoff games to determine which teams are likely to play the most number of games. Wild card teams that play four games are best, teams that play three games are also good (and likely won played in the Superbowl). Determine which teams are the most likely to make to to the Superbowl. The model currently runs 1000 simulations at one time.

3.) Initial Roster Selection: The model automatically calculates the points for a given roster using the information from the games played and the stats of the players selected. Rank the players and defence by their points stats and build some rosters based on that. Also build rosters using the information of how many games a player's team plays. Also randomly choose some rosters with high point values. These are the initial seeds for the "genetic" algorithm below.

4.) Optimize and find highest point rosters: Using the rosters generated above, the spreadsheet makes combinations (or cross breeds) of the rosters (the current model pool is 33 rosters) and I keep the highest point value rosters that are generated. Sometimes I let the model use a random player in a given roster spot to ensure that I have explored all of the possibilities (random mutation). Usually the selection is from the current list of high value rosters. This year the search did find higher value rosters than the initial seeds. I would sorely love to automate this step. Perhaps in the next version of the model.

Having already developed the model for simulating the playoffs and playoff rosters made the modifications I made this year easy, and I was able to do them in enough time to have an impact on the rosters I chose for these years Playoff fantasy football pool.

The new schema is simple. Either of the two teams with the same Sagarin ratings either team should be expected to win with a probability of 50%, since the ratings represent the number of points a team will score in the game. If a team has no points then it is expected to lose all of the time. Thus I proposed that the probability that team1 will win is...

team1 rating /(team1 rating + team2 rating).

To include the Sagarin home advantage this really becomes...

home team rating + home advantage /(home team rating + home advantage + away team rating).

For the monte carlo simulation, a random number between 0 and 1 less than the above probability means that the home team has won.

This preserves our earlier assumptions of evenly matched teams and team with no points and all of the arguments about its appropriateness fall to discussing what happens in between, and the validity of the ratings themselves. Sagarin suggests using the pure points for predicting the outcome of games rather than his ratings, so that is what I used.

Recall that we are trying to determine how many games each team will play so that we can pick players or defences that not only score points, but also have a three or four game, rather than one or two, in which to score them. The best player in only one game may not be the best choice. (The record breaking, once in the history of the playoffs, Green Bay and Arizona game notwithstanding.)

I generated 100,000 simulations of the playoffs using the model above and tabulated the team matchups in the Superbowl. Click on the chart below for larger.


Chart of the likely matchups using the Sagarin pure points sorted by the probability of the outcome. Circles represent the median of 100 trials of 1000 simulations, diamonds bracket the 25th to 75th percentiles, crossbars the 10th and 90th, and the lines extend to the maximum and minimum variation in the results. Those matchups that are already eliminated by the wild card week of games are shaded out.

The top eight outcomes in the chart are matchups with either Indianapolis (IND) or San Diego (SD) playing Minnesota (MIN) or New Orleans (NO) in the Superbowl. The top outcome is the obvious NO beating IND in the Superbowl, while the second has them beating SD. Close examination of the first eight outcomes, out of 72 possible, shows them to really be set apart from the rest of the pack, and representing almost one third of the probability. Thus I chose rosters with players representing these matchups by setting the model to fix each particular matchup by giving high ratings to teams in question and then searching the rosters using the genetic algorithm method described above.

The next matchups on the chart are New England (NE) vs. New Orleans (NO) matchups, which I did have rosters supporting, but which are now eliminated because NE lost in the Wild card weekend. There are other chances for the harsh light of reality to burn away my optimistic modeling by having one of the team I didn't pick due to low probability, Dallas or Arizona, for instance, to go all the way and destroy my roster's chance of winning.

We can check some of the predicted outcomes of the model by looking to other sources of odds or probability for teams in the Superbowl. I took the Yahoo Odds Futures sheet, collected the teams in the playoffs, and normalized the probabilities to have the total outcomes equal 100% to get a list of the teams in the playoffs and the chance that each one would win the Superbowl. I did the same with my simulations.


Above is a chart (click the chart for larger) of the winners predicted from the Yahoo odds futures and from a simulation of 100,000 outcomes using the Sagarin pure points ratings and my new scheme for randomly simulating the winner of each matchup. Those teams that are already eliminated are shaded out. The error bars on the Yahoo odds are plus or minus one standard deviation of the six betting ratings, and the ones on the Sagarin simulation reflect the standard deviation of 100 trials of 1000 simulations.

The good news is that the two four teams are the same for the Yahoo odds futures and my simulations. Yahoo odds favors IND as the top outcome by probability, whereas my simulations show New Orleans to be the top. We can redo the chart, now taking into account the results of the Wild Card week's games.

For this chart (click for bigger) I used today's yahoo Odds futures and I set my simulations to ensure that CIN, GB, NE and PHI lost their games (by either setting their ratings at 0 if there were the away team or to minus the home advantage if they were the home team). The yahoo odds still favor IND but now DAL and MIN are rising in the odds. My simulation based on the Sagarin simulation has more changes, NO is slightly favored over the others, but the evenness of probabilities between IND, MIN, SD and BAL, DAL, and NYJ is disconcerting since I have rosters built on players and matchups from the first group, and not from the second group. BAL, DAL, or NYJ wins next week are bad news for my picks. Alternatively, if ARZ does better than expected as they have already, I will also lose the Fantasy Playoff football pool.

(Potentially next post, some analysis of the actual roster from this years Fantasy Playoff football pool.)

Vice President Biden and President Obama in my neighborhood

You will be well aware that the funeral services for Vice President Biden's mother Jean were at Immaculate Heart of Mary, the church I attend just up the street from my house. In fact, on nice Sundays, we would walk to church. The occasion is a sad one, but it is interesting that President Obama attended and that many of the Delaware and National political hierarchy were at my little old parish church in my neighborhood. Even former president Clinton was there, as well as many Obama aids and cabinet members, as well as Governor Markell and Governor Minner .

Still did not get to see the motorcade as I was at work. I tried to get Lynn to go and take pictures, but it was way too cold.

I snapped some screen shots of the CNN live feed from the web, just because it is fascinating to see all these famous people in the church that I will got o on Sunday. I might run up and sit in the first pew, just to say I sat where the President did.

Vice President Biden and family in the first pew.



President Obama and Mrs. Obama and Governor Markell.


You can see the crying room in the background here. I think the reporters are back there.


President Clinton attended.

It was a very nice service and the priest gave a nice homily. After the service, Vice President Biden had some heartfelt comments about his mother. A sad occasion for these people to come to Wilmington, but it sounds like Jean Biden had a long and full life, with happiness and sadness. She got to see her children and grand children grow up and become successful people and her son become Senator and Vice President. May she rest in peace.

If Obsession (with a new idea, book, author...) is a crime, let me be guilty

It seems to me that finding a new favorite author, artist, musical group or even idea follows the same stages as falling in and out of love. (not the stages of grief, but similar).

The example I would use is my recent dalliance with the information presentation and design ideas of Edward Tufte.

Stage one: Falling in Love.

I never knew that anyone thought this way about data presentation. Tufte's ideas are terrific and visionary. Every pearl of presentation wisdom that comes from his mouth is exactly the right answer and perfectly fixes everything.


Stage two: I Am Not Worthy of This Love.

I'll never do anything even a tenth as well as Tufte. His figures produce epiphanies of insight and mine cause the viewer to suffer headaches and nausea and some to go irrevocably insane. I should just stop presenting any data to anyone in any form ever.


Stage Three: The Blinders Come Off.

I can't stop doing any presenting. Tufte seems a little rigid in his outlook on things. I may not be Mozart but Salieri had some good tunes also. My figures are good enough to get the point across. These other presentation design guys over here don't think Tufte is the final answer on data presentation.


Stage Four: The Breakup

Yeah I used to think Tufte had some good presentation idea, but he was too rigid in his standards. My friends say they never really liked him in the first place. I am so glad I am over that and can get back to work. Stephen Few has some good ideas on data presentation, I just might check that out.


And so the cycle continues.

I think you could apply the same formula to a favorite author that you just discovered, a new political philosophy, management fad, computer program, TV show, new girlfriend, or any other subject of fascination. My goal in life is to get through the cycles as fast as possible to preserve a healthy skepticism and keep a measured perspective. Skepticism is the best philosophy, I love it the most. (... here we go again.)

That old tuba argument again

This comic is very similar to discussions I have had, though without the unicycles. Really I do play the tuba, though I haven't in a long while. I need a tuba nook.

(via the excellent Wondermark, which you should read every day.)

Aspiring to Tuftian perfection - presenting data

Often financial, scientific or engineering analysis takes large amounts of data and numbers and crunches them down to a single number or decision. I know it felt that way when I was researching and writing my thesis. Much like 42 being the answer to "Life, the Universe and Everything", it doesn't seem fair to take all of the data and turn it into one number or decision. Being intellectually honest and the presentation of the data have a lot of influence on the final outcome.

That intellectual honesty and the importance of good data representation and presentation are the lifework of Edward Tufte. I have just finished reading Beautiful Evidence and Visual Explanations which are his third and fourth books on the topic of data presentation. I am going backwards in the series because that's what's available to me and because I needed to answer a question about presenting some data of my own, while keeping my intellectual integrity at the same time.

Edward Tufte describes his books in the introduction to Visual Explanations. He says that The Visual Display of Quantitative Information is about pictures of numbers, Envisioning Information is about pictures of nouns, and Visual Explanations is about pictures of verbs. Beautiful Evidence seems to be about the best examples of these pictures, where well presented data helps in decision making. He also has counter examples where poorly presented data hinders decision making. In the two books I have just read he takes especial umbrage with the presentation of the data for the Columbia and Challenger shuttle disasters. His opinion is that the data presentations failed to stop and potentially caused the disasters. He also hates Powerpoint. He has been quoted as saying "Power corrupts, PowerPoint corrupts absolutely"

In Visual Explanations, in his review of the reason for the Challenger disaster he notes how the data about O-rings should have actually resulted in a recommendation not to fly but the presentations did not get the message across. The flight day had temperatures and conditions that were far outside of any of the past experience in flight or testing that the O-ring testing and usage had, yet the data presented didn't clearly indicate that. He proposes the unclear presentation as a reflection of unclear thinking and suggests this is the cause of the disaster. There is some disagreement with Tufte's analysis of the presentation flaws leading to the bad decision to launch in cold weather.

In this book, Tufte also uses the famous origins of epidemiology story of John Snow discovering that the Broad Street well was the source of an 1854 cholera outbreak in London. Tufte cites the discovery of the pump well that caused cholera epidemic as good presentation of data but he cautions that if the data were presented in a different form it might give different conclusions. Tufte lauds the fact that Dr. Snow checked his conclusions by looking at anomalous data and finding the reasons for them to see if his hypothesis was supported.

In Beautiful Evidence, Tufte reviews the Columbia Space Shuttle disaster. When the Columbia Space Shuttle was in orbit after it appeared that the wing had been struck by debris during launch, the team on the ground had 12 days to determine if the debris that hit the wing was an issue. Once again the team could not present the information in a manner to convince people that the impact under discussion was probably far larger than any from data they had from previous testing. Tufte is extremely critical in these examples because he feels that the bad presentation was a sign of unclear thinking and was in the direct causal chain that led to the disaster.

Of course there are those who decry my "What would Tufte say?" enthusiasm as I critically analyze every chart in every presentation that I make. I wholehearted recommend reading all of his work, and I realize that Tufte's design of presentation criteria are excellent but perhaps a little perfectionist. Not every presentation I make is life or death, in fact none are. So perhaps I can get away with a "good enough" approach in which I try to keep some of his principles in mind when I must present data and still conform to a corporate fashion for PowerPoint or Excel charts of a certain type. The alternative is to despair of ever producing Tuftian presentations with a clarity of thought that only a few transcendent individuals possess. Like Salieri as portrayed in the fictional Amadeus, I can recognize his genius but can only produce mediocrity myself.

Cable Connector Quiz

Mental Floss has the Cable Connector Quiz, with cables both modern and ancient (in computer years). I scored an 80%, I am sure you can do much better.

The Cable Connector Quiz

(via Neatorama)

Water burbling under the ice on Shellpot Creek

Slowly but surely the waterfall on Shellpot Creek is accumulating more ice. This sound in this video doesn't capture the peaceful burbling of the water as much as I would like, but try to imagine it.

Shellpot Creek water fall not quite frozen yet

Even with tempertures in the 20's the past few nights the waterfall on Shellpot Creek behind my house hasn't quite frozen completely yet. This week will be cold during the day and frigid (teens) at night. I suspect we may see the water stop.

Happy New Year

Happy New Year!

Everyone says, "Welcome to the new decade", but I thought that since there was no year zero, that the decade would end with 2010, not begin. I suppose it's that change in the tens digit that has everyone excited.

There also seems to be controversy as to whether 2010 should be "two thousand ten" or "twenty ten". How are you pronouncing it?