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".
A longer time series shows the history since 1948.
It's been lower in the past, but that is a generation ago. I personally would like Congress and the President to start working on jobs now.
Upper plot: First seeds are expected to do well advancing to the elite eight on average. Next seeds two through four generally make it to the sweet sixteen. Seeds from about 5 through twelve generally make it one round, and that uncertainty is where the fun comes in.
Hard drive storage has gone from $1million/GB to pennies/GB in 30 years. That's seven orders of magnitude in 30 years. 
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.
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.
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.
The chart below just shows the faction in the various unemployment categories adding up to 100%, instead of the actual number. (click for larger)
If I have time, I want to overlay dates of unemployment extensions and see if there is any correlation. I still don't think that would be completely relevant because it is obvious that if an extension was passed then the time people receive unemployment insurance will be longer. Will I be able to see whether this in fact means they stayed unemployed longer or do extensions occur when Congress sees that people are already unemployed longer and the extension is to address that issue?
They also include nodes for the goal and for shots wide of the goal. To each of these arcs the attach statistics and probabilities from the 2008 European football championship on play pass accuracy, and goal accuracy to the arcs. One could them follow the ball through this "ball flow" network to a goal, a miss or to the other team. Combined with more calculations the group attempts to predict the outcome of soccer games.
Simulation results with this scheme show the number of simulations out of 1000 that a given seed was the champion. The actual history is here. The results in the chart show far too high a probability that low seeds are the champion in the tournament in these simulations.
A histogram of the teams with seeds and the number of times they are champions in 10,000 simulations, shows that Kansas is the most likely winner, but the spread of the data even includes the unlikely play in winner at 16 seed as a champion. This simulation is unrealistic.
I did not use the fitted line in the curve above because of its unrealistic probabilities at high seed difference. While this approach captures the history, I feel this approach neglects the variation between similar seeded teams as reflected in the Sagarin ratings. Additionally the history shows pretty wide variations in outcome.
Simulation results with this scheme show the number of simulations out of 1000 that a given seed was the champion. These results are more similar to the historical outcomes, but the matchups between evenly seeded teams will be tossups that ignore the differences as determined by the Sagarin ratings.
A histogram of the teams with seeds and the number of times they are champions in 10,000 simulations, shows that Kentucky is the most likely winner, with low seeds favored to be champions, but I fear that it neglects the difference in teams as represented by the Sagarin ratings. This simulation is unrealistic.
Thus the probabilities reflect the historical data with a more realistic and very rare chance of 16 seeds beating 1 seeds but with the Sagarin ratings to sort between evenly matched teams.
Simulation results with this scheme show the number of simulations out of 1000 that a given seed was the champion. The results is similar to the seed difference with history scheme above, but now the Sagarin ratings are included.
A histogram of the teams with seeds and the number of times they are champions in 10,000 simulations, shows that Duke is the most likely winner, and low seeds are still favored as is true historically. This is the simulation scheme we will proceed with.
Here are the final results with all of the roster's points separated by position. It pays to have a good QB on the roster, but WR, RB and K's also contribute almost the same amount of points for the roster which are towards the top. Remember that there are 3 RW's and 2 RB's so the K has more point generating power as a single player. Even the defense can be significant. Probably the TE is the least useful point generating player on a roster.
The final results separated according to the game in which the points were generated reveals a truism that has been a guiding principle all along. Rosters with players that play more games generate more points. The light blue "dusting" of Superbowl points is what determined the winner this year.
A chart with the order of the roster based on the points before the Superbowl shows a little more clearly that the Superbowl points are what changed the order around. The top contenders had many or all NO and IND players left on their sheets, especially the big point positions like QB and K. 
The rosters are shown above for the top twenty finishers, with just the players in the Superbowl on them. Realize that in the above some roster (like mine, RDK1) had players that did not play in the Superbowl and so are not listed above, however the correct total points are in the grand total at bottom. 
The simulations above are from the prediction before the Superbowl. What happened to Tim G 5? That roster started 2 points behind RDK1 before the Superbowl. It had IND K instead of NO K for who were 5 to 11 in the Superbowl for 6 more points of deficit. RDK 1 beats Tim G 5 entirely due to the choice of kickers. Even if Matt Stover (IND) had made the field goal he missed that would only have added 3.
...and back up to 24 inches at the end of the driveway.
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.
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.
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.
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.
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)
