Modeling soccer (and perhaps your work team) as a social network

Frequent readers will be aware that an occasional hobby of mine is to numerically model sports and other interesting activities yet I lack much of the time or tools to do so. I have taken on NFL playoff football, both the entire playoffs and detailed modeling of the Superbowl down to the player level. I have also attempted, unsuccessfully, to model March Madness, the NCAA basketball playoffs, performing mostly analysis as opposed building a model that helps me win a March madness pool. Thus, I love to read interesting modeling papers, especially those which model sports or games as models for other real world activities.

The contributions of individual players in sports like football, baseball and basketball are helped by the large amount to statistics collected and available for these sports. Thus the contribution for individual team members to the team success is easier to model. Science online has a report of some work done by Jordi Duch and other researchers, at Northwestern and in Spain, that attempts to model the contributions of soccer players to the success of their team.

They point out that soccer is a very fluid game compared to baseball, or football and that combined with the very low scores makes statistics like goals and assists insufficient to model the contribution of players to the performance of the team. They hypothesize that the passes and flow of the game leading up to the rare goals are important for determining the outcome of the game and they use networks to model this flow. Players are nodes in the network and the lines between the nodes, called arcs, represent passes. Much as a Facebook or Twitter can be modeled as a network with friendship and interactions or follower/following being the connections, soccer is a "social" sport.

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.

Even more interestingly, the authors apply this concept to a work team that is writing a paper with several co-authors. Instead of the nodes being soccer players in paper network, a node represents a co-author in the manuscript, and the lines between the nodes represent communications directed from one co-author to the others. The e-mails represent communications between coauthors and the effectiveness of the authors is measured by completion of tasks like performing a calculation or scheduling a meeting. In the diagram below, author A2 (I think A3 in the second chart is a typos) seems to be an important and strong contributor.

One of the authors, comments on how the scheme can be used to assess the contribution of individual team members.

"One of the issues with any kind of teamwork is assigning the right credit," says Amaral. "The wild, loud people get more credit, but with this analysis you can get a picture of how much an individual really contributes to an outcome."

As work continues to evolve to be more team driven and highly networked, perhaps a scheme like this can not only point out strong contributors to a team, but also help an entire team work at a higher level. Imagine it applied to the work of developing open source software or Wikipedia articles.

(via Science online, the paper at Public Library of Science, PLoS, figures above are from the paper can be found at this .pdf link)

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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".

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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.

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