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Old 12-04-2013, 09:06 PM
hmfdesmr1 hmfdesmr1 is offline
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Default WX In a bipartite graph with buyers rh

NFL Free Agency Analysis
The NFL free agency period seems to act in a similar manner to a firstprice open bid auction, albeit with a few twists. All free agents sit in the pool at the same time, Isabel Marant Dicker Suede Ankle Boots and bids for every player are ongoing through time. While in a first bid auction there is one item being Hollister Doncaster Jobs sold at any given time, free agency sells all players at the same time. This would present to us a very raucous and cluttered graph, where each player has anywhere from 032 connections to teams. Within the theory of bipartite graphs, each product goes to whoever is willing to pay the most for it. However, free agency is different Uggs Canada Cheap Online from this ideal model in that players might have bias toward or against certain buyers. This actually makes the ideal model seem less realistic, as selling items is not ideal all the time. For instance, Ralph Lauren Sale paying for shipping could actually make it to ensure that selling to a buyer who offers less might return a bigger profit. A company might not want to trade with Canada Goose Jacket Sale Canada another company who Longchamp Bag Australia Price employs child laborers due to their image. These examples Nike Free Australia Review run parallel towards the free agent market, where players may want to stay within a certain region, or they may believe that they fit in better with certain buyers. Actually, I would argue that the free agent market actually can be modeled more efficiently using an offspring from the bipartite method of graphing rather than an auction.
In a bipartite Discount Ray Bans graph with buyers (teams) around the right, and sellers (players) on the left, there is no way to have perfect matching, as each team signs more than one player. However, if we consider Air Jordan 14 this as the team selling a spot on the roster they are then the sellers; thus, the players are buying a spot with their talents, which makes them the buyers. This may seem strange, however Nike Blazers Low Suede it will result in a perfect matching graph with every player connected to exactly one team (assuming that each player is signed). In this way, we can ignore the money the Oakley Holbrook Cheap player is getting paid and simply focus Cheap Moncler Mens Jackets on which team they'll play for. This model factors in the human mentality, and knows that players do not only worry about the money (as an Hollister Brisbane Australia auction model would have you believe) and that other reasons influence their decisions. I've modeled this phenomenon using the top 5 free agents from 2012 on the bottom of this post.
Using this inverted approach to bipartite graphing, we are able to portray the free agent market from the NFL using methods we've learned in class. In fairness, players who're regarded as mediocre or are old will most likely simply play for whichever team would like to pay them the most, as they simply want to maximize the money they can earn. However, it is interesting to think about the free agency period like a function of bipartite graphs rather than an auction. I believe that doing this with Timberland Ireland Boots the top athletes is reasonable, as they will want to play somewhere that they like and that they think will win, and also the money is a lower priority.
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