Edit: Any way to enable embedding of images in this forum? It's kind of clunky to have to click on all of the photobucket links in this post. Over the last few months, a colleague and I worked on coming up with a “points probability model” (similar to the win probability models that have been developed for baseball—for more info, see http://www.tangotiger.net/wiki/index.php?title=Win_Probability_Added). To construct the model, in a nutshell, we used historical data from MLS (2004-2008) to calculate, for each “game state” that Team X could be in (where game state was defined by what minute the game was in, whether Team X was the home team or the away team, and how many goals Team X was leading or trailing by), how many points Team X would expect to earn from a game on average (sort of, but not exactly—if you’re interested in the details of the mathematical geekage behind this, PM me, and I’ll tell you more) if they were in that game state. Just to give a couple of illustrative examples, according to the model... ...an away team that’s ahead by 1 goal in the 26th minute will earn 1.55 points from that game on average (or, more intuitively, if they’re in that exact situation in 4 different games, you’d expect them to earn about 6 points from those 4 games) ... an away team that’s ahead by 2 goals in the 58th minute will earn 2.66 points from that game on average (or, more intuitively, if they’re in that exact situation in 5 different games, you’d expect them to earn about 13 points from those 5 games) So then, using the model, we looked at every goal that was scored in MLS in 2009 and calculated how much it was worth in terms of expected points, given the state of the game when it was scored. For instance... ...a goal scored by the home team in a tie game in the 80th minute raises the home team’s expected point total from 1.30 to 2.63, so it’s worth (2.63 – 1.30) = 1.33 points ...a goal scored by the home team when it’s ahead by 2 goals in the 75th minute raises the home team’s expected point total from 2.92 to 2.99, so it’s worth (2.99 – 2.92) = 0.07 points We also made one additional adjustment—since about 80% of penalty kicks were converted in MLS over the time frame covered by our data, we decided to work under the assumption that winning a penalty actually gets you 80% of the way to a goal, while converting a penalty only gets you the remaining 20%. In light of that, we discounted PK goals by 80% when we calculated their value. So after doing all of this, we determined, for each player in the league, the aggregate value of the goals they scored in 2009. Some notable ones are listed below. In reading through, keep in mind that this doesn’t necessarily tell us anything about the inherent quality of these players, since 1) not every goal requires the same amount of skill/quality/whatever to score and 2) it’s debatable as to whether it takes more skill/quality/whatever to score goals in “high leverage” situations (ie, situations where a goal would be more valuable). Also, it’s obvious that virtually every goal that’s scored requires a contribution from multiple players, and not just the goal scorer. We’re not taking that into account here. Regardless, though, we think it’s an interesting exercise. The top 10... Pretty much what you’d expect. although Cunningham had a few more garbage-time goals that Casey did, so those two are flip-flopped with respect to goals and EPA. Also, Cummings and Shalrie (8 goals) come in at 9 and 10, ahead of guys like Ryan Johnson (11 goals), Luciano Emilio (10 goals), and Robbie Findley (12 goals) Also interesting—Robbie Findley’s 12 goals were worth only about two-tenths of a point more than Patrick Nyarko’s 4 goals and Chris Pontius’s 4 goals as well. Other guys who scored a decent number of goals that didn’t count for as much as Nyarko’s and Pontius’s Dasan Robinson’s 1 goal this season (scored in the stoppage time to give the Fire a 3-2 lead over Colorado on 8/23) moved the needle on his team’s expected point count by almost 2 full points, about 1.4 points more than the aggregate value of Cuauhtemoc Blanco’s 5 goals for Chicago (3 of which were from the penalty spot). And then there was the least consequential goal of the year, the penalty kick converted by Mathew Mbuta last Sunday to up RBNY’s lead over Toronto from 4-0 to 5-0. That one was worth about three ten-billionths of an expected point for the Bulls. So that’s an overview. Anyone have any thoughts, criticisms, suggestions for further analysis along these lines?