1. A method for implementation by at least one programmable processor, the method comprising: assembling, over a network connection by a server, a collection of data from at least one data provider, the assembling comprising: first querying, by the server over the network connection through an application programming interface, the at least one data provider for primary data corresponding to a player, the primary data comprising at least one of a set of statistics for the player, a limiting factor for the player, and a location of an upcoming event that includes the player; second querying, by the server over the network connection, the at least one data provider for secondary data corresponding to the player, the secondary data comprising at least one of a prediction and the location; and third querying, by the server over the network connection through another application programming interface, the at least one data provider for tertiary data, the tertiary data comprising a weather condition at the location; adding, as an attribute to an internal object stored at the server, a base value of the player based on at least the primary data; mapping a modifier to a second attribute of the internal object, the modifier based on at least a portion of the secondary data and the tertiary data; generating a projected value from the base value, the generating comprising: first applying the modifier to the second attribute according to the mapping; and second applying a rule converting the modified second attribute to a projected value; generating, by an automated projection engine, a plurality of internal objects according to constraints comprising: a first constraint comprising a sum of the limiting factors of the plurality of internal objects that does not exceed a maximum factor; and a second constraint comprising a sum of the projected values of the plurality of internal objects that is a maximum, subject to the first constraint, the generating further comprising: maintaining an approximately constant computational time when executing a number of iterations randomizing column positions of a column-based list comprising a number of rows having entries of decreasing projected values of the plurality of internal objects, the maintaining of the approximately constant computational time based on limiting the number of iterations to be inversely proportional to the number of rows, the generation of the plurality of internal objects further comprising sequentially selecting a single entry from each row to be added to the plurality of internal objects, subject to the first constraint; transmitting, by the server over the network connection to a mobile application running on a mobile device, application data comprising a list representing the plurality of internal objects; and displaying, at a graphical user interface of the mobile device, a vertical band having a length based on a standard deviation of an actual point value corresponding to one of the plurality of internal objects, the standard deviation calculated from the primary data over a historical window; a first graphical element at a first location collinear with the vertical band and based on the projected point value of the corresponding one of the plurality of internal objects; and a second graphical element at a second location collinear with the vertical band and based on the actual point value corresponding to an event that the one of the plurality of internal objects is associated with.