When did the professional standards for sports come to be - formal umpires, written rules, and the organizations (NFL, NLB, NBA, etc.) that enforce them and create rules for trades, contracts, and business practices as well as rules for playing the sports?
This would vary by sport, and depend on the origin of said sport. Speaking from a North American viewpoint, something like baseball would have had formalised rules and regulations in place from around the 1860s with the formation of the first leagues, though the office of commissioner was not established until 1920.
Similarly in hockey (which I am much more able and comfortable to go into finer detail), the first set of rules (the "McGill Rules") were published in 1877, two years after the first recognised game of hockey. However it would not be until 1904 that a professional hockey league was formed, and 1917 before the current NHL was established, complete with the modern office of president (renamed commissioner in 1993). Even so the amateur leagues that existed, of which a successive chronology can be traced from 1886 to the formation of the NHL, had proper rules and regulations, and owners of teams were most definitely interested in maintaining order so as to not disrupt what was, in Canada at least, a somewhat lucrative business.
While this field is understandably under-studied, there are two very decent books on the early development of the business side of hockey that at least provide some further insight into this:
*Lords of the Rinks: The Emergence of the National Hockey League, 1875-1936 (2005) by John Chi-Kit Wong. Wong is an academic who specialises in sports history, and this book I believe is the final result of his PhD thesis. It looks at the organisational history of hockey from the beginnings until the consolidation of power by the NHL in the early 1930s, and is a real fascinating read.
*Deceptions and Doublecross: How the NHL Conquered Hockey (2002) by Morey Holzman and Joseph Nieforth. This is more focused on the business side of the early NHL, and really goes into the details of how ruthless it was in those years. In particular Holzman and Nieforth show that Eddie Livingstone, who owned a team in the NHA (predecessor of the NHL) was unfairly targeted (it was dislike and distrust of Livingstone by the others that actually led to the creation of the NHL; it forced him out of the league).
There is another book just recently published, Joining the Clubs: The Business of the National Hockey League to 1945 (2015) by J. Andrew Ross that promises to be worthwhile (he's also an academic, and this was published by a university press), but I haven't had a chance to read it yet so can't fully say how useful it would be.
With regards to Association Football, the first codified rules for soccer were created at Trinity College, Cambridge in 1848. The rules were radically different from the game as we know it, as players couldn't run with the ball and had to rely on passing. In 1863 a group of London clubs got together to create a unified rule system (The Laws of the Game) for all the clubs and to create a governing body to implement them, the Football Association.
Despite this, the Welsh FA, the Scottish FA and the Irish FA all operated somewhat different rules so in 1886 all four groups banded together to create the International Football Association Board, which exists to this day. In response to the growing popularity of the sport (largely fueled by British emigration and trade) FIFA was formed as the representative body for all the other nations and in 1913 was admitted to the IFAB.
While the Laws have adopted some more modern touches, the 1863 rules remain the core principles.
Sources: FIFA publication on the Laws of the Game, Inverting the Pyramid: The History of Football Tactics by Jonathan Wilson.