Odds themselves have been around for many hundreds of years. Since the very first day when man competed there was someone picking who would win and offering a handicap if one player or team was clearly better.
The formal use of odds for betting is thought to be at least 500 years old. It can be found in “Henry IV” by William Shakespeare:
“Knew that we ventured on such dangerous seas
That if we wrought out life ’twas ten to one”
The invention of the point spread is much more recent. This advent can be traced back to the mid 20th century and is accredited to inventor Peter K. McNeilly. I do have to add that the idea of handicapping a better player by subtracting points has probably been around much longer but McNeilly was the first to make it official.
Betting and handicapping is in human nature, there is no doubt. It only seems logical that an industry would arise and offer services allowing man to put his skills to the test. That basically sums of the modern day sportsbook.