Big 3 Sports Odds

Warning: rough analysis with flaws ahead!

Imagining a potential athlete's career trajectory, one could draw up a rough estimate of potential earnings for Major League Baseball (MLB), National Basketball League (NBA), or National Football League (NFL) salaries. Yahoo posted average salaries for each sport (http://sports.yahoo.com/nba/news?slug=ycn-10423863) and Bleacher Report posted average career lengths for each sport (http://bleacherreport.com/articles/1109952-nfl-mlb-nhl-mls-nba-which-leagues-and-players-make-the-most-money):

League	Avg Career	Avg Salary	Avg Earnings
MLB	5.6	$3,310,000	$18,536,000
NBA	4.8	$5,150,000	$24,720,000
NFL	3.5	$1,900,000	$6,650,000

Of course, this simplistic view ignores several important distinctions between the sports. In particular, the number of opportunities available are unequal which alters the probability of success in each sport. A quick comparison of the difference between the number of Division I college athletes in each sport to the number of players drafted approximates a probability of the average player finding themselves drafted:

League	NCAA Div-I players	2012 Draft picks	Draft Chance
MLB	10,093	1,238	12.3%
NBA	5,265	60	1.1%
NFL	26,737	253	0.9%

The deep minor league baseball system enables MLB to recruit more than a complete roster of new players every year. The NBA only adds a couple of bench players per team per year and the NFL adds several new players. Un-drafted free agents definitely skew these figures but the approximation demonstrates a sense of the scale of difference in the ability for an amateur athlete to find themselves signed with a pro team in each league. However, the deep MLB minor league system also clogs and slows the path from signing to competing in the pro league. I checked two rounds of the 1997, 2002, 2007, and 2012 drafts and arrived at the unscientific and unproven approximation for the chance a drafted player has a chance to play at the pro level of each league:

League	Pro Chance
MLB	21.0%
NBA	98.0%
NFL	82.0%

Essentially, NBA draft assures playing time in the NBA, NFL draft almost assures NFL playing time, but MLB - which routinely drafts players out of high school - has a very low likelihood that the drafted player ever actually plays for a MLB team. If you follow this logic, piecing together the percentages as probability of getting drafted times probability of making pro playing time, gives an aggregate probability of a pro career:

League	Draft Chance	Pro Chance	Probability
MLB	12.3%	21.0%	2.6%
NBA	1.1%	98.0%	1.1%
NFL	0.9%	82.0%	0.8%

These percentages ring true to me - making a baseball career seems a little easier given the opportunities afforded, NBA is tougher, but the sheer volume of football players makes an NFL career a little difficult to attain than the other two sports. Multiplying these probabilities by the average earnings potentials (the first data presented in this blog) gives a somewhat more realistic expected earnings potential for the average athlete among the three sports (note these salary figures were all based on outdated 2011 data sets but the ratios are what are relevant here):

League	Avg Earnings	Probability	Expected Earnings
MLB	$18,536,000	2.6%	$477,459
NBA	$24,720,000	1.1%	$276,075
NFL	$6,650,000	0.8%	$51,599

These figures makes sense (at least to me). The NFL employs the most players so earnings per player are lower and the abundance of college football talent makes for shorter careers with less money made by the average football player. NBA employs the fewest number of players so the union commands high wages for the few players able to break into the league. MLB enriches more players with a little more opportunities available and higher wages than football. Of course these figures apply towards the average, without regard to talent or position. Scarcity of course alters the situation and an elite talent may not need to factor in a concept like a probability of making the pro team, and circumstances of course dictate actual results, but at least this rough analysis bears out the notion that MLB is a little safer, but slower, opportunity for a gifted athlete... Maybe something to consider for a teenager with far more talents than I ever had...