Considering there are fewer than 800 players in the NHL, your chances of making it to the big show, and then becoming a star, fall somewhere around winning the lottery or seeing snow in Florida in the middle of July.
For those players who aren't blue-chip prospects, the odds are even worse. That's what makes this list even more remarkable. In this edition of 10 Degrees, we count down in reverse order the top active overlooked draft prospects-turned-stars.
10. Steve Sullivan
Selected by New Jersey; Ninth round (233rd overall); 1994 draft
For NHL general managers, size does matter. Despite scoring 51 goals and collecting almost two points per game in the OHL, the 5-foot-8, 155-pound Sullivan was passed over more than 200 times before hearing his name called at the 1994 draft. Finally, after averaging more than a point per game in nearly three seasons in the AHL, the speedy forward was given his NHL shot and has never looked back. Sullivan has posted eight straight 20-goal seasons. Of the 232 players chosen ahead of him in 1994, only five have scored more goals (Daniel Alfredsson, Milan Hejduk, Patrik Elias, Jeff O'Neill, Ryan Smyth).
Sullivan has scored 180 goals since being put on waivers by the Toronto Maple Leafs in 1999.
9. Henrik Lundqvist
Selected by New York Rangers; Seventh round (205 overall); 2000 draft
In the third round of the 2000 draft, the Dallas Stars selected Joel Lundqvist. Maybe they meant to say Henrik. The identical twins have always had a sibling rivalry, so when Joel was taken four rounds and 147 picks before Henrik, it didn't sit well with the newest Ranger. What bothered Henrik even more was that 21 goalies were drafted ahead of him. The last laugh has been on the GMs and scouts who didn't see any promise in this young netminder. Of those goalies taken ahead of Lundqvist, 13 have never played in the NHL and only two (Roman Cechmanek and No. 1 overall pick Rick DiPietro) have more NHL wins. With two Vezina nominations and an Olympic Gold medal to date, it hasn't taken long for the 25-year-old Lundqvist to prove he belongs in the NHL.
In 2005-06, he won 30 games, breaking the Rangers' rookie goaltending record of 29 wins that was previously held by Jim Henry (1941-42) and Johnny Bower (1953-54).
8. Jason Blake
Name a North American hockey league and chances are Jason Blake has played in it. A sniper for the USHL's Waterloo Blackhawks and a star for North Dakota, Blake still wasn't given a chance by any NHL team. Then, in 1999, the small-but-gritty forward was signed by the Los Angeles Kings at age 25. Blake played just one game that season, but he scored a goal in his NHL debut. It was a sign of things to come. Since then, Blake has collected four straight 20-goal seasons, including a career-high 40 goals last season with the Islanders. He was also a member of the U.S. Olympic team in 2006.
On July 1, 2007, he signed a five-year $20-million deal with the Maple Leafs.
7. Pavol Demitra
Selected by Ottawa; Ninth round (227th overall); 1993 draft
Considered too soft and too small to succeed in the NHL, Pavol Demitra didn't have to be as good as other players, he had to be better. Before landing an everyday job in the NHL, Demitra took a circuitous route from the Slovakian elite league to PEI in the AHL to Las Vegas and Grand Rapids in the IHL. Eleven solid NHL seasons later, Demitra has proven even the best hockey minds make mistakes. Playing mostly on teams' first lines, he has posted nine straight 20-goal seasons.
Still unproven in the NHL in 1996, Demitra was traded from Ottawa to St. Louis for Christer Olsson. The final tally? Olsson -- 25 games, two goals for the Senators. Demitra -- 494 games, 204 goals for the Blues.
6. Nikolai Khabibulin
Selected by Winnipeg; Ninth round (204th overall); 1992 draft
Fifteen goalies were taken ahead of Nikolai Khabibulin in 1992. Those goalies have fewer NHL wins than the "Bulin Wall" combined. After playing three seasons in Russia followed by a brief stint in the IHL and AHL, Khabibulin was ready to take flight with the Winnipeg Jets in 1994-95. Since then, he has been one of the game's most consistent goalies. He has won at least 25 games in a season seven times and led the Lightning to the 2004 Stanley Cup after posting a 1.71 goals-against average over 16 games.
A four-time NHL All-Star, Khabibulin was the first Russian goalie to win the Stanley Cup.
5. Brian Rafalski
Mobile defensemen who can play on special teams and effectively move the puck out of their own zone are apparently not a commodity in the NHL. At least they weren't in 1991, the year Brian Rafalski was not drafted. The Michigan native was an NCAA First-Team All-Star that went on to win a national championship with the University of Wisconsin. And he still didn't get a shot in the bigs. After four years in Europe, where he was the first non-Finnish player to win MVP honors in the Finnish elite league, Rafalski finally made his way to the NHL after being signed by the Devils. The 26-year-old rookie led all first-year defensemen in plus-minus and picked up the first of two Stanley Cup rings in New Jersey.
The three-time NHL All-Star signed a five-year $30-million deal with Detroit this past offseason.
4. John Madden
When you share the same name as an NFL coaching, broadcasting and video game legend, you're bound to get lost in the shuffle. That was the case for John Madden. After never getting the chance to play major junior in Canada and going undrafted, the forward got a shot at the University of Michigan at age 20. With the Wolverines, Madden carved out as niche as a quality two-way player, winning a national championship in 1996 and setting the NCAA record for most career short-handed goals. The national exposure helped land Madden a contract with the Devils. Ten years and two Stanley Cups later, there is no doubting Madden is one of the most effective players in the game. He's also been durable, missing only 22 games over the last seven seasons.
He won the 2001 Frank J. Selke Trophy as the league's best defensive forward. He was runner-up for the award in 2003 and 2004.
3. Henrik Zetterberg
Selected by Detroit; Seventh round (210th overall); 1999 draft
Henrik Zetterberg, the NHL's current scoring leader, barely registered a pulse as a junior prospect eight years ago when he was taken 209 picks after No. 1 overall selection Patrik Stefan. Overshadowed by the Sedin twins in his native Sweden, this import almost never made the trip across the Atlantic to play professional hockey. Once he arrived in 2002-03, Zetterberg became an instant star. He had 22 goals and 44 points over 79 games, finishing as the runner-up for the Calder Trophy and proving to be one of the flashiest and most talented players in the league. It's fair to say Zetterberg should have cost at least a few GMs their jobs by being overlooked in 1999.
After scoring his 100th career goal last season against Phoenix, Coyotes coach Wayne Gretzky said Zetterberg is "probably the most underrated player in the league."
2. Martin St. Louis
In the pre-lockout era, most NHL scouts and GMs coveted size more than speed. That may explain how one of the game's most skilled players almost never had an NHL career. Despite putting up record-setting scoring numbers and being a three-time Hobey Baker finalist at Vermont, St. Louis (5-foot-8, barely 170 pounds) was passed over at the 1997 NHL draft. Averaging almost a point per game in the IHL, the Calgary Flames finally opened the door for St. Louis, but just a crack. After three years in the Flames organization, mostly in the AHL, St. Louis was released. So, at age 25, St. Louis' NHL future looked bleak ... until the last-place Tampa Bay Lightning came calling. Three seasons later in 2003-04, the forward that no one wanted led the Lightning to a Stanley Cup.
In 2003-04, St. Louis became the first player since Wayne Gretzky (1987) to win the Art Ross and Hart Trophies and the Cup in same season.
1. Dominik Hasek
Selected by Chicago; 10th round (199th overall); 1983 draft
It seems hard to believe that one of the all-time great goalies was for years considered undersized, unskilled and too unorthodox to play in the NHL. Despite being selected as the top goaltender at the World Junior Hockey Championship, which is generally considered the best litmus test for draft prospects, Hasek couldn't convince NHL GMs he could succeed at the next level. These are the same GMs who made Brian Lawton, Andrew McBain and Norm Lacombe top-10 picks that draft year. For years after he was drafted, Hasek was still treated like a second-rate NHL prospect. He was named Player of the Year in the Czech elite league three times before he was given a shot in the NHL. Hasek was 28 before he wrestled away a No. 1 job in the bigs, but he's never looked back.
In his first season as a No. 1 starter (thanks to a Grant Fuhr injury), Hasek won the first of six Vezina Trophies in 1993. He has also won two Hart Trophies and a Stanley Cup.
ESPN reporter David Amber is a frequent contributor to ESPN.com.