After comparing the numbers of Crosby, Jagr and Ovechkin at the knockout stage of best-on-best international tournaments earlier in this thread I decided to also take a look at the numbers of the other available players here. The ones who played in an era with best-on-best tournaments available to them that is. Now the sample sizes are obviously small but I still think that it is interesting and worthwhile to do since I personally consider the knockout stage at best-on-best international tournaments to have been the highest level of competition available to players over the last 40 or so years. With this said it is not as if I base my rankings in this project that much on how the players did in the knockout stage of best-on-best tournaments but if the overall resume of two players are close to each other it is something that I could look at as deciding factor along with the overall "clutch" play of the player.
Potvin
Canada Cup 1976: 2 gp, 1 g, 3 a, 4 pts
Canada Cup 1981: 2 gp, 0 g, 1 a, 1 pts
Total at best-on-best tournaments knockout stage: 4 gp, 1 g, 4 a, 5 pts
Total at best-on-best tournaments overall: 14 gp, 3 g, 13 a, 16 pts
Bourque
Canada Cup 1981: 2 gp, 0 g, 0 a, 0 pts
Canada Cup 1984: 3 gp, 0 g, 1 a, 1 pts
Canada Cup 1987: 4 gp, 1 g, 2 a, 3 pts
Olympics 1998: 3 gp, 0 g, 1 a, 1 pts
Total at best-on-best tournaments knockout stage: 12 gp, 1 g, 4 a, 5 pts
Total at best-on-best tournaments overall: 30 gp, 4 g, 16 a, 20 pts
Messier
Canada Cup 1984: 3 gp, 1 g, 1 a, 2 pts
Canada Cup 1987: 4 gp, 0 g, 2 a, 2 pts
Canada Cup 1991: 3 gp, 2 g, 3 a, 5 pts
World Cup 1996: 3 gp, 0 g, 1 a, 1 pts
Total at best-on-best tournaments knockout stage: 13 gp, 3 g, 7 a, 10 pts
Total at best-on-best tournaments overall: 32 gp, 6 g, 20 a, 26 pts
Lidström
Canada Cup 1991: 1 gp, 0 g, 0 a, 0 pts
World Cup 1996: 1 gp, 0 g, 0 a, 0 pts
Olympics 1998: 1 gp, 0 g, 0 a, 0 pts
Olympics 2002: 1 gp, 0 g, 1 a, 1 pts
World Cup 2004: 1 gp, 0 g, 0 a, 0 pts
Olympics 2006: 3 gp, 1 g, 3 a, 4 pts
Olympics 2010: 1 gp, 0 g, 0 a, 0 pts
Total at best-on-best tournaments knockout stage: 9 gp, 1 g, 4 a, 5 pts
Total at best-on-best tournaments overall: 34 gp, 8 g, 12 a, 20 pts
Hasek
Canada Cup 1987: 1 gp, 32 saves on 37 shots, 0.865
Olympics 1998: 3 gp, 82 saves on 84 shots, 0.976
Olympics 2002: 1 gp, 26 saves on 27 shots, 0.963
Total at best-on-best tournaments knockout stage: 5 gp, 140 saves on 148 shots, 0.946
Total at best-on-best tournaments overall: 26 gp, 606 saves on 668 shots, 0.907
And here are the numbers of Crosby, Ovechkin and Jagr again. This time with their overall stats included as well.
Jagr
Olympics 1998: 3 gp, 1 g, 1 a, 2 pts
Olympics 2002: 1 gp, 0 g, 0 a, 0 pts
World Cup 2004: 2 gp, 0 g, 0 a, 0 pts
Olympics 2006: 3 gp, 0 g, 2 a, 2 pts
Olympics 2010: 2 gp, 0 g, 0 a, 0 pts
Olympics 2014: 2 gp, 0 g, 1 a, 1 pts
Total at best-on-best tournaments knockout stage: 13 gp, 1 g, 4 a, 5 pts
Total at best-on-best tournaments overall: 41 gp, 12 g, 15 a, 27 pts
Ovechkin
World Cup 2004: 1 gp, 0 g, 0 a, 0 pts
Olympics 2006: 3 gp, 1 g, 0 a, 1 pts
Olympics 2010: 1 gp, 0 g, 0 a, 0 pts
Olympics 2014: 2 gp, 0 g, 0 a, 0 pts
World Cup 2016: 1 gp, 0 g, 0 a, 0 pts
Total at best-on-best tournaments knockout stage: 8 gp, 1 g, 0 a, 1 pts
Total at best-on-best tournaments overall: 23 gp, 10 g, 5 a, 15 pts
Crosby
Olympics 2010: 4 gp, 2 g, 0 a, 2 pts
Olympics 2014: 3 gp, 1 g, 0 a, 1 pts
World Cup 2016: 3 gp, 1 g, 5 a, 6 pts
Total at best-on-best tournaments knockout stage: 10 gp, 4 g, 5 a, 9 pts
Total at best-on-best tournaments overall: 19 gp, 8 g, 12 a, 20 pts
When it comes to their performances at the knockout stage of best-on-best international tournaments the player I would rank first among the available players is Dominik Hasek. His Nagano performance in 1998 when he pretty much turned into a wall during the knockout stage is one the more impressive performances that I have ever seen. Saving 82 out of 84 shots against USA, Canada and Russia is very impressive. Not to mention his shootout performance against Canada.
Next I would probably have Crosby and Potvin. Crosby may not have been overly impressive at the knockout stage in 2010 and 2014 even if he did step up and scored the golden goal in 2010. He really stepped up in 2016 though with a truly remarkable performance where he produced at a very high level all throughout the tournament. Potvin had a very impressive tournament in 1976 and kept producing against a strong Czechoslovakian team in the finals. In 1981 Potvin also had a strong tournament even if he really struggled with the speed of the top Soviet forwards in the final. But that is really the only knock on his best-on-best tournament resume.
Then I would rank the best-on-best resume of Mark Messier. He really had a impressive knockout stage in 1991 and generally put up relatively strong offensive numbers combined with everything else that he brough to the table.
Next up Lidström and Bourque. I had expected Bourque to have stronger numbers during the knockout stage. In fact Bourque was one of the players that regressed the most offensively from the group stage (15 pts in 18 gp) to the knockout stage (5 pts in 12 gp). So somewhat surprisingly to me Lidström was more productive offensively on a per game basis. On the other hand most of Lidströms offensive production came during his very strong 2006 Olympic tournament and outside of that tournament Lidström and Tre Kronor experienced many heartbreaking losses. Still overall the best-on-best resumes of these two are probably on a pretty similar level.
Next I have Jagr whose best-on-best resume is rather average for a player of his quality. Both at the knockout stage and overall. Like I mentioned earlier I think that Jagr having by far the least support offensively on the national team (out of the players in this round) can help explain his somewhat average numbers to some degree. When including the group stage Jagr actually does have the most points scored in best-on-best tournaments out of the players in this round with 27 but that is rather a testiment to his longevity than anything else.
As I mentioned in my previous post I find Ovechkins numbers to be very underwhelming. Especially his regression from the group stage (14 pts in 15 gp) to the knockout stage (1 pts in 8 gp). His weak knockout stage numbers is also what in my opinion makes Ovechkins best-on-best resume the clearly weakest out of the players in this round.
Even if they already are on the list here are Gretzkys and Lemieuxs best-on-best numbers at the knockout stage. Just for fun.
Gretzky
Canada Cup 1981: 2 gp, 0 g, 1 a, 1 pts
Canada Cup 1984: 3 gp, 2 g, 3 a, 5 pts
Canada Cup 1987: 4 gp, 1 g, 10 a, 11 pts
Canada Cup 1991: 2 gp, 1 g, 1 a, 2 pts
World Cup 1996: 4 gp, 0 g, 2 a, 2 pts
Olympics 1998: 3 gp, 0 g, 3 a, 3 pts
Total at best-on-best tournaments knockout stage: 18 gp, 4 g, 20 a, 24 pts
Total at best-on-best tournaments overall: 45 gp, 20 g, 48 a, 68 pts
Lemieux
Canada Cup 1987: 4 gp, 6 g, 4 a, 10 pts
Olympics 2002: 3 gp, 0 g, 4 a, 4 pts
World Cup 2004: 3 gp, 1 g, 3 a, 4 pts
Total at best-on-best tournaments knockout stage: 10 gp, 7 g, 11 a, 18 pts
Total at best-on-best tournaments overall: 20 gp, 14 g, 15 a, 29 pts