Although the opportunity exists to pick some staggering upsets, experienced players have recognized that this is mostly unnecessary. Say, for example, you feel that the first round matchup between #15 seed NoName College and #2 seed Powerhouse University is a candidate for an upset...
P.U. is predicted to advance into the round of 8. Therefore you can assume that most players will be assigning it a number between 57 and 60. If you recklessly picked this upset, and gave P.U. a number from 1-32, you would likely be risking your entire entry on this one game. A far better strategy would be to assign P.U. 57 pts, and NNC 32 pts. Note that this scenario predicts P.U. to win 3 games, and NNC to lose in the first round. If the upset does not materialize, you have lost nothing, as you have still picked both teams within the same win/loss bracket as most everyone else. If the upset does occur however, you stand to achieve a modest gain. Other players can be expected to give NNC a number from 5-15, so you will gain around 20 pts on most of the field. Also, you figure to have lost less on P.U. than most other players. Furthermore, if NNC continues to win, you will keep gaining on the other players.
A more extreme position would be to give NNC 32 pts but give P.U. 56 pts instead of 57. This is more extreme because now you have picked P.U. to only win 2 games instead of 3. This frees you to give a #3 #6, or #7 seed that coveted number from 57-60. Now, if P.U. does indeed go down in the first round, there will have to be an upset team in the final 8. You have likely already gained significantly on NNC (by giving it a higher number than most) and P.U. (by giving it a lower number than most), and have the chance to gain even more if you predicted the team that actually makes it to the round of eight. The further down you place P.U. (53, 50, etc.), the more you stand to gain. Therefore, it is sound strategy to predict an upset by placing it high or low within the same bracket as others are likely to put it. Think about the numbers as groups within each bracket. If you are convinced a team CAN'T win more than one game, give it a number close to 33. Just because you think that team is better than a team ranked 45 has no bearing on your score.
Of course the above strategy by itself will not win the pool for you. To come out on top of 300 or so entries, you are going to have to make some good predictions, and be correct. It is just important to remember that is usually not a good idea to put all your eggs in one basket. By all means pick some upsets, but pick them in a way that will not cost you everything if you are wrong early.
Your 1st round upset teams might have the numbers 28-32. You didn't pick them to win, but your entry is still fundamentally intact if they lose. Similarly, favored teams you think might lose in the first round could be given the numbers 33-36. It wouldn't bother you much if they lost in the first round, but you won't be hurt unless they win a 2nd game.
2nd round upset teams might have the numbers 46-48 for the same reason. Favored teams can be given 49-51. You lose nothing if the favorite wins, and will lose less than most if the favorite loses. The most important numbers in the collection of 64 are: 32, 33, 48, 49, 56, 57, 60, 63, and 64. Good players often try to position themselves to win big and lose little by clever manipulation of these numbers.
Another VERY important consideration that many players neglect to factor into their strategy is LOCATION. While first round point spreads take geography into account, expert handicappers understand that knowing where the SECOND and THIRD rounds will be played can be incredibly important too. Let's say you were astute enough to predict that Upstart U (a #6 seed) would advance past Overrated State (a #3 seed), to the third round, but would have no chance against Perennial Power College (a #2 seed). While that may be true at a neutral site, perhaps you failed to notice that U.U. was scheduled to play their third round 45 miles from their home court. Perhaps P.P.C. was not quite as big a favorite as you thought. You might want to give U.U. a few more points.
One final thing to keep in mind is to not waste relatively high numbers on teams that cannot continue winning due to unlucky bracket placement. No matter how strong, the numbers placed on an 8 or 9 seed should not be too high if neither team has a chance against the #1 seed in the next round. Similarly, #7/#10 matchups have to meet a usually strong #2 seed in the second round. It is wasteful to give one of them a number in the high 40's if they can't realistically win that second game. Save those numbers for a #6 seed or a Cinderella #13 that might win a second game if it upsets its 1st round opponent.
I realize that some of these tips contradict others. Still, every year there are dozens of entries which have very little chance, and a handful which have NO chance. Make sure your 61, 62, 63, and 64 teams are in different regions. Make sure your 63 does not play your 64 in the semi-finals. Inspect that if you predicted everything right, you do not have two teams above 50 playing each other in the 2nd round. Sounds simple enough, but these are common mistakes people make every year. Try to pick a few upsets that gain the most and lose the least. And the most important tip - Be Lucky!