Value bracket notes added at the bottom after the probability bracket and then my personal bracket Final Four that I used in my biggest pool.
The first part of the following example is from 4 years ago. I’m short on time and felt coming up with an example from this year’s bracket and making changes would be time better spent getting this out to you.
Filling out an NCAA Tournament bracket is more than just picking the first round and then matching your predicted winners against each other in round 2, and so on. The key is to find the team that has the best chance to be at each stage of the bracket, which may be different than just picking round by round. For example, let’s say that I have #3 seed Syracuse and #6 seed Ohio State both winning their first round games in the South region and I think that Ohio State has better than a 50% chance to beat Syracuse should they meet in round 2. That does not mean that it is best to move Ohio State into the next round in your bracket because it still may be more likely that Syracuse makes it to the 3rd round even if they have less than a 50% chance of beating the Buckeyes should they meet. I’ll explain. Let’s say my ratings have Ohio State rated higher than Syracuse and I give the Buckeyes a 53% chance of winning that match-up against the Orangemen should they meet (that’s actually not quite the case but let’s assume for the purposes of this illustration). What we need to calculate is the chance that each team makes it to the 3rd round rather than which team would win that head to head match-up. Syracuse has an easier first round opponent in Western Michigan (they’re favored by 13 points) than Ohio State does in Dayton (Ohio State is favored by 6) and that has to factor in to your decision of which team is more likely to get to round 3.
I give the Syracuse an 90% chance of winning their first round game against Western Michigan and I give Ohio State a 73% chance of getting past Dayton. To figure out who has the best chance to advance to the 3rd round among those 4 teams I must calculate the chance of beating each possible round 2 opponent times the chance that they’ll be facing each team. Let’s say I give Ohio State a 53% chance of beating Syracuse if they were to meet in round 2 and a 92% chance of beating Western Michigan. To figure out Ohio State’s chance of winning a second round game (should they get there) I must multiply their chance of beating Syracuse (.53) by the chance that they’ll face Syracuse (.90) and add that to the chance they’d beat Western Michigan (.92) times the chance that they’d face Western Michigan (.10). In mathematical terms that is (.53 x .90) + (.92 x .10) = .592, so Ohio State would have a 56.9% chance of winning their second round game if they got past the first round. To find the Buckeyes’ chance of getting to the 3rd round we simply multiply their chance of winning a second round game (.569) by their chance of getting to the second round (.73), which is .415 – so Ohio State has a 41.5% chance of getting to round 3 if I give them a 53% chance of beating Syracuse should they meet.
Now, let’s do Syracuse. We already said that the Orangemen have a 47% chance of beating Ohio State if they meet and let’s say they have a 71% chance of beating Dayton if the Flyers beat Ohio State (which is 27% likely). So, Syracuse’s chance of winning their second round game, should they get that far, is (.47 x .73) + (.71 x .27) = .535, or 53.5%. In our example, Syracuse has less of a chance (53.5%) to win in the second round (if they win their round 1 game) than Ohio State does (56.9%), but the Orangemen have a better chance of getting to round 2 (90% to 73%), so their chance of getting to round 3 is (.535 x .90) = .482, or 48.2%, which is higher than Ohio State’s 41.5% chance to get to round 3 even though I gave the Buckeyes a 53% chance of beating Syracuse straight up should they meet. Now imagine doing that for all possible combinations going forward each round. The math is mind-numbing – and thankfully programmed for me by my good buddy John (thanks John).
It is also important to induce variance into a bracket if you hope to win it all, as picking the favorite to win the championship may give you the best chance to pick the winner of the tournament, but it doesn’t give you the best expected return on your investment. For example, last year Kentucky had about a 42% chance of winning the tournament based on most analytics and I actually given the Wildcats only a 33% chance. However, 59% of nation (based on data from the Yahoo sports national pool) had picked the Wildcats as the winner, so there was no value in picking Kentucky to win it all even if they had the best chance to do so. If you’re in a small pool then it was okay to pick Kentucky but you’d need to induce some variance in your other Final Four picks to differentiate yourself from the others that had picked the Cats to win it all. The idea is not to pick other teams randomly but to find where the value is. Arizona, for instance, was being picked as the winner last year by only 6.5% of the nation and I give the Wildcats a 12% chance of winning the tournament while analytics guru Nate Silver gives them a 10% chance (turns out the public was correct on that one). So, there was value in picking Arizona to win even though they don’t have the best chance to win the tournament. In a 100 person pool would you rather have a 33% chance of being one of 59 people to pick Kentucky as the winner or a 12% chance with Arizona with only 6 or 7 other people in your pool having the Wildcats as the winner. Of course, making better picks along the way would help you in any tie breakers but your chances of winning your pool last year was still better with Arizona than it is with Kentucky even though the Wildcats had a better chance to win the tournament.
I will give you two versions of my brackets – one using the probability tree method as outlined above, which will predictably leave you with a lot of high seeds advancing (since they have an easier road to travel in previous rounds). The other is a version in which I induce some variance where there is value, as choosing calculated upsets can supply you with value against the rest of your pool. Of course, this version can leave you looking like an idiot some years and a genius every so often (I won with Duke in 2010 using this version when Kansas was an overwhelming favorite to win).
Some pools also give bonus points for upsets, so I’ll also give percentages of winning straight up for each first round game so you can calculate which team is best to take in a pool where bonus points for upsets are awarded. For instance, in one of my pools the first round is worth 5 points plus the difference in the seeds if you pick an upset correctly. In that pool if you correctly pick a 6 seed to win you get the 5 points but if you correctly pick the 11 seed to win then you get 5 points plus a bonus of 5 points for the difference in the seeds. So, an 11 seed with more than a 33.3% chance of winning the game straight up is worth choosing as long as you weren’t going to use the 6 seed to move on in round 2. To calculate the minimum chance of winning to choose the upset in a pool where bonuses are given you take the amount of points earned by picking the better seeded team to win and divide that by that number plus the points you’d get for picking the upset. In that case of the #6 and the #11 seed above, I get 5 points if I pick the 6 seed and they win and 10 points if I pick the 11 seed and they win, so in math terms the equation is 5/(5 +10) = .333.
Virginia (97%), Kansas State (60%), Kentucky (64%), Arizona (89%), Loyola-Chicago (54%), Tennessee (88%), Texas (76%), Cincinnati (94%), Xavier (98%), Florida State (51%), Ohio State (78%), Gonzaga (90%), Houston (74%), Michigan (85%), Texas A&M (56%), North Carolina (99%), Villanova (99%), Virginia Tech (58%), West Virginia (88%), Wichita State (95%), Florida (78%), Texas Tech (90%), Butler (58%), Purdue (99%), Kansas (96%), Seton Hall (68%), Clemson (62%), Auburn (70%), TCU (61%), Michigan State (95%), Rhode Island (60%), Duke (98%).
Virginia (78%), Arizona (65%), Tennessee 51% (Loyola 26%, Miami 22%), Cincinnati (70%), Xavier (60%), Gonzaga (65%), Michigan (47%) (Houston 42%), North Carolina (70%), Villanova (86%), Wichita State (51%) (West Virginia 46%), Texas Tech (49%) (Florida 43%), Purdue (70%), Kansas (76%), Auburn (37%) (Clemson 36%), Michigan State (74%), Duke (84%).
Virginia (47%) (Arizona 34%), Cincinnati (51%) (Tennessee 22%), Gonzaga (45%) (Xavier 26%), North Carolina (42%) (Michigan 22%, Houston 20%), Villanova (57%) (Wichita State 20%, West Virginia 18%), Purdue (41%) (Texas Tech 23%, Florida 22%), Kansas (60%), Duke (47%) (Michigan State 41%).
Elite 8 (to get to Final Four)
Virginia 28% (Cincinnati 26%, Arizona 19%), Gonzaga 28% (North Carolina 24%, Xavier 12%), Villanova (42%) (Purdue 16%), Duke (32%) (Michigan State 28%, Kansas 27%).
Final Four Games
Virginia 18% (Gonzaga 17%, Cincinnati 16%, Arizona 11%, North Carolina 11%)
Villanova 24% (Duke 19%, Michigan State 17%, Kansas 13%, Purdue 7%)
Michigan State 11%
North Carolina 5%
This next version is the most optimal for return on investment, as it focuses on finding value in comparison with the national consensus. You might consider mixing the bracket above, which is based on a probability tree, with the one below and the bigger your pool is the more variance you need to induce to differentiate yourself from others that are picking the same champion. Your version depends on how big your pool is. It’s okay to go with the favorites to win it all in smaller pools as long as you induce some value/variance in other rounds. You can also pick one of the favorites in a big pool, but you probably won’t have much of a chance of winning unless you can pick a lower seed successfully to reach the Final Four. In big pools you’d be better off finding value in your champion and in medium size pools it may be okay to take one of the favorites to win if you have some value in the final game or Final Four.
If you want to check out the ESPN National Pool percentages you can go to
I like to start looking for value with the Champion and work my way back
Each team is listed with my chance of each team winning versus the national vote. You might want to start here and look for value if you’re in a bigger pool then go backwards to create your bracket.
Villanova (16% vs 16% nation): Villanova is a good option for any size pool given their chance of winning match up with the percentage of pools they’ve been picked to win. No value here and in bigger pools you’ll have to add some value in the runner-up spot to differentiate yourself from the others that have also picked the Wildcats
Duke (12% vs 10% nation): The math likes Duke more than the public does, which is rare. I really hadn’t considered Duke at all until the simulation was run but the Blue Devils were the #1 team prior to the season starting. It all comes down to if they get past Michigan State. I personally feel like the Spartans will win that game but Duke has a better chance to get to that game, which is part of the reason they have a better chance to win it all.
Michigan State (11% vs 9% nation): There isn’t as much value as I had hoped there would be but Michigan State was my winner in the first bracket I filled out today – before I had finished fine-tuning my ratings and before the simulation was run.
Virginia (8% vs 19%): There is absolutely no value here, as the public has bought into the Cavaliers. The injury to 6th man De’Andre Hunter dropped Virginia’s rating by 1.5 points and the Cavs tend to underperform in the tournament because they can’t improve by playing harder since they already play as hard as possible on every defensive possession.
Gonzaga (8% vs 2% nation): There is a lot of value here and the Bulldogs are a great choice for a big pool as a way to differentiate yourself from the masses. Gonzaga has half the chance of winning as Villanova does but you’ll be competing with one-eighth the number of people for the top prize.
Cincinnati (7% vs 2% nation): There appears to be value here based on the math but I don’t really like Cincinnati because I don’t think they have any room for improvement given how good their defense already is.
Kansas (6% vs 8% nation): No value here and I don’t really like this Kansas team, who I think will lose to either Duke or Michigan State in the Regional Final.
Arizona (5% vs 5%): I actually think Arizona has a better chance to win the tournament that my ratings suggest since the Wildcats have a lot of room to improve defensively and they have the most dominant player in the field in Deandre Ayton. Taking the Cats in a big pool is a good strategy since you won’t be competing with that many people for the top prize should they win it all.
North Carolina (5% vs 7%): No value here and I think the Tarheels are have too many weaknesses (shooting and perimeter defense) to win 6 games in a row.
Purdue (3% vs 3%): I have no issue with picking Purdue to win it all if you’re in a big pool or if you want to blaze a trail as a true maverick in a small or medium sized pool. The Boilermakers have a good inside-outside balance on offense and their defense can be really, really good when they’re focused, which they should be.
Final Four (to get to the Championship game)
Here I’ll show you all of the options versus what the nation is picking. Remember, it’s okay to pick the most likely teams, even in bigger pools, if you have more variance/value added elsewhere. Your chances of cashing are going to be worse but your chances of winning will be better if you don’t take the favorites the rest of the nation is taking.
Virginia (18% vs 34%): I’ll be rooting for Virginia, as I’d love to see them win it all. I just won’t be picking them to do so.
Gonzaga (17% vs 5%): Tons of value here and if you’re not picking Gonzaga to win it all then you should consider having them in the Championship game or at least in the Final Four.
Cincinnati (16% vs 6%): There is still value based on the math but I think the math is overestimating the Bearcats’ chances.
Arizona (11% vs 11%): There is no value here based on the math but I like Arizona’s upside potential.
North Carolina (11% vs 16%): No value here.
Villanova (24% vs 32%): There isn’t any value to get to the Championship game so if you’re not going to pick them to win then best not to have them in the final game.
Duke (19% vs 18%): Not much value here and I’d leave them out of this game unless you’re picking the Blue Devils to win it all.
Michigan State (17% vs 16%): I like Michigan State’s chance to out-play the math.
Kansas (13% vs 15%): No value and no interest in this team even getting to the Final Four.
Purdue (7% vs 7%): Purdue is pretty good option to have in the final game to add variance if you’re picking one of the favorites from the other side of the bracket to win it all.
I was planning on continuing with each round, but I’m running out of time and thought it best to stop now and send this out to you. Also, I’m sure you get the idea by now. Look for value by comparing my percentages to the percentages that the public is backing a team. This year I’m using ESPN’s Bracket pick percentages, but you can use whatever source you’d like.
Personal Bracket (Big Pool Edition).
My Final Four in my biggest pool, where I needed to take more chances to differentiate myself from the masses is as follows
Arizona from the South
Gonzaga from the West
Villanova from the East
Michigan State from the Midwest
Final Four Games
Gonzaga over Arizona
Michigan State over Villanova (Okay to reverse that in medium sized pools since the other Final Four teams selected adds enough variance with value that you can pick one of favorites to win it all).
Michigan State (or Villanova)