The first part of the following example is from 2 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.

**Round 1**

Oregon (99% chance of being in the next round), Cincinnati (56%), Baylor (76%), Duke (82%), Texas A&M (89%), Texas (72%), VCU (61%), Oklahoma (95%), Kansas (100%), Connecticut (56%), Maryland (83%), California (82%), Miami (94%), Wichita State (50%, the nation is picking Arizona at a high rate so value is with Wichita), Iowa (78%), Villanova (97%), North Carolina (99%), Providence (53%), Indiana (92%), Kentucky (94%), West Virginia (86%), Notre Dame (60%), Wisconsin (52%), Xavier (94%), Virginia (99%), Butler (57%), Purdue (78%), Iowa State (80%), Utah (80%), Gonzaga (51%), Dayton (52%), Michigan State (98%).

**Round 2**

Oregon (76%), Duke (46%, Baylor 42%), Texas A&M (56%, Texas 35%), Oklahoma (78%), Kansas (84%), California (47%, Maryland 44%), Miami (47%, Wichita 27%, Arizona 26%), Villanova (66%, Iowa 30%), North Carolina (89%), Kentucky (63%, Indiana 35%), West Virginia (64%, Notre Dame 22%), Xavier (62%, Wisconsin 20%), Virginia (84%), Purdue (46%, Iowa State 42%), Utah (39%, Gonzaga 29%, Seton Hall 28%), Michigan State (86%).

**Round 3**

Oregon (52%, Duke 18%, Baylor 17%), Oklahoma (52%, Texas A&M 26%, Texas 13%), Kansas (61%, Cal 17%, Maryland 14%), Villanova (40%, Miami 21%, Iowa 15%, Wichita 12%, Arizona 12%), North Carolina (59%, Kentucky 29%), West Virginia (36.5%, Xavier 35.8%), Virginia (62%, Purdue 17%, Iowa State 13%), Michigan State (67%, Utah 11%).

**Elite 8 (to get to Final Four)**

Oregon (31%, Oklahoma 30%, Texas A&M 12%, Duke 8%, Baylor 8%), Kansas (41%, Villanova 19%, Cal 8%, Miami 8%), North Carolina (44%, Kentucky 19%, West Virginia 13%, Xavier 12%), Michigan State (40%, Virginia 37%, Purdue 7%).

**Final 4 Games**

Kansas (29%, Oregon 15%, Oklahoma 14%, Villanova 11%), North Carolina (26%, Michigan State 24%, Virginia 21%, Kentucky 9%).

**Champion**

North Carolina (16%, Kansas 15%, Michigan State 14%, Virginia 13%, Oregon 6%, Oklahoma 6%, Villanova 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. 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 longshots in the final game or Final Four.

If you want to check out the Yahoo National Pool percentages you can go to

https://tournament.fantasysports.yahoo.com/t1/group/all/pickdistribution

I like to start looking for value with the Champion and work my way back

**Champion**

Once again, 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.

North Carolina 16%: The nation is only 15% on UNC, which I find surprising.

Kansas 15%: The nation is 31% on the Jayhawks to win so avoid picking them in any size pool unless you were born in Kansas and will get disowned by your kin if you don’t pick them.

Michigan State 15%: The Spartans are actually my pick to win this tournament but I am not alone. The nation is picking them 27% so in my bigger pools I will avoid taking them and would only take them in my smaller pools, in which I’d mix in more value in other spots.

**Virginia 13%**: This is where the value is, as only 4% of the nation is picking the Cavaliers to cut down the nets. This is the team that I will go with in my bigger pools because if they do win then I won’t be competing with that many other people. If you pick Virginia then you don’t need to add as much value induced variance in other parts of your pool.

Oregon 6%: The Ducks are only getting the love from just over 3% of the nation so I have no issue if you want to support the Pac 12 and take a flyer on Oregon in a really big pool. Chance are if the Ducks win then you won’t be competing with that many people for the big prize.

Oklahoma 6%: Just over 4% of the public is taking the Sooners and while there is value I really don’t like this pick. The Sooners rely too much on their 3-point shooting and it’s tough to go 6 games, including 5 against good competition, without having a randomly bad shooting game.

Villanova 5%: Only 2.4% of the public is on the Wildcats but they take far too many 3-point shots (only are actually worse than average at making 3-pointers), so the Wildcats are likely to have a game where they’re not shooting as well and that will send them home earlier than expected once again.

Other longshots: If you’re in a really huge pool and want to shock the world and claim the big prize then you might consider Miami, Cal, Maryland, Purdue or Wichita State as teams with enough talent to win it all and enough game to compete with any team in the nation.

**Final Four**

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.

Kansas 29% vs 59% nation: If you’re not picking Kansas to win it all then don’t pick them to get this far since there is no value in that.

Oregon 15% vs 8% nation: Taking the Ducks to reach the Championship game adds some value if you want to take one of the 3 favorites to win it all.

Oklahoma 14% vs 13% nation: No thanks. I’m not high on the Sooners chances if they happen to have a 30% game from 3-point range.

Villanova 11% vs 6.5% nation: There is value here mathematically but I don’t trust the Wildcats style of play (too many 3-point attempts) and this team consistently disappoints for that reason since all it takes is one off shooting night from long range against a good team to end it for them.

North Carolina 26% vs 26% nation: I’ve got no issues if you want to take North Carolina here. If you pick them to win and you’re in a big pool then you might consider taking Oregon to advance to the final too to add some value/variance to your bracket.

Michigan State 24% vs 48% nation: It’s too bad that my personal favorite to win it all is getting too much attention. But, if you want to pick Michigan State as your winner then you certainly need to pick a sleeper as the other championship game participate if you want a better chance to win a bigger pool.

Virginia 21% vs 9% nation: If Virginia is not your pick to win the Championship as a value play then the Cavaliers would be a good choice to advance to the finals if you want to pick Kansas as your champion since that would add enough value to differentiate you from the many others that also have Kansas.

Kentucky 9% vs 7% nation: Kentucky has the talent to win it all but there’s really not as much value as you’d like for a team with a 9% chance to win. Not a bad play here but I’ll probably look elsewhere.

**Elite 8 (to get to the Final Four)**

Here are some value options to make the Final Four:

Oregon (31%) / Oklahoma (30%): The nation is picking Oklahoma at a 46% clip and just 24% believe in the Ducks. Don’t take Oklahoma to go to the Final Four unless you’re going to take them to win it all. FYI, Texas A&M is 12% to make it and the nation is also at 12% on the Aggies. Duke is 8% vs 12% nation and Baylor is 8% vs 2.4% nation.

Kansas (41%) / Villanova (19%) / California (8%): 74% of the nation is picking Kansas so only use the Jayhawks to advance in bigger pools if you are picking them to win it all. Villanova is getting only 11% of the support from the public so there is some value here – although I don’t trust the Cats. California 8% vs 2% nation and the Bears actually have the talent to beat anyone. Other Options: Miami 8% vs 4% nation.

North Carolina (44%) / Kentucky (19%): North Carolina is being picked by 54% of the nation so, like Kansas, UNC should only be your choice to make the Final Four in bigger pools if you’re picking the Tarheels to win it all. Kentucky is getting 19% of the public support so there isn’t any value there. Kentucky would be a good choice here in a bigger pool if you’ve got Kansas in the final game. Other options: West Virginia 13% vs 10% nation, Xavier 12% vs 10% nation.

Michigan State (40%) / Virginia (37%): Michigan State is being picked by a whopping 70% of the public, which I want no part of unless I’m in a small pool. Virginia is the choice here in medium and bigger pools, as the Cavaliers are only being chosen by 19% of the public. Purdue (7%) is only being picked by 2% of the nation so if you’re looking for value with a longshot in a huge pool the Boilermakers are an option.

**Round 3**

Oregon 52%, Duke 18%, Baylor 17%: If you are not going to pick Oregon to go to the Final Four then this is the point where you might pick them to lose. Oregon is 52% to get past this round but the nation is picking them 56%. For Duke it’s 18% vs 28% for the nation so the Blue Devils are not a wise choice. The value is with Baylor at 17% vs only 11% chose by the nation. So, if you have all of these teams losing in the next round then you might consider Baylor here to add some value.

Oklahoma 52%, Texas A&M 26%, Texas 13%: Oklahoma is being picked by 67% of the nation so this might be a good spot to say goodbye to the Sooners if you have them losing in the next round anyway, as I do. Texas A&M has some value at 26% vs 24% nation and Texas would add some variance/value as only 4.4% are picking the pesky Longhorns to advance. If you have decent value in later rounds, then it’s okay to go with Oklahoma here but Texas A&M is a good choice if you feel you need to add some value.

Kansas 61%, Cal 17%, Maryland 14%: If you don’t have Kansas winning it all then this might be a good spot to pick the upset as both Cal and Maryland have the talent to beat the Jayhawks. Cal is #1 in the nation in 2-point defense and a sub-par outside shooting night from the Jayhawks could easily derail them in that game. Maryland, meanwhile, can beat anyone if they don’t beat themselves with foolish turnovers, which has been their problem this season. 85% of the nation is picking Kansas to advance so the value is with the other two teams. Cal is your better choice, as only 4% of the nation has picked the Beas to advance while Maryland is getting 7% of the love.

Villanova 40%, Miami 21%, Iowa 15%, Wichita 12%, Arizona 12%: Villanova is not to be trusted to win 6 games because they shoot too many 3-pointers and don’t make enough of them, so one bad shooting game would end their tournament early AGAIN. I like Miami but so does 26% of the nation. Still, taking the Canes here if you are anti-Villanova is a reasonable decision. Only 5% of the nation is picking Iowa, so there is a lot of value but I’d only take Iowa here if you’re picking all these teams to lose in the next round. Less than 2% of the public is on Wichita State and that would be give you a team that can legitimately advance while also supplying you with value. No value at all with Arizona, who are being chosen by 14% of the nation and have a terrible record against good teams. Stay away from the Wildcats.

North Carolina (59%, Kentucky 29%): Only two choices here make sense to me. If you are looking for a reason to dismiss the Tarheels before the rest of the nation does then this is your chance as the public is 65% on UNC. That’s not actually that much negative value so picking UNC to lose in a later round wouldn’t hurt you much either. Kentucky is being picked by 25% of the nation so there is not a ton of value there. I’m good either way here and this pick just depends on how much variance you need to induce into your pool. If you’re going with the other favorites to advance to the Final Four then you might consider Kentucky here to mix things up a bit.

West Virginia 36.5%, Xavier 35.8%: West Virginia’s aggressive style of play makes them a variable team that I don’t think can win too many games in a row against good competition. 43% of the public is on the Mountaineers and 38% are only Xavier so there is no value with either team. The other teams in this part of the bracket aren’t viable options either, as there is no value with Notre Dame and very little with Wisconsin. I would dismiss all of these teams in the next round anyway so it doesn’t matter who you pick here.

Virginia 62%, Purdue 17%, Iowa State 13%: There’s no value with Virginia here (73% of the nation like the Cavs), but there is in later rounds, so I’m advancing them. If you don’t agree with my assessment of Virginia then there is some value on Purdue (13% of the nation picked them) and on Iowa State (9%).

Michigan State 67%, Utah 11%: Michigan State is my choice here even though 86% of the public on are them. Utah struggled against better teams this season and I see no reason to take just a high variance pick at this stage unless you know in advance that Denzel Valentine will go missing and not show up for the game for Tom Izzo’s squad. Only twice in 18 NCAA Tournaments has Tom Izzo’s team lost before their seeding would project them to lose. In this case, that would mean a trip at least the Elite 8. If you don’t like Michigan State then you’re probably better off picking them to lose later on.

**Round 2**

Possible value changes for the Round of 32:

Duke 46% vs Baylor 42%: If you don’t have either team advancing to the next round then you are better off with Baylor here, as 60% of the nation is picking Duke to advance while only 35% have Baylor to make it to the Sweet 16.

Texas A&M 56% vs Texas 35%: The value here is with Texas (only 19% chosen by the public) but I’d rather advance Texas A&M (70% public) and use them against Oklahoma in the next round.

California 47% vs Maryland 44%: I don’t have an issue with either team here and it doesn’t matter much if you’re going to take Kansas in the next round. However, in my bigger pools I need to pick Kansas to lose and both of these teams have the talent to beat the Jayhawks. Only 34% of the nation is on the Bears while Maryland is getting support from 59% to advance here, so the value is on Cal, who I rate a bit higher also.

Miami 47%, Wichita 27%, Arizona 26%: I think your options here are Miami or Wichita since Arizona hasn’t played very well this year when facing other really good teams and I’m taking Wichita in round 1. The public has picked Arizona at a 36% clip, so there is negative value choosing the Wildcats anyway. Only 6% have picked Wichita State, which is tons of value for a team that has the talent and defense to go a long way. Miami has been picked by 55% of the public but it’s okay to pick Miami here if you like them to advance a round or two more since there will eventually be value in backing the Hurricanes in later rounds. But, if you’re going to pick Miami to lose to Villanova in the next round then you should strongly consider Wichita State here.

Villanova 66%, Iowa 30%: Consider Iowa here for value (only 12% of the public is on them) if you’re going to pick Villanova to lose in the next round.

Purdue 46%, Iowa State 42%: The public is picking Purdue here (53%) but there really isn’t any value in taking Iowa State (39% of the public is on them). If you are picking Purdue to lose in the next round then Iowa State is a pretty good play here.

Utah 39%, Gonzaga 29%, Seton Hall 28%: Utah didn’t play very well this season against other really good teams and 55% of the public is picking them. I would have all of these teams losing in the next round to Michigan State anyway so this is a pretty good place to go for value. The public is 23% on Seton Hall and only 19% on Gonzaga so I’ll go with the Zags as my pick in this round.

**Round 1**

Same as above in the probability tree bracket except for possible changes to add variance in smaller pools (the bigger the difference between the chance of being in that round and the percent the nation has them advancing the more you should consider it):

Colorado (44%) vs Connecticut (56%): Only 24% of the nation is picking Colorado to win this game and the Buffaloes have a 44% chance to do so according to my ratings. I’d pick either team to lose in the next round anyway, so Colorado is a good choice here to add some value.

Wichita State (50%) vs Arizona (50%): The nation is picking Arizona at a high rate (79%) so I’ll take Wichita State in this toss-up game.

USC (47%) vs Providence (53%): The public is only Providence at a 62% clip so the value is with USC. Advance the Trojans if you’re looking to add some value/variance in a smaller pool.

Michigan/Tulsa (40%) vs Notre Dame (60%): Only 20% of the nation likes the play in game winner but teams that win these play in games tend to advance more than they’re predicted to so consider an upset for value’s sake.

Pittsburgh (48%) vs Wisconsin (52%): Wisconsin is getting 67% of the picks by the public so the value is strongly with Pitt here and I wouldn’t advance either team past this round anyway.

Texas Tech (43%) vs Butler (57%): Butler is a 69% choice of the nation so taking Texas Tech here to mix things up isn’t a horrible idea. Of course, there are better value plays elsewhere and you don’t want too much variance in your first round picks.

Gonzaga (51%) vs Seton Hall (49%): This is a toss-up mathematically and a toss-up by the public too, who are also evenly split. Both teams can beat Utah in the next round.

Dayton (52%) vs Syracuse (48%): The public supports Dayton 52% to 48% also so I’m sticking with the Flyers.

Good luck,

Dr Bob