The first part of the following example is from 5 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 has become automated over the years. The part that’s not automated is coming up with my tournament rating for each team, which has taken me a couple of days.
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, Duke has about a 30% chance of winning the tournament based on most analytics and on Vegas odds and I actually give the Blue Devils a 30% chance too. However, over 40% of nation (based on data from the Yahoo sports and ESPN’s national pool) is picking Duke as the winner, so there was no value in picking Duke to win it all even if they had the best chance to do so.
If you’re in a small pool then it is okay to pick Duke but you’d need to induce some variance in your other Final Four picks to differentiate yourself from the others that also have picked the Blue Devils to win it all. The idea is not to pick other teams randomly but to find where the value is.
Michigan State, for instance, is being picked to make the Final Four by only 15% of the nation and I give the Spartans a 28% chance to make the Final Four while analytics guru Nate Silver gives them a 22% chance. So, there is value in picking Michigan State to at least get to the Final Four. The Spartans might also be a good pick to win the Championship in bigger pools, as I give Michigan State a 9.7% chance to cut down the nets while the public is picking them to win at just 4.8%. In a 1000 person pool would you rather have a 30% chance of being one of 400 or people to pick Duke as the winner or a 10% chance with Michigan State with only 48 other people in your pool having the Michigan State as your winner. Of course, making better picks along the way would help you in any tie breakers but your chances of winning your pool is still better with Michigan State than it is with Duke even though the Blue Devils have a much better chance to win the tournament. If you do decide to pick Michigan State to win then you don’t have to pick as many upsets in earlier rounds. If you still want to pick Duke then you’ll need to have value/variance in your other Final Four picks to differentiate yourself from the masses.
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.
Duke (100%), VCU (50.5%), Miss State (80%), Virginia Tech (88%), Maryland (65%), LSU (77%), Louisville (67%), Michigan State (97%).
Gonzaga (99%), Syracuse (57%), Marquette (67%), Florida State (79%), Buffalo (61%), Texas Tech (88%), Nevada (56%), Michigan (95%).
Virginia (98%), Mississippi (53%), Wisconsin (57%), Kansas State (52%), Villanova (72%), Purdue (92%), Cincinnati (69%), Tennessee (94%).
North Carolina (98%), Utah State (63%), Auburn (71%), Kansas (80%), Iowa State (65%), Houston (88%), Wofford (57%), Kentucky (99%).
Duke (95%), Virginia Tech (56%), LSU (40%, Maryland is 38%), Michigan State (78%).
Gonzaga (85%), Florida State (56%), Texas Tech (62%), Michigan (69%).
Virginia (85%), Wisconsin (36%), Purdue (64%), Tennessee (71%).
North Carolina (85%), Auburn (45%, Kansas is 38%), Houston (46%, Iowa State is 37%), Kentucky (80%).
Duke (80%), Michigan State (64%).
Gonzaga (71%), Michigan (44%).
Virginia (74%), Tennessee (41%, Purdue is 36%).
North Carolina (59%), Kentucky (56%).
Elite 8 (to get to Final Four)
Duke (58%), Michigan State 28%, Virginia Tech 5%.
Gonzaga (53%), Michigan (18%), Texas Tech (10%), Florida State (8%).
Virginia (50%), Tennessee (20%), Purdue (16%).
North Carolina (35%), Kentucky (33%), Auburn (8%).
Final Four Games
Duke (44%), Gonzaga (33%), Michigan State (18%), Michigan (9%).
Virginia (29%), North Carolina (14%), Kentucky (13%), Tennessee (9%), Purdue (7%).
Michigan State (10%)
North Carolina (7%)
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
Yahoo’s site is
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 (based on ESPN’s site, which likely has a larger sample size). You might want to start here and look for value if you’re in a bigger pool then go backwards to create your bracket.
Duke (30% vs 37% nation): There’s no value in picking Duke to win it all but if you do you should probably find value in your runner-up (Virginia perhaps) or other Final Four picks.
Gonzaga (16% vs 9% nation): There is solid value here, so you should certainly consider taking the Zags to cut down the nets. Gonzaga has the easiest region to navigate through and the Bulldogs are the only team to beat Duke when the Blue Devils had all of their starters playing.
Virginia (14% vs 8% nation): Virginia is another good value play and the Cavaliers enter the tournament with the best overall compensated net points per possession rating (Duke would be higher if you discard the games Zion missed). Also, Virginia’s two losses to Duke were due to really negative 3-point variance. The Cavaliers (a 41% 3-point shooting team) were outshot from 3-point range 32% to 43% by a Duke team that has made just 30% of their 3-point shots this season. Virginia also has the best 3-point defense in the nation so Duke was lucky to have that much of an advantage over Virginia in those games and the Cavaliers probably would have won both games if not for that variance. I will certainly be using Virginia in one of my bigger pools.
Michigan State (10% vs 5% nation): Everyone loves Duke so much that there seems to be value on every other legitimate contender. I really like this Michigan State team and you should consider taking the Spartans to at least make the Final Four if you’re bold enough to keep Duke out.
North Carolina (7% vs 15% nation): North Carolina is certainly good enough to win this tournament, as they only lost to a healthy Duke team by 1 points in the ACC Championship game despite making just 4 of 26 3-point shots, which is simply bad luck. However, my ratings also like Kentucky a lot and Tarheels are in the same region with the Wildcats, which is why their mathematical chance of winning is lower than the other contenders.
Kentucky (7% vs 5% nation): While there isn’t value on UNC because Kentucky is equally good there is actually some value on the Wildcats because everyone likes North Carolina so much.
Tennessee, Michigan and Purdue all have 3% chances to win and the only one of those with some value is Purdue, who you should consider as a Final Four team if you think Virginia is going to choke again.
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.
Duke (44% vs 55%): Duke will have negative value in every round so if you’re not going to pick Duke to win it all then you might consider picking them to lose sooner than this round if you have another one of the top contenders winning the Championship.
Gonzaga (33% to 15%): Gonzaga’s side of the West Region is so weak that they have the second best chance to get to the Championship game even with Michigan State and Duke in their way.
Virginia (29% to 21%): Virginia has a much higher percentage than North Carolina because the Bulldogs don’t have to face Kentucky in the regional finals, as UNC likely will.
Michigan State (18% vs 11%): Michigan State can certainly beat Gonzaga and would be a good alternative if you’re in a big pool and don’t want to be among the masses taking Duke.
North Carolina (14% vs 37%): Great team but no value.
Kentucky (13% vs 13%): Equally great team worth considering if you’re not a fan of Virginia or Tennessee from the opposing region.
Tennessee (9% vs 12%)
Michigan (9% vs 7%)
Purdue (7% vs 2%): I like the Boilermakers more than the market does but only consider them if you’re in a very huge pool. And, if you do pick such a long shot then make sure you have favorites in the rest of your regional finals and Final Four.
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.