Back in April, the NCAA Men’s Basketball Tournament came to its conclusion with the No. 1 seed Kansas Jayhawks defeating the No. 8 seed North Carolina Tar Heels to claim the 2022 national title. The Jayhawks had to beat six other teams over three weekends to earn the right to cut down the nets, as has every NCAA champion since the mid-1980s.
But, not all paths in the NCAA Tournament are equally difficult. The entire structure of the tournament is based on the idea that the better teams (i.e. higher seeds) are given the easiest draw. But sometimes upsets occur and the occasional No. 15 seed wins a game (or three), busts the bracket, and clears the path for a No. 8 seed to survive to the Final weekend. Furthermore, not all No. 1 seeds (or No. 8 seeds or No. 15 seeds) are equally strong.
Fortunately, I have devised a way to calculate the difficulty of any given NCAA Tournament draw and path. The key idea is to replace any given team in any past NCAA Tournament bracket with a historically average Final Four team using Kenpom efficiency data as a guide. Tom Izzo’s 2005 Michigan State team is a great benchmark with a pre-tournament adjusted efficiency margin of 25.62, which is very close to that average.
By artificially placing this benchmark team in literally every position in every NCAA Tournament bracket back to 2002, it is possible to calculate that benchmark team’s odds to advance through every round of the tournament. Furthermore, it is possible to calculate those odds based on all possible paths at the beginning of the tournament (i.e. the “draw”) and on the specific “path” that the team in question actually followed.
Figure 1: Difficulty of NCAA Tournament paths and specific draws for a simulated tournament where all teams are historically average for their seed
Three different data sets are shown. The green bars in the left panel represent the average draw for each seed. In other words, these are the odds that the reference Final Four team (2005 Michigan State) would have to advance to the Final Four if placed in the bracket as anywhere between the No. 1 seed and the No. 16 seed.
The green bars are a useful reference and also provide a sense of how much of an advantage it is to be a higher seed. In the No. 1 seed position, the reference team has a 27 percent chance to win the region. Those odds drop to 22 percent for a No. 2 seed placement, 19 percent for a No. 3 seed placement and 16 percent for a No. 4 seed placement.
For No. 5 seeds and lower, the odds start to level off between 11 and 12 percent. As one might expect, it is slightly better to be located in the “bottom” of the bracket, away from the No. 1 seed. In fact, of the lower seeds, the sweet spot is the No. 11 seed. This makes sense, as the No. 11 seed avoids playing the No. 2 and No. 1 seed the longest, which means there is a slightly higher chance that an upstream upset will make the actual path easier.
The other two data sets in Figure 1 represent the two extremes of specific paths that the reference team could take through the bracket. The left panel shows the most difficult “chalk” path where the reference team would face the highest possible seed in each round. For example, it would assume that the No. 1 seed would play the No. 16 seed, the No. 8 seed, the No. 4 seed and finally the No. 2 seed on the path to the Final Four. On average, the real path tends to be between four and six percentage points easier than the most difficult possible path for each seed.
Finally, the right panel of Figure 1 shows the odds for the “anti-chalk” path for each seed. As the name implies, this is the easiest possible path that each seed could take, assuming the maximum number of upsets. For the No. 1 seed placement, this would mean facing the No. 16, the No. 9 seed the No. 13 seed and finally the No. 15 seed. While this path is extremely unlikely, it would give each seed a significant advantage. Basically, any seed better than a No. 10 seed would have Final Four odds that shoot up to 55 to 60 percent.
Figure 2: Difficult of all NCAA Tournament draws from 2002-2022. A higher number is an easier draw, as it implies a higher probability of advancing to a Final Four.
In general, the shape of the curve in Figure 2 is similar to the green bars above in Figure 1. However, there appears to be more deviation at the extreme ends of the figure. Table 1 below shows the data for some of these teams at these extremes.
Table 1: Extreme examples of easy (top) and hard (bottom) NCAA Tournament draws since 2002.
The top of Table 1 shows a list of some of the easiest NCAA Tournament draws to reach the Final Four since 2002. The top two spots are held down by the 2002 Maryland Terrapins, who won the national championship, and the 2006 UCLA Bruins, who lost in the title game to No. 3 seed Florida.
A closer look at the makeup of each region gives clues as to why these two draws were so relatively easy. Figure 3 below compares the pre-tournament Kenpom efficiencies of the teams in the 2002 East Region and the 2006 West Region to the historical average values for those seeds.
Figure 3: Comparison of the Kenpom efficiency margins for the teams in the 2002 East Region and the 2006 West Region relative to historical averages (shown by the blue circles)
In both cases, No. 1 seed Maryland and No. 2 seed UCLA were grouped with other highly-seeded teams that were historically well below average. In 2002, No. 3 seed Georgia and especially No. 2 UConn were both very weak. To make the situation even easier, No. 8 Wisconsin and No. 9 Saint John’s were also surprisingly weak. In 2006, No. 2 UCLA was placed in a region with essentially a pair of weaker-than-usual mid-majors (No. 1 Memphis and No. 3 Gonzaga) as well as with a weak pair of No. 7 and No. 10 seeds as potential second round opponents.
A similar pattern arises for all of the teams listed in Table 1. A typical “easy” draw usually occurs when two or more of the top seeds in the region are remarkably weak. It also helps when the first round and potential second round opponents are below average.
The opposite is true for the teams at the bottom of the table, representing teams with surprisingly tough draws. In these cases, the region usually has two or three teams on the top few seed lines that are significantly above average. Teams that start the tournament in the First Four (play-in games) also tend to drift to the bottom of this table due to the fact that they have to play an extra game.
Overall, Table 1 also gives some hints as to years when the overall tournament field appears to have been relatively weak or relatively strong. For example, the 2003 and 2006 tournaments seem to have been particularly weak, as several teams from those years appear at the top of the table. Conversely, the 2015, 2019 and 2021 tournaments all seem to have been relatively strong.
Finally, I should note that Michigan State does have one team that appears in Table 1. The snake-bitten 2016 team ironically had the 17th easiest draw in NCAA Tournament history. That region also contained a fairly average No. 1 seed in Virginia and a very below average No. 3 seed in Utah. Unfortunately, that region also contained a surprisingly good (at least on that day) No. 15 seed called Middle Tennessee State.
For completeness, Table 2 below gives the remaining strength of draw data for all of Michigan State’s tournament appearances since 2002.
Table 3: Summary of Michigan State's NCAA Tournament draw difficultly since 2002.
As expected, Michigan State’s draws were generally better in the years when the Spartans were a No. 1 or No. 2 seed, with some notable exceptions. The Spartans’ draws in 2016 and 2009 as a No. 2 seed were both a little easier than the draw in 2012 as a No. 1 seed. The draw in 2014 as a No. 4 seed was relatively easy, as were the pair of ill-fated draws as a No. 10 seed in both 2002 and 2011.
Michigan State’s draw in 2021 was obviously the most challenging since it involved the First Four round. The 2022 draw was also difficult, but so was the Spartans’ draw in 2015 as a No. 7 seed, which resulted in a Final Four.
Table 4: NCAA Path difficulty for the last 19 National Champions.
Once again, the numbers in the table represent the calculated odds for an average Final Four team (such as Izzo’s 2005 club) to advance through each round up through the national championship game. Most of the past champions played a path where the benchmark team would have had between a four percent and nine percent chance to win the tournament.
Interestingly, this year’s champion, the Kansas Jayhawks, had a path that was twice as easy as the team in second place, the 2006 Florida Gators. As noted previously, the 2006 tournament appears to have had a very weak field. So, what happened in 2022?
On their way to the title, the Jayhawks defeated a No. 16 seed (Texas Southern), a No. 9 seed (Creighton), a No. 4 seed (Providence), a No. 10 seed (Miami), a No. 2 seed (Villanova) and a No. 8 seed (North Carolina). Kansas was certainly aided by drawing a No. 10 seed and a No. 8 seed so late in the tournament. But that is not all.
Creighton, Villanova and especially Providence were all relatively weak teams for their seed. In fact, the only opponent that Kansas faced in the entire tournament who was above average for their seed was No. 16 Texas Southern. This combination of factors resulted in a historically easy run to the title for the Jayhawks this year.
Ironically, last year’s champion, the Baylor Bears, have the record for the most difficult tournament path since 2002. Of Baylor’s six tournament opponents, only No. 3 seed Arkansas was below average for its seed.
Finally, Table 4 below gives the path difficulty data for a selected number of other Final Four teams, including Michigan State’s five Final Fours since 2002.
Table 5: NCAA Tournament Path difficulty selected Final Four teams since 2002.
As for paths to the Final Four, this year Kansas passed the 2021 Houston team for the easiest path to the final weekend in the Kenpom era. Prior to 2021, the 2005 Illinois and 2004 Connecticut teams held down the top-two spots.
Regarding paths to the title game, North Carolina’s 2016 team held the top spot until this year, with the 2006 UCLA squad and Michigan’s 2018 team rounding out the current top-four.
As for the most difficult paths to both the Final Four and the final game, Texas Tech’s 2019 team holds that record. Notably, the Red Raiders beat out both the 2011 VCU team and the 2021 UCLA team, both of whom advanced to the final weekend from the First Four.
Of Michigan State’s five Final Four appearances, the 2010 appearance was the easiest path, thanks in large part to No. 9 Northern Iowa’s upset of No. 1 Kansas in the second round. The 2015 team took the most difficult path of Izzo’s recent teams. Finally, the 2009 Michigan State team can claim the ninth most difficult path to the championship game back to 2002.
So far in this series we have performed deep dives into wins and losses, performance metrics versus expectations and the difficulty of various tournament paths. In the final installment of this series, we will explore the madness itself by looking at the overall odds for teams to win the tournament, as well as the odds to pick a perfect office bracket. Stay tuned.
But, not all paths in the NCAA Tournament are equally difficult. The entire structure of the tournament is based on the idea that the better teams (i.e. higher seeds) are given the easiest draw. But sometimes upsets occur and the occasional No. 15 seed wins a game (or three), busts the bracket, and clears the path for a No. 8 seed to survive to the Final weekend. Furthermore, not all No. 1 seeds (or No. 8 seeds or No. 15 seeds) are equally strong.
Fortunately, I have devised a way to calculate the difficulty of any given NCAA Tournament draw and path. The key idea is to replace any given team in any past NCAA Tournament bracket with a historically average Final Four team using Kenpom efficiency data as a guide. Tom Izzo’s 2005 Michigan State team is a great benchmark with a pre-tournament adjusted efficiency margin of 25.62, which is very close to that average.
By artificially placing this benchmark team in literally every position in every NCAA Tournament bracket back to 2002, it is possible to calculate that benchmark team’s odds to advance through every round of the tournament. Furthermore, it is possible to calculate those odds based on all possible paths at the beginning of the tournament (i.e. the “draw”) and on the specific “path” that the team in question actually followed.
Comparison to Historical Averages
Before jumping directly into the numbers for a given tournament, it is helpful to understand the context for some of the numbers to come. To this end, I made a set of calculations based on a reference tournament consisting of an imaginary set of perfectly average teams that each are assigned the average Kenpom efficiency for their seed. It is then possible to calculate the difficulty of each teams’ “draw” or “path.” Figure 1 below gives the results of these calculations.
Figure 1: Difficulty of NCAA Tournament paths and specific draws for a simulated tournament where all teams are historically average for their seed
Three different data sets are shown. The green bars in the left panel represent the average draw for each seed. In other words, these are the odds that the reference Final Four team (2005 Michigan State) would have to advance to the Final Four if placed in the bracket as anywhere between the No. 1 seed and the No. 16 seed.
The green bars are a useful reference and also provide a sense of how much of an advantage it is to be a higher seed. In the No. 1 seed position, the reference team has a 27 percent chance to win the region. Those odds drop to 22 percent for a No. 2 seed placement, 19 percent for a No. 3 seed placement and 16 percent for a No. 4 seed placement.
For No. 5 seeds and lower, the odds start to level off between 11 and 12 percent. As one might expect, it is slightly better to be located in the “bottom” of the bracket, away from the No. 1 seed. In fact, of the lower seeds, the sweet spot is the No. 11 seed. This makes sense, as the No. 11 seed avoids playing the No. 2 and No. 1 seed the longest, which means there is a slightly higher chance that an upstream upset will make the actual path easier.
The other two data sets in Figure 1 represent the two extremes of specific paths that the reference team could take through the bracket. The left panel shows the most difficult “chalk” path where the reference team would face the highest possible seed in each round. For example, it would assume that the No. 1 seed would play the No. 16 seed, the No. 8 seed, the No. 4 seed and finally the No. 2 seed on the path to the Final Four. On average, the real path tends to be between four and six percentage points easier than the most difficult possible path for each seed.
Finally, the right panel of Figure 1 shows the odds for the “anti-chalk” path for each seed. As the name implies, this is the easiest possible path that each seed could take, assuming the maximum number of upsets. For the No. 1 seed placement, this would mean facing the No. 16, the No. 9 seed the No. 13 seed and finally the No. 15 seed. While this path is extremely unlikely, it would give each seed a significant advantage. Basically, any seed better than a No. 10 seed would have Final Four odds that shoot up to 55 to 60 percent.
Strength of Draw
With that background established, it is now time to look at the results of the draw and path difficulty calculations for all NCAA Tournament teams stretching back to 2002. The full data set with reference to Final Four draw difficulty is shown in Figure 2.
Figure 2: Difficult of all NCAA Tournament draws from 2002-2022. A higher number is an easier draw, as it implies a higher probability of advancing to a Final Four.
In general, the shape of the curve in Figure 2 is similar to the green bars above in Figure 1. However, there appears to be more deviation at the extreme ends of the figure. Table 1 below shows the data for some of these teams at these extremes.
Table 1: Extreme examples of easy (top) and hard (bottom) NCAA Tournament draws since 2002.
The top of Table 1 shows a list of some of the easiest NCAA Tournament draws to reach the Final Four since 2002. The top two spots are held down by the 2002 Maryland Terrapins, who won the national championship, and the 2006 UCLA Bruins, who lost in the title game to No. 3 seed Florida.
A closer look at the makeup of each region gives clues as to why these two draws were so relatively easy. Figure 3 below compares the pre-tournament Kenpom efficiencies of the teams in the 2002 East Region and the 2006 West Region to the historical average values for those seeds.
Figure 3: Comparison of the Kenpom efficiency margins for the teams in the 2002 East Region and the 2006 West Region relative to historical averages (shown by the blue circles)
In both cases, No. 1 seed Maryland and No. 2 seed UCLA were grouped with other highly-seeded teams that were historically well below average. In 2002, No. 3 seed Georgia and especially No. 2 UConn were both very weak. To make the situation even easier, No. 8 Wisconsin and No. 9 Saint John’s were also surprisingly weak. In 2006, No. 2 UCLA was placed in a region with essentially a pair of weaker-than-usual mid-majors (No. 1 Memphis and No. 3 Gonzaga) as well as with a weak pair of No. 7 and No. 10 seeds as potential second round opponents.
A similar pattern arises for all of the teams listed in Table 1. A typical “easy” draw usually occurs when two or more of the top seeds in the region are remarkably weak. It also helps when the first round and potential second round opponents are below average.
The opposite is true for the teams at the bottom of the table, representing teams with surprisingly tough draws. In these cases, the region usually has two or three teams on the top few seed lines that are significantly above average. Teams that start the tournament in the First Four (play-in games) also tend to drift to the bottom of this table due to the fact that they have to play an extra game.
Overall, Table 1 also gives some hints as to years when the overall tournament field appears to have been relatively weak or relatively strong. For example, the 2003 and 2006 tournaments seem to have been particularly weak, as several teams from those years appear at the top of the table. Conversely, the 2015, 2019 and 2021 tournaments all seem to have been relatively strong.
Finally, I should note that Michigan State does have one team that appears in Table 1. The snake-bitten 2016 team ironically had the 17th easiest draw in NCAA Tournament history. That region also contained a fairly average No. 1 seed in Virginia and a very below average No. 3 seed in Utah. Unfortunately, that region also contained a surprisingly good (at least on that day) No. 15 seed called Middle Tennessee State.
For completeness, Table 2 below gives the remaining strength of draw data for all of Michigan State’s tournament appearances since 2002.
Table 3: Summary of Michigan State's NCAA Tournament draw difficultly since 2002.
As expected, Michigan State’s draws were generally better in the years when the Spartans were a No. 1 or No. 2 seed, with some notable exceptions. The Spartans’ draws in 2016 and 2009 as a No. 2 seed were both a little easier than the draw in 2012 as a No. 1 seed. The draw in 2014 as a No. 4 seed was relatively easy, as were the pair of ill-fated draws as a No. 10 seed in both 2002 and 2011.
Michigan State’s draw in 2021 was obviously the most challenging since it involved the First Four round. The 2022 draw was also difficult, but so was the Spartans’ draw in 2015 as a No. 7 seed, which resulted in a Final Four.
Strength of Path
The ease or difficulty of the NCAA Tournament draw is important to compare initial brackets — once March Madness actually begins, what is more important is the actual path that a team takes along the road to the Final Four and beyond. Table 3 shows the difficulty of the actual NCAA Tournament path for the past 19 NCAA champions.Table 4: NCAA Path difficulty for the last 19 National Champions.
Once again, the numbers in the table represent the calculated odds for an average Final Four team (such as Izzo’s 2005 club) to advance through each round up through the national championship game. Most of the past champions played a path where the benchmark team would have had between a four percent and nine percent chance to win the tournament.
Interestingly, this year’s champion, the Kansas Jayhawks, had a path that was twice as easy as the team in second place, the 2006 Florida Gators. As noted previously, the 2006 tournament appears to have had a very weak field. So, what happened in 2022?
On their way to the title, the Jayhawks defeated a No. 16 seed (Texas Southern), a No. 9 seed (Creighton), a No. 4 seed (Providence), a No. 10 seed (Miami), a No. 2 seed (Villanova) and a No. 8 seed (North Carolina). Kansas was certainly aided by drawing a No. 10 seed and a No. 8 seed so late in the tournament. But that is not all.
Creighton, Villanova and especially Providence were all relatively weak teams for their seed. In fact, the only opponent that Kansas faced in the entire tournament who was above average for their seed was No. 16 Texas Southern. This combination of factors resulted in a historically easy run to the title for the Jayhawks this year.
Ironically, last year’s champion, the Baylor Bears, have the record for the most difficult tournament path since 2002. Of Baylor’s six tournament opponents, only No. 3 seed Arkansas was below average for its seed.
Finally, Table 4 below gives the path difficulty data for a selected number of other Final Four teams, including Michigan State’s five Final Fours since 2002.
Table 5: NCAA Tournament Path difficulty selected Final Four teams since 2002.
As for paths to the Final Four, this year Kansas passed the 2021 Houston team for the easiest path to the final weekend in the Kenpom era. Prior to 2021, the 2005 Illinois and 2004 Connecticut teams held down the top-two spots.
Regarding paths to the title game, North Carolina’s 2016 team held the top spot until this year, with the 2006 UCLA squad and Michigan’s 2018 team rounding out the current top-four.
As for the most difficult paths to both the Final Four and the final game, Texas Tech’s 2019 team holds that record. Notably, the Red Raiders beat out both the 2011 VCU team and the 2021 UCLA team, both of whom advanced to the final weekend from the First Four.
Of Michigan State’s five Final Four appearances, the 2010 appearance was the easiest path, thanks in large part to No. 9 Northern Iowa’s upset of No. 1 Kansas in the second round. The 2015 team took the most difficult path of Izzo’s recent teams. Finally, the 2009 Michigan State team can claim the ninth most difficult path to the championship game back to 2002.
So far in this series we have performed deep dives into wins and losses, performance metrics versus expectations and the difficulty of various tournament paths. In the final installment of this series, we will explore the madness itself by looking at the overall odds for teams to win the tournament, as well as the odds to pick a perfect office bracket. Stay tuned.
