## Bracket Optimization- A Research Paper based on Ken Pomeroy’s Efficiency Model

Disclaimer: This exercise intends to identify a method in which to eliminate potential Final Four teams from contention as such based upon the statistical significance of their efficiency profile. This is an opposite and completely different exercise than picking the correct Final Four. Conversely, we will attempt to narrow down the contenders and then sort them in tiers in terms of their overall likelihood to advance that far based on historical data as it pertains to their efficiency profile.

Looking at KenPom data going back to 2002, after which there have been 13 years of Final Fours, or 52 teams, we find the following:

– 45 of the 52 teams (87%) owned an efficiency number in the Top 50 of both offense (AdjO) and defense (AdjD).

– Of the 7 teams over that timespan to advance without a Top 50 efficiency number on one side of the ball, 5 of them ranked either first or second on the other:

* 2003 Texas (#1 AdjO, #80 AdjD)

* 2003 Marquette (#2 AdjO, #119 AdjD)

* 2006 LSU (#65 AdjO, #2 AdjD)

* 2010 Butler (#57 AdjO, #2 AdjD)

* 2012 Louisville (#116 AdjO, #1 AdjD)

Notably, none of these teams won the National Title, and only one (Butler) advanced to the Title game.

– That leaves just two teams to have made the Final Four over the past thirteen years that fell outside the top 50 in one efficiency measure while failing to dominate at the other. Not surprisingly, they are widely considered the two biggest upset appearances in Final Four history (the only two 11 seeds to ever advance besides LSU in 1986.) Making up just 3.8% of the sample size, they fall outside of two standard deviations from the mean, and can be considered extreme outliers/ dismissable flukes:

* 2006 George Mason (#58 AdjO, #13 AdjD)

* 2011 VCU (#25 AdjD, #84 AdjD)

Now, we can use these historical trends to apply more specific criteria to what a potential Final Four team would look like, and assign probability to the chance that a Final Four team will possess this criteria in its profile. Importantly, this is much different than saying that a team that possesses this criteria will have the stated probability of making the Final Four, as there are many teams that may possess the same necessary criteria. We are simply identifying the probability that some of those teams will occupy the Final Four in order to confidently rule out a larger portion that will not.

Again, the number below is the probability that any one Final Four team will possess the specified criteria:

Top 50 in BOTH AdjO and AdjD OR Top 2 in one or the other: **96.2%**

Not outside of the Top 25 in BOTH AdjO and AdjD: **96.2%**

Top 50 in BOTH AdjO and AdjD: **86.5%**

Top 10 in either AdjO OR AdjD: **80.8%**

Top 25 in BOTH AdjO and AdjD: **59.6%**

Top 25 in BOTH AdjO and AdjD, Top 10 in one or the other: **50%**

Top 10 in BOTH AdjO and Adj D: **25%**

Average Combined Efficiency Number (AdjO rank+ AdjD rank): 35.6

By dismissing the results of the sample that fall outside two standard deviations from the mean (95%), the elimination process is fairly simple:

When evaluating potential Final Four teams, ELIMINATE:

– Any team ranked outside the Top 25 on both sides of the ball.

– Any team ranked outside of the Top 50 on either side of the ball, unless they rank 1st or 2nd on the other.

Among the remaining teams, consider with extreme scrutiny:

-Any team ranked outside the Top 50 on one side of the ball if they rank 1st or 2nd in the other. (9.6% success rate historically)

-Any team that does not rank in the Top 10 on at least one side of the ball (19.2% success rate historically)

Now that we have whittled down the teams that we believe have any chance whatsoever for a Final Four run, the next step is to evaluate the chances of those teams relative to one another. This can be accomplished by dividing the teams into tiers based on the strength of their efficiency profile.

Five types of Final Four contender teams:

Top 25 in AdjO and AdjD and Top 10 in one or the other: **50%** (26/52)

Top 50 in AdjO and AdjD/ Top 10 in one or the other: **21%** (11/52)

Outside Top 50 in AdjO or AdjD/ Top 2 in one or the other: **10%** (5/52)

Top 25 in AdjO and Adj D but not Top 10 in either: **10%** (5/52)

Top 50 in AdjO and AdjD/ Top 25 in one or the other: **2%** (1/52)

Outliers based on Standard Deviation from mean of elimination criteria: 7% (4/52)

**TIER 1: **

-Any team that ranks in the Top 25 of both AdjO and AdjD, and in Top 10 on one side of the ball. (50% success rate)

**Kentucky (5,2)**

**Arizona (11,3)**

**Villanova (4,13)**

**Gonzaga (6,20)**

**Utah (18,8)**

**TIER 2: **

– Teams that show a Top 50 efficiency ranking on one side of the ball, and a Top 10 in the other. (21% success rate)

**Wisconsin (1, 30)**

**Virginia (27, 1)**

**Oklahoma (50,5)**

**Kansas (37,7)**

**TIER 3:**

– Teams ranked in the Top 2 on one side of the ball, and outside the Top 50 on the other. (10% success rate)

– Top 25 on both sides of the ball but Top 10 on neither. (10% success rate)

**Notre Dame (2, 112)**

**Northern Iowa (15,16)**

**Witchita State (20,15)**

**TIER 4: **

-Top 50 on both sides of the ball but Top 25 on just one side of the ball. (2% success rate)

**Baylor (13,33)**

**North Carolina (12,45)**

**SMU (24,43)**

**Texas (42,19)**

**Georgetown (41, 25)**

What can we conclude overall about this analysis? For starters, it’s quite obvious that offensive and defensive balance is a key component of a Final Four team. The very fact that the only statistically significant unbalanced Final Four teams were only able to make up for it with extreme dominance on the other side of the ball confirms this. Still, it has to be considered interesting that in the absence of balance, teams with areas of extreme strength on one side of the ball and mediocrity on the other are still preferable to teams that are above average on both sides of the ball. We see this clearly as teams with profiles rated Top 10 on one side of the ball and outside of the Top 25 on the other (a #5 AdjO and #40 AdjD, for example) appear more frequently in the Final Four than teams that appear more balanced on paper in terms of the sum of their efficiencies (a #20 AdjO and #20 AdjD, for example). This seems to indicate that while extreme balance on both sides of the ball is certainly preferable, more often than not, Final Four teams first and foremost need to have an identity in terms of where their strength comes from even if it is on just one side of the ball. Many times, it appears these areas of extreme strength can offset weakness more frequently than simply being above average with no observable calling card.

Another interesting quirk of probability that we can see here is that the most likely annual Final Four approximately consists, on average, of two Tier 1 teams (50%), one Tier 2 team (21%) and one Tier 3 team (20%), leaving some small probability for a Tier 4 team or a team eliminated by this criteria to surprise. This information leads to two different potential strategies for filling out your bracket. On the one hand, you could try to identify the two Tier 1 teams, the Tier 2 team, and the Tier 3 team that you feel have the best opportunity to advance. Of course, since there will likely be multiple teams in each Tier, you are taking the chance of missing all of the Final Four teams if you are wrong and all your teams fall short within those Tiers. It is a high risk, high return strategy, but probably offers to most entertaining way to analyze your bracket. Conversely, by picking all four teams from Tier 1, you can be fairly confident of getting two of the Final Four teams correct, but it is highly unlikely that you will be right about all four. However, this offers a highly conservative approach for those who would prefer to concentrate on the early rounds and feel covered into the Regional Finals and Semifinals.

**NATIONAL CHAMPION**

Now that you have identified your Final Four, it’s time to move on to picking the Champion. Since there are only thirteen samples in the distribution, these statistics are not nearly as meaningful, but are worth a look nonetheless:

– No team has won the National Championship over the timespan with an efficiency rating worse than #40 on either side of the ball. The worst over that timespan on each side:

* 2014 UConn (#39 AdjO, #10 AdjD)

* 2009 North Carolina (#1 AdjO, #21 AdjD)

Using the same method from above, here are the probabilities based on the data that the National Champion will possess each stated criteria, with the exceptions to the rule notated:

Top 50 in BOTH AdjO and AdjD: 100%

Top 25 in BOTH AdjO and AdjD: 92.3% (UConn ’14 is the only exception)

Top 10 in either AdjO OR AdjD: 84.6% (UConn ’11 and Syracuse ’03 are the exceptions)

Top 10 in BOTH AdjO and AdjD: 53.8%

Average Combined Efficiency Number: 17.2

We’ll give some small leeway on these parameters given the small sample size, but suffice to say, while AdjO and AdjD seem equally important to achieving a Final Four Run, it would appears that AdjD becomes nearly doubly important for a team in order to win it all.

When evaluating potential Champion teams, ELIMINATE:

-Any team ranked outside of the Top 50 on either side of the ball

-Any team ranked below 25th in AdjD.

Consider with extreme scrutiny:

-Any team ranked outside of the Top 25 on either side of the ball (6.8% success rate historically)

-Any team ranked outside of the Top 10 on both sides of the ball (15.4% success rate historically)

Identify teams that lie above positive mean trends:

-Any team ranked in the Top 10 of both AdjO and AdjD (53.6% success rate).

-Any team with a combined efficiency number below 17 (mean).

**UPSETS**

One of the most important ways that this data can be used is in regards to upsets- not necessarily to predict upsets, but rather to have an understanding of a possibly highly seeded team’s susceptibility to be upset relative to other teams. Recognizing this can result in taking picking a team to lose earlier than many people will without taking significant risk.

So, let’s take a trip down memory lane and re-live some of the biggest tournament upsets in the KenPom era. Again, the goal is not to prove that we could have predicted the upset, but rather to show that there were signs that could have signified picking the team that was upset to lose earlier than the average bracket would have based on our already established criteria. As always, nothing is fool proof, and some of these upsets remain massive head-scratchers, which is still part of the fun…March Madness should never become a stranger to the unexplained, nor will it ever become anything close to an exact science.

**Biggest NCAA Tourney Upsets in KenPom Era (since 2002):**

Formula for ranking the upset: (Winning Seed/ Losing Seed ) + (Winning Seed- Losing Seed)

* Efficiency numbers included are for the losing team only.

#1: 2006: 11) George Mason over 1) UConn

(2nd AdjO, 25th AdjD)

This defensive ranking below 21st eliminated UConn as a potential National Title team.

#2: 2011: 11) VCU over 1) Kansas

(7th AdjO, 11th AdjD)

Upset not explainable by our criteria.

#3: 2012: 15) Norfolk State over 2) Missouri

(1st AdjO, 146th AdjD)

This defensive ranking way outside of the Top 50 eliminated Missouri as a potential National Title team and gave them a very slim chance to make the Final Four, only because of their dominance on offense.

#4: 2012: 15) Lehigh over 2) Duke

(10th AdjO, 81st AdjD)

This defensive ranking outside of the Top 50 without a dominant offensive ranking eliminated Duke from both National Title and Final Four contention.

#5: 2013: 15) Dunk City over 2) Georgetown

(78th AdjO, 2nd Adj D)

This offensive ranking outside of the Top 50 eliminated Georgetown from National Title contention and gave them a very slim shot at the Final Four only due to their dominant defense.

#6: 2010: 9) Northern Iowa over 1) Kansas

(2nd AdjO, 9th AdjD)

Upset not explainable by our criteria.

#7: 2004: 9) UAB over 1) Kentucky

(27th AdjO, 9th AdjD)

Upset not explainable by our criteria.

#8: 2013: 9) Wichita State over 1) Gonzaga

(2nd AdjO, 37th AdjD)

This defensive ranking below 21st eliminated Gonzaga as a potential National Title team.

#9: 2005: 14) Bucknell over 3) Kansas

(13th AdjO, 25th Adj D)

This defensive ranking below 21st eliminated Kansas as a potential national title team, and the lack of a Top 10 efficiency on either side of the ball gave Kansas a very slim chance to make the Final Four.

#10: 2006: 14) Northwestern State over 3) Iowa

(151st AdjO, 1st AdjD)

This offensive ranking well below 39th eliminated Iowa as a potential National Title team and gave them a very slim chance to make the Final Four, only because of their dominant defense.

Others:

2013: 14) Harvard over 3) New Mexico

(53rd AdjO, 18th AdjD)

This offensive ranking outside of the Top 50 without a dominant defense eliminated New Mexico as a Final Four candidate.

2014: 14) Mercer over 3) Duke

(2nd AdjO, 116th Adj D)

This defensive ranking eliminated Duke from National Title contention, and they had very slim chance at the Final Four only thanks to a dominant offense.

2010: 14) Ohio over 3) Georgetown

(10th AdjO, 61st Adj D)

This defensive ranking outside the Top 50 without a dominant offense eliminated Georgetown from Final Four contention.

2002: 8) UCLA over 1) Cincinnati

(6th AdjO, 5th AdjD)

Upset not explainable by our criteria.

2004: 8) Alabama over 1) Stanford

(49th AdjO, 3rd AdjD)

This offensive ranking below 39th eliminated Stanford as a national title contender, and they only narrowly maintained status as a Final Four contender as the offense held Top 50 status by the skin of its teeth without a dominant (Top 2) defense.

2011: 8) Butler over 1) Pitt

(4th AdjO, 22nd AdjD)

Upset not explainable by our criteria.

So, out of the 16 biggest upsets in the Ken Pom area, 11 of the losses (69%) can be anticipated earlier than expected based on the criteria. This is different than proclaiming that the winning team was easy to predict, which is an important distinction to make. We are simply saying that more than two thirds of the time, evidence existed indicating that these teams would lose before the National Championship game and in most cases, before the Final Four. Our criteria indicated that a whopping 8 of the 16 teams “upset” (50%) had a slim to none chance to make the Final Four to begin with.

Good luck with your brackets, and welcome to March Madness.

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