Bracket Science: Picking your Final 4 and champion

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Bracket picking time is nearly upon us, and if you're like me, a tiny part of you is thinking, "Maybe -- just maybe -- this year I can build the perfect bracket."

Don't listen to that part of you. It has an extremely tiny hold on reality. Try one nine-quintillionth of your sanity. Or to be more specific, one in 9,223,372,036,854,775,808, two to the 63rd power. Those are the odds of picking up a bracket sheet, dashing off your picks and having everything fall perfectly into place.

Of course, these are just the theoretical odds of picking a perfect bracket, since 16 seeds are virtually assured of losing out of the gate, 15 seeds are 96 percent likely to lose, etc. Still, the odds are astronomical. Let's just assume for the sake of argument we want to be absolutely 100 percent sure we achieve perfection; we'll still have to fill out all those nine quintillion brackets.

It goes without saying that nine quintillion is a big number. How big? Consider this:

There are, according to various sources, 134,548 schools in America, from pre-K through college, both public and private. Let's say that they all had a standard 94- by 50-foot college-sized basketball court (a stretch, I know). Let's assume further that you had the time, gas mileage and payload capacity to cart all these brackets to each school and evenly paper their courts. Every school would get 9.4 billion brackets -- and that would create stacks all around the country 591 miles high. That's the distance from St. Louis to New Orleans ... or, for West Coast fans, the distance between San Francisco and San Diego.

Bottom line: You're not going to fill out a perfect bracket. If you're like me, though, you'll happily take solace in winning your pool. In this case, the challenge is a tad easier. Depending on the number of people you're up against and your round-by-round scoring method, you'll need to make somewhere between 48 and 54 correct picks out of the 63 tourney games to come out on top. This works out to a more manageable 76 to 85 percent accuracy rate.

Forecasting the Final Four

Considering that most pools give greater weight to correct picks in later rounds, you're probably going to need to correctly identify at least three of the Final Four contenders. Simple, eh? In fact, picking all four semifinalists is 141 trillion times easier than building the perfect bracket. That's the good news: the bad news is that the odds of nailing the Final Four are still 1 in 65,536 (16 to the fourth power).

This assumes, of course, that every team has an even chance of advancing to the semifinals. And we know that's not true. Since the tournament expanded to 64 teams, only five squads seeded lower than six have reached the Final Four (eight seed Villanova in 1985, 11 seed LSU in 1986, eight seeds Wisconsin and North Carolina in 2000, and 11 seed George Mason in 2006.) By just eliminating the seven through 16 seeds, you improve your odds to about 1 in 1,296, allowing for 95 percent accuracy.

So what's the best strategy to boost your odds of getting the Final Four right? Well, you could play it safe and advance all the top seeds to the semifinals. 24 of the 25 tourneys in the 64-team era have had at least one top seed in the Final Four (11 have had two, three have had three and 2008 was the only dance to have all four). That's comforting -- until you realize that the only exception happened just four years ago in 2006 (UCLA was a two, Florida was a three, LSU was a four and George Mason was an 11).

Besides, a "top-seed" strategy would almost certainly doom your chances of winning a pool -- unless we have another "by-the-numbers" upset-free March Madness like we've had in the past two years. I don't see that happening this year. The fact is, fewer than two top seeds reach the semis on average. In the 25 tourneys of the 64-team era, 44 of the 100 Final Four contenders (or 1.76 per year) have been one seeds. The trick is to figure out how to identify the 56 top-seeded pretenders -- and replace them with the right mix of lower seeds.

That's a pretty neat trick. Unfortunately, there's no single factor that separates Final Four teams from the pack. But semifinal squads do share common attributes. If you know what they are, you can significantly improve your odds of forecasting the right Final Four teams.

The anatomy of a Final Four contender

The 100 Final Four teams of the modern era are made up of:

• 44 one seeds
• 22 two seeds
• 13 three seeds
• Nine four seeds
• Four five seeds
• Three six seeds
• Three eight seeds
• Two 11 seeds

If you separate the teams at every seed position that make the Final Four from those that don't, you'll find that the winners tend to share attributes that the losers don't possess. Let's take a look at each of the top six seeds (we're dropping all seeds lower than six and conceding five lost Final Four predictions) and identify the factors that separate Final Four contenders from pretenders.

Top seeds: Instead of examining the factors that top-seeded Final Four contenders possess, let's identify the characteristics that disqualify a one seed from reaching the semifinals. Beware of a top seed that has any one of these 11 attributes:

1. They didn't go to the previous dance.

2. They've lost two or more games in a row.

3. Their coach has been to the dance five or more times without reaching the Elite Eight.

4. They have a winning percentage lower than .780.

5. They have a "strength of schedule" (SOS) rating weaker than 80.

6. They score 72 or fewer points per game.

7. They allow 80 or more points per game.

8. Their scoring margin is 10.5 points per game or less.

9. They get imbalanced scoring, relying on either the backcourt or frontcourt for 73 percent or more of their points.

10. They get outrebounded.

11. They shoot less than .465 from the floor.

Top seeds possessing any of these attributes are just four for 37 in reaching the Final Four, a 10.8 percent success rate. The four exceptions are Oklahoma in 1988 (gave up 81.4 points per game), Minnesota in 1997 (didn't go to the dance in 1996), Texas in 2003 (Barnes had been to the dance 11 times without reaching the Elite Eight) and UConn last year (two-game losing streak). Meanwhile, top seeds that aren't hampered by any of these weaknesses are 40 for 63 in reaching the Final Four -- a 63.5 percent success rate. That's a 44.3 percent improvement over the typical success rate of top-seeded semifinalists. Just as important, these exclusion rules identify 40 of the 44 actual contenders, for an accuracy rate of more than 90 percent.

Two seeds: There are also 11 attributes that mark second-seeded pretenders. Avoid any two seed with one or more of these characteristics:

1. They've won fewer than six of their past 10 pre-tourney games.

2. Their coach has been to the dance fewer than four times.

3. Their winning percentage is lower than .765 or higher than .900.

4. They have an SOS rating weaker than 40.

5. They give up 56.8 points per game or less, suggesting a slow-tempo style of play.

6. Their scoring margin is less than 8.7 or more than 18.5 points per game.

7. They rely on guards for more than 77 percent of their points.

8. They have more than one freshman starter or more than three senior starters.

9. They get outrebounded.

10. They shoot less than .450 from the floor.

11. Their assist-to-field goal percentage is less than .500.

Two seeds that possess any of these qualities are an astounding 0-52 in their quest for the Final Four. Meanwhile, second-seeded teams without any of these attributes are 22-48 in reaching the final weekend. That's 45.8 percent reliability, much lower than the exclusion rules for top seeds. But here's the deal: It's more than twice as good as the typical 22 percent success rate of two seeds in getting to the Final Four. Not only that, but the rules accommodate every single two seed that has reached the semifinals.

Three seeds: The three seeds that have the best chance to reach the Final Four share these attributes:

1. They've won between six and eight of their past 10 pre-tourney games.

2. They've haven't lost two or more pre-dance games in a row but haven't won more than two in a row either.

3. They score more than 76 points a game.

4. They allow more than 66.5 points per game (indicating an up-tempo team).

5. They beat opponents by more than 7.3 points a game.

6. They have an SOS rating that's not too tough (higher than 20) but not too easy (lower than 70)

7. They don't rely on guards for more than 67 percent of their points.

8. If they're a mid-major, they have an All-American on the team.

Three seeds with these qualities have advanced to the semifinals 10 times in 21 tries, for a 47.6 percent success rate. That's 266 percent better than the typical one-in-eight odds. Third-seeded teams that don't meet these criteria have a dismal 3-66 record in reaching the Final Four. The only three seeds to defy the odds were Utah in 1998, Georgia Tech in 2004 and Florida in 2006. That's not good. Florida was the champion three tourneys ago. But, as we'll see in a moment, this doesn't necessarily mean that they're out of contention for bracket consideration.

Four seeds: The four seeds that reach the Final Four have to fight their way past top seeds in the Elite Eight. What qualities do they need to topple the giants? Here are the seven attributes to look for:

1. A coach who has been to the tourney before.

2. A winning percentage between .740 and .880.

3. Solid momentum with eight or nine wins in their past 10 and no worse than a single-game losing streak.

4. A scoring average above 74 points a game.

5. A points-allowed average above 63 points.

6. An average scoring margin of more than 7.5 points.

7. Imbalanced scoring, getting more than 64 percent of their points from the frontcourt or over 66 percent from the backcourt.

Fourth-seeded squads teams possess all these attributes are a perfect 7-0 in reaching the Final Four. The rest of the fourth-seeded schools are just 2-91 in getting to the semifinals. The only two four seeds that advanced to the semifinals without possessing these traits were Oklahoma State in 1995 and Arizona, the champion of 1997.

Five and six seeds: What do fifth- and sixth-seeded semifinal contenders have in common? How about all of these conditions?

1. They have a coach who has made between two and eight tourney trips -- and if he's danced more than twice, he's reached the Elite Eight at least once.

2. They're from a Big Six conference.

3. Their winning percentage is between .645 and .790.

4. They've won between six and eight of their past 10 games.

5. They have no more than a one-game end-of-season losing streak and no better than a three-game win streak.

6. They score more than 70 points a game.

7. They allow fewer than 78 points a game.

8. Their average scoring margin is more than 5.5 points.

9. They've got a balanced attack, with guards getting more than 35 but less than 70 percent of their points.

10. They don't crutch on their starters or the bench, getting between 75 and 81 percent of their points from the starting unit.

11. They shoot better than .450 from the floor.

Got all that? Good, because fifth- and sixth-seeded teams fulfilling all these conditions are a respectable 5-8 (40 percent successful) in reaching the Final Four; the rest of the teams are a paltry 2-185. The only exceptions to the rules above were Mississippi State in 1996 and Florida in 2000.

Merging seed qualifiers into a pool of Final Four candidates

The combined "Final Four advancement" rate of the teams satisfying the seed-based rules above is 55.3 percent (84 of 152 teams). That's 25.6 percent better than the advancement rate of top seeds (44 of 100). Plus, the rules above describe almost twice as many Final Four candidates -- and 84 percent of the 100 teams in the 64-team era. Think of it another way: only 16 of the remaining 1,423 tourney teams (around 1 percent) have reached the semifinals. Even if you restricted the comparison to other first- through sixth-seeded teams, only eight of 448 (1.8 percent) "outside-the-rules" teams reached the semifinals.

So you can feel pretty good. You're armed with a set of rules that describe 84 percent of the semifinalists while narrowing your selection to an average about six teams per tourney. But your work isn't done. You still have to determine which of the 152 qualifying teams are the actual 84 Final Four contenders. When you assign these 152 teams to their year and region, four conditions emerge:

1. In 41 regions, only one team met the Final Four requirements.

2. In 41 regions, two teams made the Final Four grade.

3. In nine regions, more than two teams qualified as semifinal contenders.

4. In nine regions, there were no teams that met the Final Four requirements.

The next step is to develop rules that address each of these types of conflicts. Condition No. 1 is easy: you advance the single team to your Final Four -- and pat yourself on the back, since those 41 teams are an impressive 35-6 in reaching the semifinals. For condition No. 4, since the seed factors didn't identify any teams, consider the top three seeds and evaluate them with the condition No. 3 "multi-candidate" rules.

That leaves the dual and multi-candidate conditions. For the 41 regions where two teams met the Final Four criteria, settle the conflict like this: first off, automatically advance the fourth-seeded teams since we know they're perfect in reaching the Final Four. Now, settle the rest of the regions by following these rules in order:

1. Eliminate all five seeds.

2. Eliminate any one seed that's won fewer than eight of their past ten games.

3. Eliminate any snakebitten coach (more than five tourney trips without an Elite Eight appearance) in a region with a coach who has been to the Elite Eight more than once.

4. Pick veteran teams with four or five junior/senior starters and more than the competing candidate in the region.

5. Eliminate any team with an average scoring margin of fewer than 10 points, and pick any team with an average scoring margin greater than six points more than opposing candidates in the region.

6. Avoid teams with two or more freshman starters.

7. For all remaining regions, take the higher scoring team.

The "dual candidate" rules also result in a 35-6 record in identifying Final Four contenders. Pretty darn good. Fair warning, though, which I'll repeat in the summary: These rules identify the attributes that correlate to advancement in the tournament, but it doesn't mean they're the cause.

For the 18 multi-candidate conditions, follow these seven rules in order, advancing any team once they're the only squad left in the region:

• Automatically advance four seeds.
• Eliminate any squad that gets less than a third or more than 70 percent of its points from guards.
• Eliminate any team that has fewer than three junior/senior starters.
• Eliminate top seeds without All-Americans.
• Eliminate all non-top seeds with SOS ratings lower than 40.
• Eliminate snakebitten coaches with more than five tourney appearances and no Elite Eight runs.
• In all the remaining matchups, take the higher seed.

That's a lot of numbers to chew through -- but don't worry. After Selection Sunday, I'll do this heavy lifting for you. Look on this site listing the teams that meet these and all the other rules I identify. At this point, just remember this: Historically, applying these guidelines to the multi-candidate regions gives you a 13-5 record in pegging the right Final Four contender.

So what would your Final Four prediction record be if you filtered the 152 eligible semifinal teams using the rules above? Let's revisit the scenarios for the regional breakdowns and tally the records:

1. 41 single-team regions: 35-6

2. 41 dual-team regions: 35-6

3. 18 multi-team regions (including the nine open regions): 13-5

Altogether, that works out to an 83-17 (.840) record in identifying Final Four candidates. That's about 89 percent or 39 games better than simply picking top seeds to advance to the semifinals. This strategy also retains 23 of the 25 tourney champions, missing only Villanova in 1985 (what model would've predicted that one?) and Arizona in 1997. A top-seed strategy would've only retained 15 champions. Here's a look at the teams our forecasting strategy identified (correct picks shaded light blue, champion shaded in teal):

This model identified a slightly lower percentage of Final Four teams than last year's model, which was 81 for 96, 84.4 percent correct, in picking semifinalists. Last year, the rules admitted about the same number of teams (153 to 152), yet fewer correct possibilities (82 to 84). The seed-exclusion rules have pretty much the same number of conditions, but I did discover stronger correlations between SOS and coaching success (or failure in the case of the snakebitten ones) and Final Four advancement. Last year's rules got North Carolina, UConn and Michigan State right, missing only on Villanova. This year's rules would have also pegged the Wildcats.

Picking your champion

It's one thing to settle on your Final Four contenders. It's another to figure out which of those squads to anoint as your champion. Given the model's performance in identifying semifinalists, the best result we can expect is to correctly identify 23 of the 25 champs.

What are the tell-tale attributes of a tourney champion? If you want a quick way to filter the field, look for teams that possess these attributes:

• They score more than 75 and don't allow more than 79 points a game (applies to 24 of 25 champions, missing only Villanova in the first year of the 64-team era).
• They haven't lost two or more games in a row -- or won more than 13 straight (only Arizona in 1997 failed to meet this requirement ... and we've already lost that year).
• They've won more than six of their last 10 games (Villanova and Arizona are the only expectations again).
• Their frontcourt accounts for between 37 and 71 percent of their points (every champ satisfies this condition).
• Their coach has been to the dance at least three times, but isn't snakebitten, with more than five tourney trips and no Elite Eight runs (Michigan in 1989 was the only exception here; Steve Fisher was making his tourney debut).
• They either have an All-American or a winning rate above .785 (only Louisville in 1986 and Arizona in 1997 failed to meet this condition).

After eliminating all the teams in our Final Four grid that failed to meet these criteria, seven tournaments get decided. Six are wins -- 1990, 1995, 1999, 2003, 2007 and 2009. One is a loss. Instead of picking Michigan in 1989, which was coached by newbie Steve Fisher, our rules tabbed second-seeded Syracuse.

So far, then, we're 6-3 in picking tourney champs, with 16 dances and 39 teams left. To determine the rest of the years, following these rules in order, slotting in your champion once they're the only squad left:

• Eliminate mid-majors.
• Eliminate any team that has won all their past 10 games.
• Retain teams that get between 30 percent and 60 percent of their points from guards.
• Eliminate any team without an All-American.
• Eliminate any team that allows fewer than 68 points a game.
• Pick the team with an older starting unit.

Following these rules, you'd be 15-1 in pegging the champ for the tourneys still in play. The only tourney you'd lose is 1986, when Mid-Major Louisville cut down the nets. Combined with the 6-3 record from the two years we had no shot at and the seven that were resolved with the initial disqualifiers, these rules would yield a 21-4 record in picking the champ. At the left, here are the champs you'd get right (in light blue) ... and the pretenders you'd get wrong (in white).

A word of warning before you get revved up to number-crunch the stats on this year's field. As I mentioned earlier, after Selection Sunday, I will be presenting the teams that these statistical rules say will be the 2010 Final Four contenders and ultimate champion. So if you're not up for pulling an all-nighter, let me do it for you.

Of course, every March Madness forecasting strategy should come with a gigantic disclaimer: Past performance does not guarantee future results. Each tournament manages to violate rules that were once considered ironclad. The fact is, all the rules described don't cause a team to advance to the Final Four or win the championship; they merely correlate with the majority of teams that have accomplished these feats. And this particular year, by adding more stringent rules to the "seed-exclusion" process, I've probably pre-conditioned the field of potential semifinalists to be one or two seeds. So if you're feeling like the 2010 tourney will be more free-wheeling -- and given that there aren't any North Carolina juggernauts out there, that's entirely possible -- you may want to cast a cold eye on this approach to picking your Final Four and champion.

Freelance writer Pete Tiernan has been analyzing the NCAA Tournament for 19 years. E-mail him at bracketscience@comcast.net or go to www.bracketscience.com to view eight different models for making your bracket picks.