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Probability of a Perfect Bracket
Introduction
A question I get a lot in March is, "What is the probability of filling out a March Madness bracket completely perfectly?" A frequently quoted statistic in the media is 1 in 9,223,372,036,854,780,000. This quotation is based on guessing randomly, which nobody does, and makes the hair on the back of my neck stand up. Here I will give a basic strategy you can follow, knowing nothing about basketball, and an estimate of your probability of success with said strategy.
Rules
Following are the rules of the tournament. If you already know them, you can skip this part.
For most intents and purposes, the tournament is single elimination, starting with 64 teams. To satisfy my perfectionist readers, there are actually 68 teams, where eight of them are matched up in four games. The winners of those four games, and 60 other teams, result in 64 teams, which is when the bracket picking typically begins.
The 64 teams are divided into four different conferences, North, South, West, and East, of 16 teams each. Each team in each conference will have a "seed," from 1 to 16, which is meant to be a ranking of their ability, although it is an imperfect method. Next the following will happen:
- The four 1 seeds will play the four 16 seeds.
- The four 8 seeds will play the four 9 seeds.
- The four 5 seeds will play the four 12 seeds.
- The four 4 seeds will play the four 13 seeds.
- The four 6 seeds will play the four 11 seeds.
- The four 3 seeds will play the four 14 seeds.
- The four 2 seeds will play the four 15 seeds.
- The four 7 seeds will play the four 10 seeds.
- After the games in steps 1 to 8, the 64 teams will be narrowed down to 32.
- The winners from rule 1 will play the winners from rule 2.
- The winners from rule 3 will play the winners from rule 4.
- The winners from rule 5 will play the winners from rule 6.
- The winners from rule 7 will play the winners from rule 8.
- After the games in steps 10 to 13, the 32 remaining teams will be narrowed down to 16.
- The winners from rule 10 will play the winners from rule 11.
- The winners from rule 12 will play the winners from rule 13.
- After the games in steps 15 and 16, the 16 remaining teams will be narrowed down to eight.
- The winners from rule 15 will play the winners from rule 16.
- After the games in step 18, the eight remaining teams will be narrowed down to 4. This will establish a winner from each of the four divisions.
- The winner of the regional that had the #1 overall team as determined by the NCAA basketball committee when selecting the tournament teams plays the winner of the regional that had the #4 overall team; with the winner advancing.
- The winners of the two regions, not mentioned in rule 20, play each other, with the winner advancing.
- The winners of steps 20 and 21 will play, the winner winning the tournament.
Once it gets to 64 teams, there are 32+16+8+4+2+1=63 games in the tournament.
Basic Strategy
Always pick the team with the higher-ranking seed, or lower number. For example, in the four games where a number 1 seed plays a number 16 seed, pick the number 1 seed. Of the 136 times a 1 seed has played a 16 seed, the number one seed won 135 times. 2018 saw the first number one seed lose to a 16 seed when UMBC (which has a great chess team) beat the University of Virginia.
When you get down to a number one seed winning each of the four divisions, pick the remaining three games randomly.
Matchups
The following table shows many face-offs there have been among all unbalanced match-ups have that happened at least once. This does not include games where teams of equal seed played against each other. The right column shows the probability the higher ranked team won.
Unbalanced Matchup Results
| Higher Seed | Lower Seed | Games Played | Higher Seed Wins | Probability |
|---|---|---|---|---|
| 1 | 2 | 67 | 36 | 0.537313 |
| 1 | 3 | 36 | 22 | 0.611111 |
| 1 | 4 | 64 | 47 | 0.734375 |
| 1 | 5 | 48 | 40 | 0.833333 |
| 1 | 6 | 13 | 10 | 0.769231 |
| 1 | 7 | 7 | 6 | 0.857143 |
| 1 | 8 | 75 | 60 | 0.800000 |
| 1 | 9 | 71 | 65 | 0.915493 |
| 1 | 10 | 6 | 5 | 0.833333 |
| 1 | 11 | 8 | 4 | 0.500000 |
| 1 | 12 | 20 | 20 | 1.000000 |
| 1 | 13 | 4 | 4 | 1.000000 |
| 1 | 16 | 144 | 143 | 0.993056 |
| 2 | 3 | 56 | 34 | 0.607143 |
| 2 | 4 | 7 | 3 | 0.428571 |
| 2 | 5 | 5 | 0 | 0.000000 |
| 2 | 6 | 30 | 23 | 0.766667 |
| 2 | 7 | 82 | 57 | 0.695122 |
| 2 | 8 | 7 | 2 | 0.285714 |
| 2 | 9 | 1 | 0 | 0.000000 |
| 2 | 10 | 52 | 34 | 0.653846 |
| 2 | 11 | 18 | 15 | 0.833333 |
| 2 | 12 | 2 | 2 | 1.000000 |
| 2 | 15 | 144 | 134 | 0.930556 |
| 3 | 4 | 7 | 4 | 0.571429 |
| 3 | 5 | 4 | 2 | 0.500000 |
| 3 | 6 | 75 | 45 | 0.600000 |
| 3 | 7 | 15 | 9 | 0.600000 |
| 3 | 8 | 2 | 2 | 1.000000 |
| 3 | 9 | 2 | 2 | 1.000000 |
| 3 | 10 | 12 | 8 | 0.666667 |
| 3 | 11 | 49 | 32 | 0.653061 |
| 3 | 14 | 144 | 122 | 0.847222 |
| 3 | 15 | 2 | 2 | 1.000000 |
| 4 | 5 | 75 | 42 | 0.560000 |
| 4 | 6 | 4 | 2 | 0.500000 |
| 4 | 7 | 5 | 2 | 0.400000 |
| 4 | 8 | 9 | 4 | 0.444444 |
| 4 | 9 | 3 | 2 | 0.666667 |
| 4 | 10 | 2 | 2 | 1.000000 |
| 4 | 12 | 39 | 26 | 0.666667 |
| 4 | 13 | 144 | 113 | 0.784722 |
| 5 | 6 | 1 | 1 | 1.000000 |
| 5 | 8 | 3 | 1 | 0.333333 |
| 5 | 9 | 3 | 1 | 0.333333 |
| 5 | 10 | 1 | 1 | 1.000000 |
| 5 | 12 | 144 | 93 | 0.645833 |
| 5 | 13 | 19 | 16 | 0.842105 |
| 6 | 7 | 9 | 6 | 0.666667 |
| 6 | 8 | 1 | 0 | 0.000000 |
| 6 | 10 | 7 | 4 | 0.571429 |
| 6 | 11 | 144 | 90 | 0.625000 |
| 6 | 14 | 15 | 13 | 0.866667 |
| 7 | 8 | 2 | 1 | 0.500000 |
| 7 | 10 | 144 | 87 | 0.604167 |
| 7 | 11 | 3 | 0 | 0.000000 |
| 7 | 14 | 1 | 1 | 1.000000 |
| 7 | 15 | 5 | 3 | 0.600000 |
| 8 | 9 | 144 | 74 | 0.513889 |
| 8 | 11 | 1 | 1 | 1.000000 |
| 8 | 12 | 2 | 0 | 0.000000 |
| 8 | 13 | 1 | 1 | 1.000000 |
| 8 | 16 | 1 | 0 | 0.000000 |
| 9 | 11 | 1 | 0 | 0.000000 |
| 9 | 13 | 1 | 1 | 1.000000 |
| 10 | 11 | 3 | 1 | 0.333333 |
| 10 | 14 | 1 | 1 | 1.000000 |
| 10 | 15 | 5 | 5 | 1.000000 |
| 11 | 14 | 7 | 6 | 0.857143 |
| 12 | 13 | 12 | 9 | 0.750000 |
Analysis
The way I used to analyze the probability of a perfect bracket was to look at historical experience of any one seed beating another seed. For example, the probability of a 4 seed beating a 5 seed. At the time of this writing, with 36 years of data from 1985 to 2021, such a matchup has happened 75 times, with the 4 seed winning 42 of them, for a probability of 56%. This is a decent method, but suffers from a small sample size problem. I think a better way to get at the probability of the higher seeded team winning any given game, according to the two seed numbers, is to look at all 2,268 tournament games played in the 36 years between 1985 and 2021. Doing so gave me the opportunity to smooth out the ups and down in the data and make for a better estimate. I get into how I did more more deeply in my page on March Madness.
The following table shows the probability of the higher seeded team winning any possible matchup necessary to win if the player picked the higher seeded team every game. In the case of a 1 seed playing a 1 seed, I assume a 50% chance of winining any given game. The "old method" probability looks at the exact probability, based on historical experience. The "new method" is based on my method of smoothing out the data to get a more accurate picture of the strength of any given seed.
Probability Favorite Wins
| Round | Event | Games Played | Probability Old Method |
Probability New Method |
|---|---|---|---|---|
| 1 | 1 beats 16 | 4 | 0.993056 | 0.993049 |
| 1 | 2 beats 15 | 4 | 0.930556 | 0.933458 |
| 1 | 3 beats 14 | 4 | 0.847222 | 0.887485 |
| 1 | 4 beats 13 | 4 | 0.784722 | 0.832170 |
| 1 | 5 beats 12 | 4 | 0.645833 | 0.768372 |
| 1 | 6 beats 11 | 4 | 0.625000 | 0.697340 |
| 1 | 7 beats 10 | 4 | 0.604167 | 0.620749 |
| 1 | 8 beats 9 | 4 | 0.513889 | 0.540650 |
| 2 | 1 beats 8 | 4 | 0.800000 | 0.792047 |
| 2 | 4 beats 5 | 4 | 0.560000 | 0.540873 |
| 2 | 3 beats 6 | 4 | 0.600000 | 0.622246 |
| 2 | 2 beats 7 | 4 | 0.695122 | 0.702952 |
| 3 | 1 beats 4 | 4 | 0.734375 | 0.668944 |
| 3 | 2 beats 3 | 4 | 0.607143 | 0.551538 |
| 4 | 1 beats 2 | 4 | 0.537313 | 0.578959 |
| 5 | 1 beats 1 | 2 | 0.500000 | 0.500000 |
| 6 | 1 beats 1 | 1 | 0.500000 | 0.500000 |
Before going on, let me use the notation of pr(x) = probability of event x happening. For example, pr(rolling a total of 7 with two dice) = 1/6.
Remember that there are four divisions in the tournament, so for the first four rounds, the player will have to win any given matchup four times.
The probability of winning all 32 games in the first round and advancing to round 2 is: [pr(1 seed beats 16 seed)*pr(2 seed beats 15 seed)*pr(3 seed beats 14 seed)*pr(4 seed beats 13 seed)*pr(5 seed beats 12 seed)*pr(6 seed beats 11 seed)*pr(7 seed beats 10 seed)*pr(8 seed beats 9 seed)]^4.
Under the new method, this probability of surviving to round 2 is 1 in 4,354.
In round 2, the player will have 16 games to win. Assuming he survives round 1, the probability of surviving round 2 will be [pr(1 seed beats 8 seed)*pr(2 seed beats 7 seed)*pr(3 seed beats 6 seed)*pr(4 seed beats 5 seed)]^4. This probability, using the new method is 1 in 811. The probability of surviving both rounds 1 and 2 is 1 in 3,531,138.
In round 3, the player will have 8 games to win. Assuming he survives rounds 1 and 2, the probability of surviving round 3 will be [pr(1 seed beats 4 seed)*pr(2 seed beats 3 seed)]^4. This probability, using the new method is 1 in 54. The probability of surviving to this point, from the beginning, is about 1 in 190 million.
In round 4, the player will have 4 games to win. These will all be 1 seed vs. 1 seed games. Let's assume a 50% chance of winning each game. The probability of winning all four games is (1/2)^4 = 1 in 16. The probability of surviving to this point, from the beginning, is about 1 in 1.7 billion.
In round 5, the player will have 2 games to win. These will all be 1 seed vs. 1 seed games. Again, let's assume a 50% chance of winning each game. The probability of winning both games is (1/2)^2 = 1 in 4. The probability of surviving to this point, from the beginning, is about 1 in 6.8 billion.
The player will still have one more game to win, the championship game. If he survived this far, it will be another 1 seed vs. 1 seed. Let's again assume a 50% chance of winning. That brings the probability of survival through the championship game, for a perfect bracket, to about 1 in 13.6 billion.
By the way, using the old method results in a probability of a perfect bracket of 1 in 56.7 billion.
Warren Buffett Prize
Warren Buffett has offered $1,000,000 per year, for life, to any employee of his who can fill out a perfect bracket. Warren has about 377,000 employees (source). Assuming each one followed the strategy above, and lived 60 more years, the expected value per employee is 0.4 cents and the expected cost to Mr. Buffet over all his employees is $1,667.
If you don't want to risk sharing the glory of a perfect bracket with someone else following my strategy, I'd suggest picking one or two 9 seeds to beat an 8 seed. The probability of the nine seed beating an eight seed is 47.8%, so a small sacrifice to increase your chances at hogging the glory of a perfect bracket to yourself.
Compare Online NBA Odds
Basketball : Basketball Euroleague
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Fri Dec 13th 12pm
Anadolu Efes Panathinaikos |
⇗10.00 |
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Anadolu Efes is expected to win due to strong home record. Panathinaikos struggles away. Focus on Efes' shooting guards and Panathinaikos' defensive weaknesses. |
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Fri Dec 13th 2pm
FC Barcelona Bàsquet Pallacanestro Olimpia Milano |
⇗10.00 |
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FC Barcelona Bàsquet's strong home performance may challenge Olimpia Milano's resilience. Expect a competitive game with potential standout plays. Watch key players' impact, especially in clutch moments. |
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Fri Dec 13th 2pm
KK Crvena zvezda Olympiacos |
⇗10.00 |
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Crvena Zvezda's home advantage may be key. Olympiacos's strong defense challenges Zvezda's offense. Watch for turnovers. Close game expected. Player form crucial. Betting odds may fluctuate. |
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Fri Dec 13th 3pm
ASVEL Lyon Villeurbanne Paris Basketball |
⇘5.00 |
⇗215.00 |
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ASVEL Lyon is favored due to home advantage and recent form. Paris Basketball's victory would be an upset. Key players and defense will be crucial. |
Basketball : NBA
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Fri Dec 13th 7pm
Philadelphia 76ers Indiana Pacers |
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Philadelphia 76ers have a strong home record, but the Indiana Pacers' recent form is impressive. Key players’ performance will be crucial in determining the game's outcome. |
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Fri Dec 13th 7pm
Cleveland Cavaliers Washington Wizards |
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The Cavaliers' strong defense faces the Wizards' offense. Player performances and injury updates are crucial for betting decisions. Analyze recent matches for trends and team strategies. |
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Fri Dec 13th 8pm
Chicago Bulls Charlotte Hornets |
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⇗5.00 |
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Analyze team form, player injuries, and head-to-head stats. Bulls have strong defense; Hornets excel in offense. Check recent performances and betting odds for informed decisions. |
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Fri Dec 13th 8pm
Minnesota Timberwolves Los Angeles Lakers |
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Consider Timberwolves' improved defense and Lakers' home court advantage. Star performances from LeBron James and Anthony Edwards are key. Watch for bench contributions and shooting efficiency. |
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Fri Dec 13th 8pm
Memphis Grizzlies Brooklyn Nets |
-600
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Memphis Grizzlies strong at home, while Brooklyn Nets struggle on the road. Key players: Grizzlies' Morant, Nets' Durant. Watch for scoring patterns and defensive matchups. Consider recent form and injuries. |
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Fri Dec 13th 9pm
Denver Nuggets Los Angeles Clippers |
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Denver Nuggets rely on Jokic's playmaking against Clippers' defense. Clippers need Kawhi's scoring to win. Nuggets' bench depth may decide the game. |
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Fri Dec 13th 9pm
Utah Jazz Phoenix Suns |
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⇗5.00 |
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Consider Suns' strong home record and Jazz's recent form. Watch for player injuries. Betting on the under/over might be wise, as both teams have fluctuating offenses. |
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Fri Dec 13th 10pm
Portland Trail Blazers San Antonio Spurs |
140
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⇗5.00 |
The Portland Trail Blazers' strong offense challenges the Spurs' young roster. Watch for Damian Lillard's performance. Spurs' defense improvement is key. Close game expected with potential for high scoring. |
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Sat Dec 14th 4pm
Milwaukee Bucks Atlanta Hawks |
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-105 (229.5)
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Bucks strong at home, Giannis impacts both ends. Hawks rely on Young’s shooting. Defensive rebounding crucial. Consider home edge, but watch injury reports for last-minute changes. |
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Sat Dec 14th 8pm
Oklahoma City Thunder Houston Rockets |
⇗5.00 |
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-105 (213)
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Oklahoma City Thunder have strong draft picks. Houston Rockets focus on rebuilding. Key players' health is crucial. Expect a close game, with minor odds favoring Oklahoma if they perform consistently. |
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Wed Dec 25th 12pm
New York Knicks San Antonio Spurs |
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The Knicks have a strong defense this season, while the Spurs struggle on the road. Expect a low-scoring game with the Knicks as favorites. |
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Wed Dec 25th 2pm
Dallas Mavericks Minnesota Timberwolves |
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Consider player matchups, recent performance trends, and home-court advantage. Dallas's offense versus Minnesota's defense could be pivotal. Injuries and bench strength might influence outcomes. |
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Wed Dec 25th 5pm
Boston Celtics Philadelphia 76ers |
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The Boston Celtics have a strong lineup but face tough competition from the Philadelphia 76ers. Consider player injuries and recent performance trends for informed betting. |
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Wed Dec 25th 8pm
Golden State Warriors Los Angeles Lakers |
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Warriors' strong perimeter shooting meets Lakers' tough defense. Watch Curry vs. LeBron duel. Lakers' size advantage could be key. Close match expected with high-scoring potential. |
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Wed Dec 25th 10pm
Phoenix Suns Denver Nuggets |
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Consider Denver's strong home record. Suns' depth increases their competitiveness. Check injury reports for impact players. Nuggets' Jokic is a key factor. Look at recent head-to-head performance. |
Basketball : NBA Championship Winner
| Sat May 31st 6pm | Competitor/Team | Quote |
|---|---|---|
| Boston Celtics |
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| Oklahoma City Thunder |
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| New York Knicks |
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| Dallas Mavericks |
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| Cleveland Cavaliers |
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| Denver Nuggets |
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| Golden State Warriors |
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| Milwaukee Bucks |
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| Phoenix Suns |
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| Los Angeles Lakers |
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| Minnesota Timberwolves |
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| Memphis Grizzlies |
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| Houston Rockets |
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| Orlando Magic |
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| Philadelphia 76ers |
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| Miami Heat |
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| Los Angeles Clippers |
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| Sacramento Kings |
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| Indiana Pacers |
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| Atlanta Hawks |
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| San Antonio Spurs |
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| New Orleans Pelicans |
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| Chicago Bulls |
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| Utah Jazz |
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| Brooklyn Nets |
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| Charlotte Hornets |
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| Detroit Pistons |
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| Toronto Raptors |
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| Portland Trail Blazers |
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| Washington Wizards |
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Basketball : NCAAB
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Fri Dec 13th 7pm
GW Revolutionaries Army Knights |
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NBA matchup: Revolutionaries have strong defense but inconsistent offense; Army Knights excel in fast breaks. Consider under 200 total points. Key player: Revolutionaries' center. |
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Fri Dec 13th 7pm
Merrimack Warriors Boston Univ. Terriers |
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Merrimack's strong defense faces Boston's dynamic offense. Key players may influence game outcomes. Consider recent performance trends and player stats when betting. |
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Fri Dec 13th 7pm
Louisiana Tech Bulldogs Georgia Southern Eagles |
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Louisiana Tech's fast pace challenges Georgia Southern's defense. Player matchups crucial, offensive rebounds may decide. Watch shooters' accuracy and rotations for betting edge. |
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Fri Dec 13th 8pm
St. Thomas (MN) Tommies Western Michigan Broncos |
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Consider team form and player stats. St. Thomas focuses on defense while Western Michigan excels in offense. Analyze recent game performances for betting insights. |
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Fri Dec 13th 8pm
Nebraska Cornhuskers Indiana Hoosiers |
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Analyze team stats, player performance, recent form, head-to-head records. Nebraska may struggle against Indiana. Consider Indiana's home advantage and defensive strengths. Stay updated on injuries and odds. |
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Fri Dec 13th 8pm
Northern Iowa Panthers Omaha Mavericks |
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Northern Iowa Panthers will likely have the edge due to solid defense. Omaha Mavericks struggle in offensive plays. Consider Panthers for a safe bet. |
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Fri Dec 13th 8pm
UTSA Roadrunners North Dakota Fighting Hawks |
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The game is unpredictable with both teams showing inconsistent forms. Monitoring live betting for momentum shifts may offer better odds. Consider team stats and injury updates. |
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Fri Dec 13th 9pm
Utah Tech Trailblazers Weber State Wildcats |
140
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Utah Tech's strong defense meets Weber State's dynamic offense. Consider home court advantage and recent performance trends. Both teams have depth but watch for key injuries before betting. |
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Fri Dec 13th 9pm
Colorado Buffaloes South Dakota St Jackrabbits |
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Consider Colorado's strong defense and home advantage. South Dakota State's offense is potent. Look for a competitive match. Monitor player injuries for better insights. |
External Links
Discussion about this page in my forum at Wizard of Vegas.