With March Madness just over one month away, the hunt for a bracket saving model has begun. This year, I am using a metric known as PATRIOTS (Performance Adjusted Team Rating Incorporating Outside Tournament Statistics), a metric named after the 2006 George Mason Patriots, who shocked the world on their Cinderella Final Four run. Much like the ‘06 Patriots, who would fall in the 94th percentile of ratings over the last four years, the PATRIOTS metric values selfless and gritty play. Here’s how the model works:
Team Statistics (PATS):
PATRIOTS is an adaptation of PATS (Performance Adjusted Team Score), which focuses on the regular-season performance of any given team. PATS takes into account ten different statistics that are compositions of standard box score numbers. It is worth noting that in making statistical models the multiplier factors are not always founded in statistical data, but are sometimes adjusted to more accurately value the different components of the formula.
Stat I- Turnover Ratio:
Formula: (blocks + steals) / (Turnovers committed)
Fairly straight forward, this value is the number of steals and blocks, the latter of which does not always lead to a turnover but is valuable towards this statistic nonetheless, divided by the turnovers committed by the team.
Stat II- Effort:
Formula: (assists + rebounds) / 1000
It is hard to measure the heart of a basketball team, however, performance on the glass and a willingness to give up the ball are certainly good indicators. This value is the sum of the assists and rebounds divided by 1000.
Stat III- Offense:
Formula: (field goals made + offensive rebounds) / (field goals attempted)
This is where the formulas begin to pull from various parts of the standard box score in making the different statistics. The “Offense” rating comes from the number of field goals made plus the number of offensive rebounds divided by the total field goal attempts. This allows for some flexibility in regards to the advantage of potentially missing a shot but getting the offensive rebound opens up a better shot (see Grantland’s piece on the Kobe Assist). This statistic also rewards teams willing to fight for a second chance on the offensive boards.
Stat IV- Defense:
Formula: (points allowed) / (minutes played)
The “Defense” rating was a newer addition to the metric after I realized that the only substantial reward for a stout defense was in the turnover ratio, which even that did not have a tremendous impact on the final rating. This data point, however, takes into account the points allowed per minute, taking total points given up divided by the minutes played. This plays to the advantage of teams like the Virginia Cavaliers who emphasize exceptional defense and a slower pace of play.
Stat V- Shooting:
Formula: (0.7 x (free throw percentage)) + (0.3 x (three-point percentage))
Two numbers that tend to dictate the success of a college basketball team are the ability to make free throws and three-pointers, with more emphasis on the former. Take for instance the North Carolina Tar Heels who left seventeen points on the free-throw line and squandered a thirteen point lead with four and half minutes remaining, ultimately losing in overtime to their archrival, the Duke Blue Devils. In order to penalize teams who fail to convert from the charity stripe, free throw percentage accounts for 70 percent of this number and their three-point percentage makes up the other 30 percent. Multiplying each of those shooting percentages by their respective weights and summing those to values provides the shooting value.
Stat VI- Fouls Per Minute:
Formula: (total personal fouls) / (minutes played)
Another straightforward statistic, simply the number of personal fouls committed divided by the total minutes played. This value benefits teams who possess the discipline to avoid racking up fouls.
Stat VII- Point Ratio:
Formula: (points scored) / (points allowed)
This works just like the “turnover ratio,” and is the number of points scored divided by the number of points allowed. This tends to be of greater value for teams who win low scoring affairs and therefore have low point differentials simply due to volume of points. (ie. a team who wins 50-25 has a lower point differential but a higher point ratio than a team who wins 80-50, despite allowing half the points).
Stat VIII- Winning:
Formula: (winning percentage) + 1.25 x ((away wins + conference wins) / (away games played + conference games played))
This metric is a direct attempt to forecast the performance of a team come March. No teams are slated to play on their home court during March Madness, so the ability to play in foreign environments plays a crucial role in tournament success. Furthermore, the stakes are elevated during March Madness, and while it is not an exact comparison, conference games tend to carry the most weight during the regular season so incorporating performance in those situations is valuable to predicting long term success. The last portion of this metric is the overall win percentage, simply to account for raw performance in regards to wins and losses. The final formula for this statistic is the overall win percentage plus 125% of the combined win percentage in their conference and away games.
Stat IX- Strength of Schedule:
Formula: √((conference score) x (conference win percentage))
Perhaps the most arbitrary metric in PATS is the “Strength of Schedule” statistic. This number is based on the square root of the product of the conference value multiplied by the conference winning percentage. The conference value was determined using Sports-Reference.com’s simple rating system (SRS) for each conference. The values are in the table below:
Stat X- Selflessness:
Formula: ((assists) / (field goals made)) + ((assists) / (field goals attempted))
The most recent statistic to be added is the “selflessness” measure. This character trait was crucial to George Mason’s dance to the Final Four, and it carries a heavy role in PATS. It is the sum of the assists per made field goal and the assists per shot attempted. The two sections of the statistic are weighted equally because of the intrinsic value of having the willingness to give up a shot for a better shot elsewhere.
The Final Product:
The official PATS rating is a combination of the individual metrics that were detailed above. This number is a projection going into March Madness before the brackets are even set. Once the brackets are set, there are additional calculations that produce a new rating, PATRIOTS, based on their seed. Now as for the regular season ratings, buckle up, because this is going to get messy:
Part I- Margin of Victory:
Formula: 20 x (2 x (Winning) x (Point Ratio))
This portion measures their ability to win and by how much they are winning (or losing) those significant matchups.
Part II- In-Game Performance:
Formula: 12 x (0.35 x (Selflessness) + (30/Defense) + 0.25 x (Effort) + 0.2 x (Offense) + 0.2 x (Shooting))
This part is an accumulation of most of the team variables. The in-game performance has an emphasis on the hustle metrics, selflessness, defense, and effort, over typically highlight reel statistics such as shooting and offense. As far as defense is concerned, PATS favors low defense values, which indicate fewer points allowed per game.
Part III- Strength of Schedule:
Formula: 8 x (Strength of Schedule)
The strength of schedule is the third most heavily weighted category but is roughly a quarter of the total value of Parts I and II. This is largely because teams with difficult schedules can collapse quite easily in the madness of March, just as teams with easy schedules can sometimes hold their own with the powerhouses of college basketball.
Part IV- Errors:
Formula: 6 x (0.3 x (1/Turnover Ratio) + 0.3 x (Fouls per Minute))
The last section of PATS is the errors committed by a team: fouls and turnovers. This weights the two equally, given both provide the opposing team with extra chances to score. The turnover ratio is taken as the inverse of that value to penalize teams who are prone to giving up the basketball.
The final rating is the sum of these four parts.
The product is far from perfect, and there are certainly teams who have slipped through the cracks, and a simple rationalization would quickly dismiss the result. For instance, East Tennessee State owns the 11th best PATS rating this season, despite likely not having a feasible chance of making the sweet sixteen. However, the seven highest PATS ratings belong to the top seven teams in the most recent AP poll.
Outside Tournament Statistics
There is no question that it is much easier to win the National Championship if you have a top seed. In fact, twenty-one of the thirty-four NCAA Men’s Basketball Division I National Champions have been number one seeds, good for 62% of the time. Even the first round is much easier as a number one seed unless you’re Virginia. As a result, it is only natural that seeding plays a factor in the final rating for the field of 64 before opening day. This next section discusses how this information is incorporated into the final PATRIOTS rating.
Part I- Score Multiplier:
Formula: 6 x (PATS)
The first aspect of PATRIOTS is a multiplier that accounts for 60% of the final number. It multiplies the PATS by six, because in large part, the regular season performance is a better indicator of a team’s March Madness success, as opposed to seeding. If seeding was more influential on a team-by-team basis, there would be little sense in choosing upsets, and a chalk bracket would be the safest way to go.
Part II- Seeding:
Formula: 4 x ((PATS) x ((1 – ((seed) / 17)) x (seeding percent)2)
The final piece to the PATRIOTS puzzle is the effect of seeding on the likelihood of victory. This formula takes into account two pieces of information: the seed of the team and how well that seed has performed in the past. The seed of the team is taken by dividing the seed by 17, one more than the lowest seed to avoid creating a zero value and subtracting that number from one. The resulting number is multiplied by the first round winning percentage of past teams with that seed. Below are those winning percentages of the top eight seeds according to betfirm.com (their first-round matchups would naturally have 100 minus the winning percentage of their reciprocal seed):
How This Factors Into Making Bracket Picks
As far as applying PATRIOTS into making picks in March, this metric has a margin of error, which in some cases can be the difference between a forecasted win and a forecasted loss. Here is how this affects making picks and the best way to utilize PATRIOTS.
Who Will Win?
The age-old question when filling out a bracket: Who will win a crucial sweet sixteen game to come within one win of the Final Four? Enter PATRIOTS that will provide a probability of victory for each team. This is calculated by dividing the team of interest by the sum of the PATRIOTS ratings in the match. An example from the 2019 tournament is below:
Based on the PATRIOTS rating, Mississippi State was given a 49.46% chance of winning, and by the corollary, Liberty was favored with a 50.54% chance to win. Ultimately, Liberty rallied to beat Mississippi State by four in the opening round.
Calculating the Margin of Error:
There have been two rating systems discussed thus far, PATS and PATRIOTS. The defining difference between these two is that one takes into account how seeding could impact performance and the other simply evaluates regular-season performance. That being said, both models can be used to project winners, and for this reason, both metrics are part of the margin of error calculation.
Taking the previous example with Mississippi State and Liberty, where Mississippi State was only given a 49.46% chance of winning by PATRIOTS, despite being a far superior seed. If we run the same calculations with PATS, Mississippi State’s chances drop to 45.47%, a drop of almost 4%. This is the root of the margin of error calculation used to give a range of likelihood on the outcome of the game. The average gap between PATRIOTS and PATS probabilities is 5.51%. This value is divided by two, which results in 2.76%, and this is added and subtracted to the PATRIOTS win probability to create an upper and lower bound for the outcome. Continuing with the Mississippi State and Liberty game, factoring in the margin of error, PATRIOTS forecasted Mississippi State’s win probability to fall between 52.22% on the upper end and 46.72% on the lower end.
This can be very useful when choosing upsets and recognizing potential Cinderella teams. Take for instance a 2019 tournament game featuring the Syracuse Orange and the Baylor Bears who were the eighth and ninth seeds respectively.
PATRIOTS gave Syracuse a 50.88% chance to win, however, on the lower end of the margin of error, it gave Baylor a slight advantage. If one was to factor in the small chance that Baylor would end up taking the victory and pick the Bears, they would have been rewarded as Baylor won in a decisive fashion, 78-69.
PATRIOTS is a living, breathing model that will continue to be adapted and revised leading up to the tournament. I hope it will be of assistance when filling out brackets, and I look forward to seeing if it can weather the storm of March Madness.