Super Bowl LI Patriots Records Differences and Percent Increase

Mathematical Odds of Atlanta Winning and their Mathematical Blunders:

Super Bowl LI was an historic game for 21 reasons. The Patriots and its players broke 21 records in the greatest comeback in Super Bowl history. The children and I discussed the mathematical odds of the Patriots winning the Super Bowl after the first half and how the Atlanta Falcons ignored the math. Here are the highlights:

With eight minutes and 30 seconds left in the third quarter, the New England Patriots were down 28-3 and the Atlanta Falcons had a 98 percent chance of winning. But they inched forward until they pushed the game into overtime—a first for the Super Bowl—and Patriots quarterback Tom Brady marched his team down the field to win Super Bowl LI. It was an epic turnaround, but it wasn’t really the Patriots that made it happen. Every mistake that let them come back could have been avoided.

Every wrong decision by the Atlanta Falcons can be explained by simple math. If you analyze the thousands of football games played in the last 10 years, you can devise a set of rules that almost always lead to a win. Computers do the hard work: They take all the possible situations and calculate the probability of each outcome. A coach could input possession, down, distance, and score and come up with one best decision for the team at that moment. All you need to do is follow the math. It took the Patriots six minutes to score a touchdown from their 25 point deficit and up 28-9 with two minutes left, the Falcons had a 99 percent chance to win the game. 

The first mistake that quarterback Matt Ryan and the Falcons made was not letting the clock run down to fewer than 10 seconds on every play. Every second that they waste is a second that the Patriots don’t have to advance. Simple. But in play after play, the Falcons snapped the ball when they didn’t need to, sometimes with more than 20 seconds left to go. The team has between 25 and 40 seconds to snap the football.

The second basic strategy mistake the Falcons made was not rushing the football when they had a comfortable lead. Over the course of the game, the Falcons were gaining an above-average 5.8 yards per rush (the league average is around 4.3 yards per play). Very little good could come from a pass at this point in the game—an incomplete pass is bad, a sack is bad, and a holding penalty is bad—especially when you’re already averaging 5.8 yards per rush. Again, this basic strategy would have carried little risk.

The third basic strategy mistake the Falcons made was not kicking a field goal with 4:40 left. They had the ball at the Patriot’s 22-yard line with an eight-point lead. Again, that’s a stunning 99 percent chance to win based on the score, along with the fact that the Falcons had the ball with almost a sure field goal. Any simulation going forward would tell you the Falcons just needed to run. They could have taken a knee three times in a row and kicked a field goal. But instead they decided to pass. And pass. And pass.

The attached pdf shows the 21 records the Patriots made in Super Bowl 51, the five records they tied and 30 fun facts about the Super Bowl.

Difference:

During class, the 1-2nd graders were tasked to find the differences between the old record and the new record. For example, Tom Brady beat his old record of most passing completions in a Super Bowl by six (new record: 43 and old record in 2015: 37). We discussed a strategy of subtraction of focusing on the multiple of ten between the two numbers: 40. Add three to get to 40 from 37 and add another three to get to 43 from 40 for a total of six.

Percentage Increase:

The 3-6th graders were challenged to first find the differences between the two records and then divide that difference by the old record and multiplying that decimal by 100 to give the percentage increase. For example, Tom Brady had the most passes in any Super Bowl with 62 surpassing the old record by Jim Kelly from Buffalo in 1992 with 58 passes. Dividing the difference of 4 by the old record of 58, you .068 or 6.8%. I had the children first simplify each fraction so 4/58 = 2/29 and use a calculator to divide 2 by 29. However, we also discussed a strategy of looking at a denominator of 29 which is about one third of 100, so 1/30th is a little more than 3%; so 2/30th is a little more than 6%. 

The children should always look for differences and percent increases in their daily lives. They scored 10 goals in soccer last year vs. 12 goals this year. That is a 20% increase over last year and so forth.