The Indianapolis Colts pulled off a remarkable comeback Sunday evening vs. the New England Patriots. Fans watched arguably the two most dominant franchises in the NFL for the last decade, each led by unbelievable quarterbacks, go head-to-head for 60 minutes. For most of the game, the visiting Patriots controlled the game, leading 31-14 early in the 4th quarter.

Peyton Manning and his teammates quickly responded with two touchdowns, sandwiched around a New England field goal. Trailing 34-28, it appeared Indianapolis would get the ball back on a punt when New England faced a 4th and 2 from its own 28 yard line. Instead, legendary New England Coach Bill Belichick left his offense on the field to try to seal the game with one more first down. New England lined up to snap the ball as announcers began to question the strategy. When New England completed a pass, but was short of the first down, the Indianapolis crowd erupted. Peyton Manning had only 28 yards to go, and he won the game with a touchdown to Reggie Wayne with 13 seconds left.

The comeback was amazing, but many felt it paled in comparison to the decision Coach Belichick made to go for the first down. Conventional football says to punt the ball away and let the defense hold the lead. The response from the media to Belichick's decision was generally one of disbelief. One of Belichick's former All-Pro defenders, Rodney Harrison said on NBC's postgame show, "This is the worst decision I've ever seen Bill Belichick make. It was a really bad coaching decision by coach Belichick. I have all the respect in the world for him, but he has to punt the ball. The message that you are sending in the locker room is: I have no in my young guys on my defense."

Trent Dilfer, an ESPN analyst and former NFL quarterback and Super Bowl Champion was asked if the decision reflected arrogance on Belichick's part. He responded, "Wisdom should outweigh that confidence and arrogance. You have to make decisions that are wise and discerning...and that wasn't one of them...This is an unparalleled decision right now in coaching in the National Football League. It is absolutely crazy."

Harrison and Dilfer were not alone in their scathing criticism of Belichick. Although the decision clearly did not turn out well, a closer look at statistical probabilities indicates that Belichick's decision may not have been unwise or lacking discernment. I began calculating the probabilities based on rough estimates of success rates for the likelihood of the Patriots getting a first down and the Colts scoring a touchdown, after either stopping the Pats on 4th down or receiving a punt backing the Colts up into their own territory. Fortunately, there is a website that provides actual stats on each of these scenarios:

http://www.advancednflstats.com/2009/09/4th-down-study-part-1.html

Scenario 1: "Play it safe" and punt: If the Pats punted the ball, the expected net punt would be 38 yards, leaving the Colts with the ball at their own 34. Based on historical data, the Colts would score a touchdown approximately 30% of the time (one could argue that we might expect the Colts to be more successful than the average team).

Scenario 2: Take the "risk" and go for it: If the Patriots converted the 4th down try, they could kneel on the ball and run the clock out. This would happen 60% of the time based on historical data (just as we did above with the Colts, one could also argue that we might expect the Pats to be more successful than the average team in converting on 4th down).

If the Pats failed to make the 1st down, the Colts would get the ball at the New England 28 with two minutes left, a position where teams score 53% of the time. In this case, the Patriots would still win 47% of the time. Combining these two probabilities leads to New England winning 79% of the time by going for it on 4th down.

60% + (47% * .40) = 78.85

Thus, playing it safe would lead to a new England victory 70% of the time, whereas "taking the risk" would actually not be a statistical risk, but rather a wise decision that would lead to a victory nearly 79% of the time. So why the uproar over Belichick's decision???

Part of the answer lies in our aversion to risks when we have something to lose. Imagine this scenario:

You win a prize of $250. You can either

a) Take the $250, or

b) Have a 1 in 4 chance at $1000

Now, the expected value of each of the choices is $250. If four people chose A, their average payout would be $250. If four people chose B, their average payout would also be $250 (one would typically win $1000, and the other three would get nothing). Amazingly, more than 85% of participants choose option (A), the more conservative strategy. When options are framed in terms of a gain (or win), people become quite conservative. This helps explain why Bill Belichick's decision received so much - most people tend to avoid risks in these situations. This may be particularly true in professional sports, where the heavy turnover among coaches is often referred to as the coaching carousel. One catastrophic loss can cost a coach and his assistants their jobs.

Interestingly, when options are framed in terms of a loss, we observe the opposite pattern of results. For example, imagines these two choices:

a) You lose $750, or

b) You have a 3 in 4 chance of losing $1000

In this case, nearly 90% of participants will choose (b), the riskier strategy in terms of a larger loss. Once again, both options have the same average payout, but when options are framed in terms of a loss, we tend to make riskier choices. This helps explain why gamblers at a casino may set a limit of losing $100, but once they are down $100, they will frequently continue to gamble, willing to take risks when they are already behind because they feel they have less to lose when they are already behind.

Making a risky decision (whether it is actually risky or simply perceived that way) puts a coach in jeopardy of being criticized, and even fired. In Coach Belichick's case, his team's prior successes will certainly insulate him from some perceived risks like the one he took on Sunday evening. Other coaches who lack the same job security as Coach Belichick are more likely to go along with the masses, making conservative, conventional calls that contradict the statistical evidence.

One final point that was made about Belichick's decision concerned the seeming lack of confidence he demonstrated in his young defense by going for it on 4th down. Many perceived going for it on 4th down as Belichick telling his team there was no way they could stop the Colts. Of course, it is just as likely that Belichick was showing supreme confidence in both his offense and his defense.

Although I doubt many of his players are statisticians, it seems possible Belichick could take a page out of the framing research described above and instill confidence in both his offense and defense with his decision by telling his players something along the lines of, "I have so much confidence in our offense that I think we'll make this first down. Furthermore, I have so much confidence in our defense that I don't care if the Colts get the ball on their 28 or our 28 yard line, I know we're going to find a way to keep them out of the end zone." I don't think Belichick was conceding a loss if the Colts got the ball back.

Frankly, I don't think Belichick was showing exaggerated or diminished confidence in his defense, nor do I think he was making a "risky decision". Rather, I think Coach Belichick was merely playing the percentages, and ignoring potential criticism, in an attempt to give his team what he believed (and what statistics support) was their best chance possible to defeat the Indianapolis Colts.

Kudos to the Patriots and the Colts for an entertaining (and thought provoking) game on Sunday!