Playing to Win, or Playing for OT? - Rams vs. 49ers, November 2, 2014

In Week 9 of the 2014 NFL season, San Francisco 49ers were losing to the St. Louis Rams 10-13 with just seconds left to go in the game. The 49ers could have taken the "safe" play and kicked a field goal, or taken a more risky play to win the game right away by going for a touchdown. With time running out, most people would have taken the field goal try, gone to overtime, and taken their chances, but what's really the right move here? It turns out it depends, but not necessarily on what you think.

The Factors

The real question to ultimately answer is: Which choice gives the 49ers the best chance to win? Many people say the game isn't played by math, but by players which is of course true. However, if coaches can accurately estimate the chances of success in given situations, it would give them better data with which to make decisions.

Since the game is near the end, we only really have to analyze a few factors: 1) the chance of making the 20 yard field goal try, 2) the chance of making the 3rd and 1 attempt, and 3) the chance of winning the game, if the game goes to overtime.

Fortune Favors the Bold - Seattle vs. San Francisco - NFC Championship Game January 19, 2014

The Seattle Seahawks are going to Super Bowl XLVIII on the strength of a 23-17 victory over the visiting San Francisco 49ers.  The big play was the 4th and 7 touchdown pass from Russell Wilson to Jermaine Kearse from the 49ers 35 yard line.  Fortune favors the bold, and while some coaches might have opted to take the 53 yard field goal attempt or a punt to pin the 49ers deep in their own territory with plenty of time to get the ball back.  Coach Pete Carroll opted to go for it, and was rewarded.

Seahawks Jermaine Kearse catches this 35 yard TD pass from QB Russell Wilson

Though the decision paid off, we want to look at the mathematics behind the decision to figure out if it was a correct one or not.  Which option was the best in this situation?

The Situation and Options

At the start of the 4th quarter (13:52 remaining), the Seahawks trail 13-17.  The ball is at the 49ers 35 yard line and it's now 4th and 7.  The three options here are all seemingly reasonable:

1. Punting
2. Attempting a Field Goal
3. Going for it

In order to figure out which option is the best, we'll have to make some assumptions and use the Win Probability calculator from Advanced NFL Stats, to break down the expected outcome of each situation.