Who Should be Calling Timeouts? A Simplified Bayes Theorem problem - PIT @ BAL, Thursday November 28, 2013

In an individual game, football is a zero-sum game.  Whatever is good for me is bad for my opponent, and whatever is bad for me is good for my opponent.  So, if I should call a timeout, my opponent definitely shouldn't, right?  What do the announcers think?

Down by 8 points with under 4 minutes to go, the Pittsburgh Steelers need to score a Touchdown and convert a 2 point conversion (2PAT) just to tie it up and potentially send the game to overtime.

The Situation

Pittsburgh is behind Baltimore 14-22 with under 2 minutes left to go in the game.  They need a touchdown and a 2PAT just to tie and potentially send the game to overtime.  Steelers QB Ben Roethlisberger threw an apparent touchdown pass to Heath Miller at 1:52 left, but the replay official rules he was down at the 1/2 yard line.  Announcer Cris Collinsworth remarks that it's a good thing the Steelers haven't scored yet since it allows them to burn some more time off the clock, presumably so if they score, the Ravens can't come back and win the game.  When he said that, the message board I was following at the time blew up and said how wrong he was in case the Steelers don't convert the 2PAT.

After a run for no gain, Baltimore takes its last timeout with 1:32 left.  Should they have taken that timeout?  If not, should the Steelers have done so with 2 timeouts remaining?

This leaves the Steelers with potentially conflicting goals.  If they do tie the game, they want to take as much time off the clock.  However, if they fail to do so, they want as much time on the clock as possible if they recover an onside kick to try to win.

The Factors

The most important, and obvious, factor is whether Pittsburgh can score or not.  However, this point is entirely moot.  At the 1 yard line, even with only 1:32 left, the clock is not the enemy.  Also, if the Steelers can't score in 3 more downs, it doesn't matter whether what's left on the clock since the Ravens will be able to run out the clock.

Another factor is the likelihood the Steelers will recover an obvious onside kick.  This number is less than 20% (to be generous).  If the Steelers don't recover the kick, then the clock doesn't matter.

Ben Watson and the Pythagorean Theorem - AFC Divisional Game Patriots vs. Broncos Jan 14, 2006

The 2005 divisional playoff game (January 14, 2006) between the Patriots and the Broncos featured Patriots TE Ben Watson making one of the greatest hustle plays I had ever seen in my life.  Watch below:

 

A great play, though ultimately for naught as Denver maintained possession at the 1 yard line and would ultimately punch it in on a Mike Anderson TD run.  New England would go on to lose the game, snapping Tom Brady's streak of 10 playoff wins without a loss.

How Far Did Ben Watson Run?

Linebacker Tedy Bruschi said, "We saw Ben was on the other side of the field so he basically had to run like 120 yards, even longer than that, to get that."

A great hustle play for sure, but how far did Ben Watson actually run on that play, and how much further did he go than Champ Bailey, one of the fastest players in the NFL?

Positioning of Watson and Bailey at the time of the interception

Playing not to lose in OT? Packers vs. Vikings Nov. 24, 2013

My buddies give me a lot of flack for suggesting to always go for it on 4th down or for a 2 point conversion, so when my instincts said to kick a field goal, but my friend Tony wanted to go for it, I had to take a step back and see if I was wrong. Even though Tony likes trolling, I think he might be onto something.

The situation: 

Green Bay Packers have the ball at 4th down and Goal at the 2 1/2 yard line in overtime.  This is the first possession in OT, so a field goal does not win the game for the Pack outright but gives the Vikings a shot at matching.  Scoring a touchdown ends the game right there for the home team Packers.

The question: What decision gives the Packers the best chance to win the game?  Going for the touchdown, or kicking the field goal?  How do we decide this?

The first question we have to ask is what factors do we have to consider to make this decision?  There are many, many factors that can go into this calculation.  For example, how good is your offense?  How good is the opponent's offense? How good is your kicker?  Do you have momentum on your side?  It would be impossible to evaluate the effect of each of these factors perfectly, but ultimately, they boil down into one of 4 factors:

1) What is the probability of making the field goal?
2) What is the probability of scoring a touchdown?
3) What is the probability of winning the game, if you go for a touchdown and miss?
4) What is the probability of winning the game if you attempt a field goal?

The coaches know (or SHOULD know) this information very, very well.  Even if they can't perfectly quantify it, their gut instinct is usually pretty good at figuring out these percentages.  However, if they're off, then the future calculations might be off as well.

The second part to this decision is how does the math shake out once we figure out what are the relevant factors. Even if one decision is "too risky", is the other decision the better choice, or is it even riskier?  While we won't be able to 100% accurately figure out the percentages, we can at least attempt to decide the best course of action, given the information we have.

Ultimately, we need to look at the chances of winning (or Win Probability, abbreviated WP) of each decision.

if WP(Field Goal) > WP(going for it), then the Packers should have kicked.
if WP(Field Goal) < WP(going for it), then the Packers should have went for it.
if WP(Field Goal) = WP(going for it), then it doesn't really matter either way.

Welcome!

This blog will attempt to simplify NFL mathematics, to see whether or not coaches are making the right decision given many factors.  While it's impossible to accurately estimate all the factors (and their probabilities) involved, we can see how decisions and probabilities can change potential decisions depending on those factors.

From there, we can look at the probabilities of success given the options available.  Of course, even if the right decision is made, an unfavorable outcome may occur.  The opposite is also possible, a team could make an incorrect decision and have a favorable outcome occur.  Certain numbers may be simplified to get a "general idea" of things.

We will also try to take away emotional decisions like "momentum" and "trusting your defense" instead choosing to try to quantify those if possible.

If you're a math or statistics teacher, please feel free to use material from this blog in writing lesson plans or for classroom examples.

Comments are welcome, please keep them civil.