With just over 14 minutes remaining in their game against the Packers, the Vikings scored a touchdown to make the score 17-12. Head coach Brad Childress elected to go for the 2-point conversion attempt. Down by 5 at that point, a 2-point conversion would put the Vikings within a field goal. At first glance, it makes sense. But was this a good decision? And how would we know anyway?

I think the best way to judge a decision like this is to use win probability. Essentially, WP is the probability a team will win a game given the current state of the game. We can compare the WPs for a team down by 5, 4 and 3 according to the likelihood of the outcomes of each extra point conversion option.

First, let's look at the conversion probabilities. Extra point kicks are good 99% of the time, and 2-point conversions are successful 44% of the time.

Second, lets look at the WP for the potential score differences at about 14 minutes left in the game. A team down by 5 has a 17% chance of winning, a team down by 4 has a 19% chance, and a team down by 3 has a 20% chance.

Combining the probabilities gives us the following probabilities of winning:

Kicking the extra point:

= (0.99 * 0.19) + (0.01 * 0.17)

= 0.19

Going for the 2-point attempt:

= (0.44 * 0.20) + (0.56 * 0.17)

=0.18

So it's approximately a wash. The Vikings would have a 19% chance of winning by kicking the extra point and an 18% chance of winning by going for the 2-point conversion.

Childress' decision seemed unusual. It's not that I'd expect him to do the math, but NFL coaches typically will only make the less-conventional decision when the odds are painfully obvious. Why would he make that decision without much to gain?

My theory is that he was tempted by the lure of the 3-point deficit. Field goals are obviously easier to come by than touchdowns, so we could say he was playing for the tie. I think he overestimated the chance of winning when being down by 3. Even if the Vikings were able to tie up the game with a field goal and go into overtime, they'd still only have a 50% chance of winning.

I just found the blog and I love it but I have a question about this. I figure every team has essentially the same conversion percentage with kicking the extra point but are there enough data to confidently conclude that each team converts two-point conversions at a rate of about 44%?

It also seems to me that WP is a league wide stat and I haven't read too much of your stuff yet but I would imagine WP would vary for different team profiles.

Are my concerns about context relevant in this instance?

I think both points are valid.

1. I don't think that there are enough 2-point conversions for each team since 1994 to make inferences about any single team's ability to convert them. Certainly Childress has no reason to believe at this point in the season that his team will be either significantly better or worse than the league average at doing so.

2. Yes, WP is a league-wide estimate. But I think it's useful to generalize here. First, it's week one, and no one can really know the true relative strengths of each team. Second, and more importantly, being down by 5 (or any other amount) is a fair representation of the true relative strengths of each opponent. In other words, better teams tend to be leading throughout games, and poorer teams tend to be trailing. Over a large data set, WP will capture those relative strengths and tendencies.

You don't have enough data about two-point conversions, but I'm sure you have enough data for all plays at the 2 yard line.

If it can be proven that a team is able to convert two-point conversions at better than 50% then that would mean that it is better to go for two all the time correct?

In New York everyone was making a big deal about the Jets going for two when their kicker, Mike Nugent, got hurt and was unable to kick an extra point. "Can't anybody on that bench come out and kick an extra point?" was the line I heard all day. So assuming a 44% conversion rate on a two-point conversion, the random player off the bench would have to hit extra points at 88% in order to make it worth it to have him kick. I'll put my money on Favre.

Brian: even if a team had a >50% rate on 2 point conversions, there would still be situations in which kicking would be better. The most obvious of these is if you score a touchdown to tie the game with no time left on the clock. While your expected gain may be lower, all points are not equal.

Hey,

I work for a company called Protrade and just stumbled upon your blog - very nice. We used to focus on advanced statistical analytics in sports (we called it a "Moneyball-esque" approach to determining impact on winning).

Anyways, we built a very extensive Win Probability module for the NFL (we also had MLB, and NBA), that took many many game state factors into account and could tell you the chance of winning at any point in time. The output was used extensively on ESPN.com back in 2006, but has not been used much by us as our business model has shifted away from analytics (although we still do use the models to consult for some teams).

Anyways, for the situation above, our model says the Vikings had a 31.3% chance if they tried for 2, and 31.0 with the PAT.

If you are ever interested in discussing this more, I love to get nerdy on stuff like this, so just drop me a line at mkamal@protrade.com

-Mark

what surprises me is that the WP (at 14 minutes) for down a field goal (20%) and the WP for being down a touch down (17%) are so close.

Not being a stats guy like yourself but have coached a little and appreciate what you do, I think Childress' decision to go for 2 was a good one. The Vikings were successful at it last year going 4 for 4 if I remember correctly, but that was last year and only attests to past performance and the ability of most of the same players.

Going for 2 and getting the game to within 3 points with time ticking off the clock means you do not have to drive the ball as far to score and tie the game. Say you get the ball at your 20, you'll only have to drive down to the opponents 35 yard line for a field goal instead of the extra 35 yards for a TD. It should take less time to drive less distance plus allows more play options from the playbook. I would think with more available in your arsenal to draw upon the greater chance of success.

You are correct that playing for a tie still leaves you with a 50% chance of winning, but it gives you more time to get to the right side of the 50% and it sure beats 18, 19, or 20%. When you are behind, the more time to catch up the better.

I love your stuff and even linked to for the Vikings coaching staff to read if they spy my blog. Childress and Bevell need to work on their run/pass synergy and game theory.

Hi Luft. I don't disagree with the decision to go for 2, just surprised by it.

One other thought--I think coaches (and fans) sometimes forget that FGs are far from automatic. On average they're an 85% proposition.

Brian Burke,

In golf they talk about "bounce back" percentage: How often a player follows a bogie with a birdie. Not surprisingly, Tiger is highly ranked in this statistic.

Converting a 2-pointer or recovering an on-side kick may be rare but likely the equivalent of a bounce back, a momentum shift. The players are newly energized, the crowd is into the game again, the coach shows his confidence in the offense by even making the call, etc. So, if the conversion is successful, how does that impact the following kick-off coverage, defensive stand, etc? Any room for intangibles? A way to measure the elusive "momentum" Madden is always talking about?

Always putting up the "easy" point-after also seems to fly in the face of the merits of random play-calling. Hell, go for 2 once in awhile when the game's NOT on the line.

Peter

Hi Peter,

Interesting about golfer "bounce back." I'm not surprised Tiger has the highest bounce back rate. Not because of any kind of psychological edge he might have, but simply because he get the most birdies. I bet it's going to become one of those "clutch"/"hot hand"/"momentum" topics golf stat guys will debate.

One thing to note about 2-pt conversions is that it's not a strategy. You're never going to surprise an opponent by doing it, unless it's a fake kick (which is a real bad idea given their success rates).

My unproven opinion is that teams don't do well because they feel like they have momentum. They feel like they have momentum because they did well.

Say my football team randomly scores a TD on 1 out every 4 drives. Sometimes I'll score 2, 3, even 4 in a row. Most people would think that's momentum, when it's really just a random distribution.

"Say my football team randomly scores a TD on 1 out every 4 drives. Sometimes I'll score 2, 3, even 4 in a row. Most people would think that's momentum, when it's really just a random distribution."

my point is that just cause something can have the same result as a random sequence, does not imply that a random sequence caused it. It is simply unknowable.

-bob

the other thing to consider in this situation is this: is it probable that we'll stop the other team from at least a field goal at this point in the game? I think it was probable that the Packers would at least get a field goal in the time remaining, and thus the two point conversion was not needed. you go for one here with the probability that a team that has moved the ball all second half will continue to do so.