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I've created a two-point conversion model and a calculator and visualization to accompany it. There are several other two-point models, and they each have their weaknesses. This new model remedies those weaknesses in important ways. 

The traditional Vermeil chart used by most if not all teams was created in in early 70's for college ball. It doesn't err much from the right answers in most cases--it will always be a good idea to go for two when trailing by two or leading by one point in the final minutes. But the Vermeil chart leaves the second most important consideration, time remaining, as a mystery.

Harold Sackrowitz improved on things with his dynamic programming model which made optimal recommendations for a typical 1998 team. Its major contribution was the inclusion of an important consideration--the number of possessions remaining in the game. But this still left it to coaches to figure out how many possessions likely remain. This alone is a complex problem, and it depends on time remaining, pace, and timeouts remaining for both teams.

Bill Krasker of fame took things a step further with his own dynamic programming model that directly incorporated time at three-minute increments. But it's not clear (to me) how time is considered. If I understand the model correctly, it uses an average time equivalent for possessions. In other words, it is actually possession-based rather than time-based. It also added the 'break-even' approach, which allows a coach to modify the generic recommendation based on game variables, like relative team strength and matchups. 

My new model incorporates those advances and adds others.
  • It is based on the WP 2.0 model and very few assumptions.
  • It incorporates number of timeouts remaining for both teams.
  • It considers relative team strength.
  • It considers time directly, and not as a proxy for possessions remaining.
  • It accounts for the way opponents tend to behave in reality, such as how coaches tend to play for the tie in the endgame.
  • It is based on relevant, contemporary league data, starting with the 2008 season.
I built a calculator tool, similar to the other tools here at AFA. Users can enter time, score, timeouts, and relative team strength to the interface. The results compares the win probabilities for the various possibilities of success and failure along with their respective expected WP values. The bottom line is a break-even probability of success needed to make the two-point conversion attempt worthwhile. If the break-even probability required is below a team's expected success rate, they should go for two. If the success probability required is high, they should kick the extra point.

I've also built a visualization to accompany the model. It plots the break-even required success probability for a given score across the entire second half. The curve dynamically responds to changes in the inputs. For example, adding or subtracting timeouts results in shifts in the graph. The approach is the same as detailed in the analysis of the recent KC-DEN game.

The viz plots the break-even probability of success for a given score across the second half. The league-average success rate on two-point conversions is indicated by the red dashed line (46%). Where the break-even is below that red line, the model recommends going for two. Where the break-even line is above the red line, the model recommends kicking the XP.

In some cases the model is indifferent. For example, with only a few minutes remaining, a very large lead or deficit means that a team's WP is the same or nearly the same whether they go for two or kick an XP. In these cases the model doesn't care. Graphically, the break-even line goes haywire in these situations, so I've chosen to simply not draw it in that region.

Unfortunately, these tools will be part of the client package, which means they won't always be publicly available. However, I've decided to open up them to readers for a limited time so you can get a sense of what's under the hood when write up an analysis on an interesting game situation.

One big insight stands out already. It's that teams should be thinking about going for two much earlier than they normally do, especially teams with better than average goal line offenses or facing weaker goal line defenses. This effect is compounded when a team has prematurely used some of its second half timeouts, which effectively reduces the number of possessions available.

There are some counter-intuitive insights as well. As we learned in the early days of the WP model, being down by 4 isn't strictly worse than being down by 3 due to the way offenses maneuver for ties in the endgame. This phenomenon has implications for two-point strategy. The two-point model likes going for two in the final few minutes when a touchdown puts you within 4 points of the lead. It's saying that it's not so bad being down 4 rather than down 3, and hey, if you do convert and get two more points, now a field goal can win it for you. It would undoubtedly take a lot of convincing for coaches to buy this, but there it is.

The Two-Point Conversion Calculator

The Two-Point Conversion Break-even viz