(AP Photo/Al Behrman)

Based on statistics, San Francisco 49ers quarterback Colin Kaepernick is worth twice as much as Andy Dalton, but the Cincinnati Bengals disagree. On Monday, they inked their star quarterback to a six-year, $115 million contract extension., numbers that are similar to the deal Kaepernick got from San Francisco recently.

“We never wavered in our support for Andy,” Coach Marvin Lewis said. “I never wavered. [Owner] Mike Brown never wavered. Quarterback is Mike’s position, and he loves Andy. Andy’s our guy, and will be.”

If the $115 million number sounds high it’s because it is. Mike Florio of Pro Football Talk has the details:

The most important numbers are the numbers fully guaranteed at signing. Dalton receives a signing bonus of $12 million and a roster bonus in three days of $5 million. That’s a total of $17 million out of the gates. Coupled with his $986,000 base salary (which isn’t guaranteed as a legal matter but it is as a practical matter), Dalton will make $18 million in the first year of the deal.

Then, on the third day of the 2015 league year in March, Dalton earns a $4 million roster bonus. He also has a $3 million non-guaranteed base salary in 2015. That’s $25 million over two years.

The rest of the base deal is simple. In addition to annual workout bonuses of $200,000, Dalton has base salaries of $10.5 million in 2016, $13.1 million in 2017, $13.7 million in 2018, $16 million in 2019, and $17.5 million in 2020.

This turns the question from “What is Dalton worth?” to “Did the Bengals invest their $18 million wisely?”

When we looked at Dalton’s value in relation to Kaepernick’s, we found that teams spend $1 million for every 0.18 in win probability added a quarterback generates for both the regular season and playoffs. That means Dalton would have to surpass 3.42 WPA in 2014 to justify his $18 million in guaranteed money. He accumulated 1.68 WPA in 2013, so, he has to be more than twice as influential in his team’s won/loss record in 2014 than he was last year.

Here are the quarterbacks who exceeded the 3.42 WPA threshold last season: Peyton Manning, Phillip Rivers, Tom Brady, Drew Brees, Andrew Luck, Aaron Rodgers and Kaepernick. That group also comprises six of the top 10 quarterbacks in ESPN’s QBR rating, a statistical measure that incorporates the contexts and details of a quarterback’s passes and what they mean for wins. Historically, a quarterback has needed a QBR rating of 61 or higher the past few years to make it in the top 10. Dalton fell short last season with 55.8, and it is possible we are already seeing the best Dalton can be.

There isn’t enough historical data on WPA or QBR to properly set an aging curve, but we can use adjusted net yards per attempt, which correlates highly with winning games. Below is a chart of the ANY/A index, which adjusts for league and era, for 77 quarterbacks since 1970 with at least three season’s of above-average production. A score of 100 is average and higher is better.

ANYA index

The chart says a quarterback tends to peak between the ages of 26 and 30, and with 26-year-old Dalton posting his best ANY/A of his short career (6.3), we may not see much improvement going forward. And as a result, the Bengals won’t see full value on their investment.