Last season Mike Nugent made 23 of 28 field goal attempts, which is an 82.1 percent success rate. The rest of the NFL made 811 of 959 field goal attempts for an average of 84.6 percent. This means Nugent was below average, by about 2.5 percent on field goal accuracy.

The average NFL team attempted 30.9 field goals in 2015.

If you take these 30.9 attempts and multiply them by the difference by which Nugent misses worse than the league average, you find that during the 2015 NFL season, Nugent missed 0.75 more field goals than a “league average” kicker would have missed.

30.9 x (84.6% - 82.1%) = 0.75 field goals missed

If you remove the three teams who were just atrocious at kicking field goals, the Rams, Saints, and Buccaneers (who were all below 73% accuracy), you find that Nugent missed 1.25 more field goals than a “league average” kicker.

30.9 x (86.2% - 82.1%) = 1.25 field goals missed

So what we see here is that compared to a kicker who is a run of the mill, average kicker, Nugent misses about one more field goal than his middle of the road counterpart would have missed.

So how much of an impact does one missed field goal mean over the course of the season?

In the Bengals’ last five playoff seasons, 21 percent of their games have been decided by three points or less, which is one field goal. Since Nugent misses one more field goal than league average, there is a 21 percent chance that a Nugent miss could directly affect a win or loss, and a 79 percent chance that his extra miss would not affect the final score. Of course there are other factors that come into play following a made or missed field goal which affect in-game tactics, but for the sake of the math, we’ll just focus on a final score difference.

By holding onto Nugent, instead of trying to upgrade to a kicker who is at least league average, the Bengals incur a 21 percent chance for one more loss than they would otherwise have during the season. Does a 21 percent chance of losing one more game really matter? Consider that one more win in 2015 would have given the Bengals a first round bye in the playoffs, instead of a Wild Card round playoff game.

Keeping Nugent gives the Bengals a 21 percent chance of losing one more game than they otherwise would if they have an average kicker. But how much worse are the Bengals with Nugent compared to a good kicker, and not just an average one?

The top five kickers in the NFL last year managed to hit on their field goal attempts an average of 93 percent of the time. Comparing Nugent’s numbers to this, we see that a good kicker would have made three and one third more field goals than Nugent would have made.

30.9 x (93.0% - 82.1%) = 3.37 field goals missed

We already saw that 21 percent of the Bengals games have been decided by three points or less. With Nugent missing more than three and one third additional field goals that the best kickers, one could take this 21 percent and see it occur three and a half more times. So having Nugent instead of a kicker like Graham Gano, Dan Bailey, or Stephen Gostkowski, the Bengals likelihood of incurring one more loss jump up to roughly about 50 percent, compared to what they would have with one of the league’s best kickers.

Last season, three teams had kickers who were much worse than Nugent, 10 teams had kickers who were comparable to Nugent and 19 teams had kickers who were better than Nugent. So if you were to replace Nugent by randomly grabbing an NFL kicker, you would only carry three in 32 odds of downgrading, but 19 in 32 odds of upgrading.

Should the Bengals replace Nugent? Is the difference from Nugent to another kicker really significant? What would you do?