It’s fourth-and-short in the opponent’s territory. Do you know what your head coach is doing?

If that coach is Joe Judge, he is probably ordering a punt. Or settling for a field goal. Or making another decision more likely to result in a narrow Giants loss than a narrow Giants victory.

Judge is among the worst fourth-down decision makers in the N.F.L., according to most analytical models. The EdjSports Critical Call Index, which calculates win probabilities based on the possible outcomes of every fourth-down decision, ranks Judge 27th overall. ESPN Stats and Info ranked Judge 28th overall entering Week 13.

The Giants’ 20-9 loss to the Miami Dolphins on Sunday provided multiple examples of Judge’s overconservative, counterproductive decision making. The Giants punted on fourth-and-3 from the Dolphins’ 47-yard line early in the game, on fourth-and-4 from the Dolphins’ 48-yard line with the score tied late in the second quarter and on fourth-and-2 from the Dolphins’ 46-yard line while trailing by 4 points late in the third quarter.

Your father’s high school coach, who believed the forward pass was invented by hippie subversives, may have approved of the punts, but all three were mistakes, according to the EdjSports model. Judge cost the Giants 4.5 percentage points of win probability. That may not sound like much, but the Giants did not have very much win probability to squander, particularly with a backup, Mike Glennon, at quarterback.

Judge has made similar errors throughout the season, even when the offense was at full strength. The Giants settled for a field goal on fourth-and-2 from the 5-yard line in their 30-29 loss to Washington in Week 2. They punted on fourth-and-4 from the Falcons’ 39-yard line in their 17-14 Week 3 loss. They kicked another field goal on fourth-and-2 from the 5-yard line and punted too readily twice in their 20-17 loss to the Kansas City Chiefs in Week 8. Each of those decisions cost the Giants from 3 to 5 percentage points of win probability in close losses, per EdjSports.

Surprisingly, the Giants have attempted 18 fourth-down conversions this season, the 11th highest total in the N.F.L. Many of those attempts, however, came during the desperate circumstances the Giants so often find themselves in. For example, the Giants went for it three times after the Los Angeles Rams took a 31-3 lead in Week 6.

Conversion attempts are much rarer when Judge has much choice in the matter. The Giants have succeeded on a few relatively daring fourth-and-goal “gambles,” but Judge routinely misplays the percentages when the Giants are beyond the 1-yard line.

Judge is unlikely to be swayed by statistical arguments. He harrumphed about analytics when confronted about his proclivity for punting after the loss to the Falcons. “You can look at a stat sheet all you want,” he said. “I promise you, if Excel was going to win football games, Bill Gates would be killing it right now.”

By contrast, the Giants’ next opponent ranks first in the N.F.L. at making high-leverage fourth-down decisions, according to the Critical Call Index. The Los Angeles Chargers have attempted 21 third-down conversions, very few of them in hopeless, end-of-game circumstances. Brandon Staley, the team’s first-year head coach, went for it on fourth-and-9 from the Chiefs’ 35-yard line with the score tied and 48 seconds left in regulation in Week 3; the Chargers picked up a first down on a penalty and drove to score a touchdown to secure a 30-24 upset.

Conversions on fourth-and-7 and fourth-and-8 when the Chargers were in field-goal range led to much-needed touchdowns in a 47-42 victory over the Cleveland Browns. The Giants’ special teams unit would probably have trotted onto the field unbidden in such situations.

The mathematics of fourth-down decisions run counter to conventional wisdom, which in turn runs counter to common sense. Old-school coaches attempt field goals on fourth-and-2 from the 5-yard line because they do not trust their offense to gain 2 yards, never realizing that an offense incapable of gaining 2 critical yards is also unlikely to reach the 5-yard line again, making a touchdown an even greater priority. The same outdated illogic applies to midfield punts: What’s the point of “trusting the defense” to get the ball back after a punt if the offense cannot be trusted to gain a necessary yard or two?

The fact that the Giants are not a good team in the first place is baked into all of these calculations, as is the reliability of kicker Graham Gano. The “spreadsheets” do not assume that a team with Glennon at quarterback will have the same probability of success as a team led by Tom Brady, the Chargers’ rising star Justin Herbert or even the Giants’ usual starter, Daniel Jones. In fact, the models would penalize Judge’s decisions even more harshly if the Giants’ offense was more effective. Judge is being graded on a curve based on his own team’s shortcomings, yet still failing.

A third-string quarterback, Jake Fromm, is likely to start for the Giants on Sunday because of injuries to Jones and Glennon. Judge may be tempted to become even more conservative with Fromm under center, which could trap the Giants in a failure spiral in which they give up on whatever drives Fromm musters and offer Herbert additional opportunities to beat them. That’s what happens when a team is philosophically predisposed to surrender.

Judge rose through the New England Patriots ranks as a special teams coordinator, and his infatuation with the kicking game would be perceived as a charming traditionalist quirk if the Giants were showing other signs of progress. Unfortunately, the franchise is approaching yet another crossroads. General Manager Dave Gettleman is reportedly mulling retirement, decisions loom about Jones and other key players, and Jason Garrett has already been dismissed as offensive coordinator.

All the punts and field-goal attempts do not only impede victory, but they also make Giants games dreary to watch as 4-point deficits seem insurmountable. Quantitatively incorrect fourth-down decisions, which cannot be blamed on injuries, faulty headsets or anything else, reflect poorly on Judge as the Giants organization enters yet another period of transition.

That’s the trouble with scoffing at probability: By definition, the odds are always against you.