Statistical analysis suggested the decision barely affected the 49ers' probability of winning.
Albert Larcada of ESPN's analytics team echoed those thoughts and offered some elaboration:
"Our win probability model is based on all NFL plays since 2001. We look at the game context and situation for each play and determine the probability each team has to win the game based on results from teams in similar situations historically.
"By choosing to take the three points, the 49ers were up 10 points with 11:16 left. Playing at home and kicking off from midfield because of the penalty (essentially guaranteeing a touchback) gave the 49ers a 91.4 percent chance to win at that moment.
"If instead the 49ers had chosen to take the 15-yard penalty, they would have had first-and-10 on the Cowboys' 22-yard line, up by seven points instead of 10. Given this situation, our win probability model says the 49ers would have had a 91.6 percent chance to win.
"One argument that has been made is that this does not take into account the time the 49ers would have 'wasted' by keeping the ball. This is not actually true since such a tactic would have been used historically to arrive at the odds quoted above. One reason for this is that keeping the ball and running the clock down is inherently risky.
"It certainly is possible the 49ers could have scored a touchdown and put the game away or made another field goal. However, it is also possible they could have walked away with no points via a missed field goal or turnover. This added variability in outcomes is not something a team playing at home with the lead in the fourth quarter wants to have.
"Given the added risk and the negligible difference in win probability, Jim Harbaugh made at least a solid choice, if not the right choice."
Harbaugh's decision was the highest-profile tactical move an NFC West coach made in Week 2. Arizona's Ken Whisenhunt made an interesting call during the Cardinals' 22-21 defeat at Washington. With two timeouts remaining and the Redskins leading by a field goal midway through the third quarter, Whisenhunt threw his challenge flag to gain 13 yards in field position following a Kevin Kolb interception.
The challenge produced a reversal. We can assume Whisenhunt, armed with extra time provided by a TV timeout, knew with great certainty his challenge would prevail. Blowing a timeout in that situation would have made little sense.
Upon review, referee Peter Morelli ruled Redskins linebacker London Fletcher down by contact at the Washington 11-yard line. Without the challenge, the Redskins would have had the ball at the 24. Arizona's defense allowed a 40-yard completion on the next play. The Cardinals eventually got the ball back at their own 10.
Had there been no challenge and had the Redskins' ensuing drive covered the same distance, Washington would have had fourth-and-5 from the Arizona 43 instead of from its own 44. Either way, the Redskins likely would have punted.
Challenging the play also bought time for the Cardinals' defense, perhaps diminishing the psychological effects of a quick-change situation. That could have been another consideration.