Who would have thought that Ted Ginn Jr.'s absence might have made all the difference in the NFC championship game?

Kyle Williams' two fumbles on punt returns kept the Giants in the game and all but won it for them in OT. During the course of this 22-punt game, Jim Harbaugh was forced with a few 4th-down decisions. Earlier this year, Brian wrote about Harbaugh's decision to keep the 3 points after David Akers made a 55-yard field goal and the Cowboys were called for a 15-yard penalty. In the third quarter, down 10-7, the Niners were faced with a similar conundrum, this time with a punt.

On 4th-and-6 from midfield, Andy Lee hits a beautiful punt the to the Giants' 7-yard line. Justin Tuck is called for running into the kicker, but Harbaugh declines and takes the punt, pinning the Giants deep. But, was this the right decision?

After the punt, the 49ers win probability was 37% (and their expected points were +0.34, meaning they were actually expected to be the next team to score even though the Giants had the ball). So the question is as follows: does going for it on 4th-and-1 after the penalty increase the Niners' chance of winning? The estimated success rate on 4th-and-1 is 74%. If San Francisco succeeds, their win probability jumps to 47%; if they fail, it falls to 31%. So, if we let *x *be the chances of converting on 4th-and-1, we have the equation 0.31*(1 - *x*) + 0.47**x* > 0.37. Thus, the 49ers should go for it if *x* > 37.5%. Since the estimated conversion rate is 74% (almost twice our break even point of 37.5%), this seems like a no-brainer: the correct decision would be to take the penalty and go for it.

Now this should be qualified slightly, since we are using the league-average historical rates and this game has somewhat different circumstances. Things like the sloppy weather, how well the Giants' front four had been playing, the defensive nature of this game in particular, will all have an effect on the numbers. Regardless, the sum of those things do not cut the probability of converting in half.

Looking at it purely from an efficiency standpoint, the San Francisco expected points on a success would have been +2.49 versus -1.7 on a failure. Doing the same math, purely based on the expected points, it makes sense for the Niners to go for it if their probability of converting is above 48.7%. This is just one play in the game, and it could have easily gone either way, but the right decision would have been to take the penalty.

Harbaugh was faced with another decision at the beginning of the 4th quarter, on 4th-and-1 from the Giants' 46 and elected to take the delay of game penalty and punt (a punt that only netted 31-yards). If the 49ers had gone for it and succeeded, their win probability would have been 79%, if they failed, 61% (versus the expected 70% from a punt). The break-even point was a 50% conversion rate, 24% less than the estimated conversion rate.

Tough loss for the Niners, but a hell of a season for the team that finished 6-10 last year with a first year coach. Now, on to the Super Bowl.*Keith Goldner is the creator of Drive-By Football, and Chief Analyst at numberFire.com - The leading fantasy sports analytics platform. Follow him on twitter @drivebyfootball or check out numberFire on Facebook. *