There is a "gut feel" reaction to 3rd and 4th downs among fans. Most people believe in the "heroic deeds" of players for a team to win. However, for data junkies, that is not true. Here is the analysis that determines that 3rd and 4th downs have little to no impact on wins.
Data: ESPN 2013 Regular Season (http://espn.go.com/nfl/standings/_/year/2013)
Each column represents the probability Wins, 3rd downs and 4th downs. The last column shows the Yards/Penalty.
Prior to formulating a multi-variate regression, I ran a simple Correlation across these 3 factors
The Correlation shows that 3rd and 4th down probabilities are positively correlated to probability of wins. In other words the higher the probability of 3rd and 4th downs, the higher the probability of a win. The reverse is true for Yards/Penalty. This is quite inituitive. However, let us not fall into the Correlation trap to predict without examining the Causation (multi-variate regression)
Formulating a multi-variate regression shows that the variability in Wins is explained only about 12.5% by the variability in the 4 factors above.
Analysing the variance using the ANOVA reinstates this further
The large Significance F and the relatively high P-values lead to the fact that the PROBABILITY of a WIN is NOT related to a HIGH PROBABILITY of 3rd DOWNs and 4th DOWNS. Nor does YARDS/PENALTY have a statistical significance on the PROBABILITY of a WIN.
The other interesting fact is that Denver and Seattle had the same Win probability in the regular season. Seattle had a lower probability of 3rd and 4th Downs and a higher Yards/Penalty lost. We all know who won.
Now that we see that 3rd and 4th Down conversion probabilities have no statistical significane explaining the variability in Wins, we can conclude that a higher probability of a 1st down eliminates the pressure to convert a 3rd and/or 4th Down. Therefore, let's stick to the 1st Down as the key driver for Touchdowns...