This sort of article irritates me personally so I am treating this as I would when I do peer reviewing for journals. Thus the long post.
It is not a secret that the NRA's ILA donations are much less than other groups primarily due to the lack of large donors (ILA donations come in small amounts from a large number of contributors). Bloomberg's donations alone swamp what the NRA has been doing for last several years. However, this supposed new analysis is not really that good. Basically they take 2010 and 2012 elections and focus primarily on Senate elections. As someone who has personally conducted campaign financing research in the past involving U.S. House, Senate, gubernatorial, and even local, this time span is too small and the number of senate elections in this supposed study are too small to determine anything regarding statistical significance.
It takes multifactor analysis which usually requires some sort of linear regression models adopted for the binary nature of elections (win or lose) or alternatively using percentage of the vote. What complicates the analysis in Senate elections as they are not a random sample but occur in specific states with specific circumstances with specific candidates. For example, the analysis only follows what they call competitive races which leaves out those with incumbents who are not challenged for whatever reason. However, there is no empirical reason to leave these races out other than researcher choice. Given incumbency is a strong predictor of candidate success, this tends to skew the analysis to those state contests where the partisan makeup etc. are competitive which means these attract better candidates. Now instead of 66 races, you are only talking about far fewer campaigns.
What is generally used in the campaign literature as factors include (this is off the top of my head as major factors but not all inclusive--this is for nitpickers):
Underlying partisan and demographic makeup of the state electorate
Whether the election is a presidential (even 1st and second term differ) or mid term election
News of the day including economics, scandals affecting one party or the other, foreign policy, supreme court, etc.
Candidate quality (holding office, well recognized favorable celebrity, no scandalous past, etc)
Incumbency or open seat
Unified or divided party reflected in primary contests for the nomination
Campaign funding
Issues raised in the campaign
Last, but not least, each state's culture differs on firearms and without a variable that includes percentages of firearm ownership, current gun laws/restrictions, and increasingly liberalism (as apart from partisan breakdown) as a ideology held by a percentage of state residents, then the analysis is flawed on determining the effectiveness or not of NRA participation.
A good analysis of the NRA's ILA contributions in Senate races requires that these other factors that can affect candidate success as a pct of vote or win/lose, be considered before analyzing the impact of their contributions. In that story they cite appropriate peer reviewed studies but do not reflect on those studies findings other than to support their position. That is not honest research--that is pseudo dialectic (an argument disguised as objective research) meant to confuse audiences with the veneer of scientific research as it cherry picks from other studies what supports the position posited but not any contrary information nor caveats on those studies. Notice the lack of caveats in the "story" about limitations in the data, method, contrary findings by other researchers, etc. When all of the evidence points one way and that contradicts how politicians act, then the reader is getting snowed. For a fact, I know that Bill Clinton worried about the NRA's political impact, in part, because he was a governor of a state with a very high percentage of gunowners and strong NRA presence in the state. In that state, and many others, NRA F grades effectively prevented a candidate from winning in either party.
The most powerful thing that the NRA does however is in U.S. House, state and local elections--these low attention affairs can be swayed by the NRA report card regardless of any campaign contributions. However, the effect is not uniform across the nation nor a state--California and New York and to some extent Illinois politics are controlled by urban megalopolises that effectively control those states. Most large cities' mayors and other politicians elected from those districts are hostile to firearms for a variety of reasons and probably reflect the opinion of those places. Obviously then NRA endorsements in those areas would be ineffective or even negative. In others, a candidate opposing guns would never even get to the starting point (rural Idaho or Wyoming for example).
Thus, to determine relative effectiveness of the report card, you would need to analyze those districts that were mixed--suburbs perhaps, etc. on gun ownership and attitudes toward firearms--to determine the real effectiveness of these. In a similar fashion, you would need to carry out comparisons on Senate competitive elections over a number of years and determine the marginal increase or decrease in vote share and/or likelihood of victory that could be attributed to NRA contributions alone--which was not presented in the article and to the best of my knowledge has never been conducted (haven't kept up with this literature for the last five years or so). Heck, maybe I will do it if only for fun after I finish some other projects on the front burner.
BTW--The NRA itself cannot be involved directly into campaigns and your membership dues cannot be spent that way due IRS regulations on non-profits of a certain category--that is why the NRA's affiliated ILA group which is allowed by IRS rules to engage in political activity hits people up for money all of the time to support campaign contributions as a PAC and for lobbying as it can do so as well as conduct lobbying).