There are published reports from AAMC that may be worth looking at:
ERAS® Statistics
The "math" here is complex. The impact of signals will depend upon 1) the number of signals, 2) the number of applicants, and 3) the number of programs. I am assuming that all applicants will use all signals -- any other strategy is foolish. Keeping everything constant, increasing the number of signals will have an overall linear effect on the number of signals received by programs. Increasing the number of applicants would do the same. Increasing the number of programs would decrease the impact of signals (all else constant).. It also depends upon the number of interviews each program offers (i.e. the interview:slot ratio).
But, it's more complicated than that because we know that signals do not distribute evenly. The top 10% of programs will get 25% of the signals, and the top 25% of programs will get 50% of the signals. Hence when we increase the number of signals, they won't distribute evenly.
From a program standpoint, there are three possibilities:
1. A program could have nearly all applicants signal. In that case, there's little benefit to considering signals at all, and the import of your signal will be small.
2. A program could have "just enough" applicants signal so they can pick their interviewees only from signaled apps.
3. A program could get too few signals. IN that case, they will need to review their non-signaled apps for interviewees, and you could get an interview without a signal.
From looking at the data link above (and the presentations on signals):
The average number of applications by USMD students to Neurology programs was 43 in 2024.
Signals resulted in about a 50% interview rate, where non-signals resulted in a 10% rate. (Again as above, this is an average and the actual impact on each program will vary based upon their signal rate)
Specialties with large numbers of signals saw lower levels of non-signaled interviews. At the extremes (i.e. Ortho), the rate was essentially zero without a signal.
As the number of signals increases, the distribution of signals becomes more even.
It's impossible to tell whether Neuro increasing from 3 to 7 signals will push it into "the ortho zone". Probably not. One might be able to predict this by calculating a "signal density" which I have completely made up and is (# of applicants X # of signals) / # of slots. This gives you a signal/open slot ratio. Programs want to have rank lists that are often at least 10:1 for their slots (some more, some less). Data above shows a signaled interview rate of around 40-50%. Hence one might expect that once the signal density goes above about 20 or 30, the chances of getting an interview if you don't signal should drop precipitously. Neuro's signal density last year was 8. With the increase to 7 signals, it would rise to 18. IM, EM, GS, Psych all have signal densities of 7-20 and have non signal interview rates of 5-10%. Ortho has a signal density of 56 and has a non-signal invite rate of 1%. Derm is similar. But this isn't perfect -- Interventional Rads has a density of 30 and a non-signal interview rate of 15% which is suprisingly high.
