When it's a low-percentage shot, take a lot of them. Credit: Getty

The best way to get grant proposals funded once success rates fall to around 15% is to bombard the market with applications, a mathematical analysis suggests.

But, warns the paper, published in PLoS ONE, it also hampers scientific productivity by increasing the time that researchers need to spend on writing proposals1.

When success rates fall below 15%, "conditions are really bad for conducting science", says Paul Roebber, an atmospheric scientist at the University of Wisconsin-Milwaukee who conducted the research with meteorologist David Schultz at the University of Manchester, UK. "At about 20%, you can have some success without resorting to flooding the proposal market, but when success rates reach 15%, churn becomes the more effective strategy."

Success rates at research agencies have plummeted around the world. Many now hover at around 20%, with the trend continuing downwards.

Scientist's dilemma

The researchers drew on game theory to look at the 'Scientist's Dilemma' of whether to approach scarcity in funding by working collectively to submit fewer proposals or working individually to submit more. They modelled the funding success of two hypothetical groups of 500 scientists whose proposals had the same range in quality but who had different strategies for submitting applications.

One group produced one proposal a year, and if funding was gained, ceased submissions until the last year of its grant. The other group produced one proposal every six months irrespective of whether a grant was awarded. All proposals were reviewed by five scientists who were 'correct' (recommending funding only for high-quality proposals), 'selfish' (declining proposals that were superior to their own) or 'harried' (assessing quality imperfectly). The proportion of selfish reviewers was set at 20%, with the other two types varying.

When the decision to fund a grant allowed one negative review, the 'sweetest spot' for the prolific group — in which the researchers won more than 60% of the available funding — occurred when the success rate was between roughly 10% and 20% for most mixes of reviewers. The less prolific group did better, winning more than 50% of the funding only when success rates were upwards of 20% or dipped below about 5%, and 60% of the funding when success rates were above 25%. When success rates edge down, "inefficiencies in the system take over", explains Roebber. "The only way to counteract them is by putting in more and more proposals."

Cool your jets

The paper also modelled the effect of a 'cooling-off' period — in which repeatedly unsuccessful scientists are barred from reapplying for a year. Here, the prolific group won more funding, receiving 57.7 per cent of available funding. Individual scientists in that group had a success rate of 17.4% compared with 12.5% for the less prolific group. This approach has controversially been used by Britain's Engineering and Physical Sciences Research Council (EPSRC) to try to lessen the number of proposals it receives.

"This cooling-off period has the unfortunate effect of favouring the people who write more proposals because their competitors are increasingly weeded out," says Schultz, adding that it may not be the end result funders were intending.

Stefan Thurner, an expert in complex systems from the Medical University of Vienna, says that the model is "reasonable" and helps to understand the system from the perspective of the crowd. But he warns against using it as the sole basis for decision-making. "The main value I see as being an 'eye-opener' for sometimes unexpected behaviour," he says.

A spokeswoman for Britain's research councils says that the councils are continuing to seek an active dialogue with researchers about levels of demand and funding rates. "Contrary to the analysis, the EPSRC has found that its demand-management policies have resulted in a sustained improvement in success rates that are now at 35%," she says.