marathon oil corporation notes to consolidated financial statements stock-based performance unit awards 2013 during 2018 , 2017 and 2016 we granted 754140 , 563631 and 1205517 stock- based performance unit awards to officers . at december 31 , 2018 , there were 1196176 units outstanding . total stock-based performance unit awards expense was $ 13 million in 2018 , $ 8 million in 2017 and $ 6 million in 2016 . the key assumptions used in the monte carlo simulation to determine the fair value of stock-based performance units granted in 2018 , 2017 and 2016 were: .
18 . defined benefit postretirement plans and defined contribution plan we have noncontributory defined benefit pension plans covering substantially all domestic employees , as well as u.k . employees who were hired before april 2010 . certain employees located in e.g. , who are u.s . or u.k . based , also participate in these plans . benefits under these plans are based on plan provisions specific to each plan . for the u.k . pension plan , the principal employer and plan trustees reached a decision to close the plan to future benefit accruals effective december 31 , 2015 . we also have defined benefit plans for other postretirement benefits covering our u.s . employees . health care benefits are provided up to age 65 through comprehensive hospital , surgical and major medical benefit provisions subject to various cost- sharing features . post-age 65 health care benefits are provided to certain u.s . employees on a defined contribution basis . life insurance benefits are provided to certain retiree beneficiaries . these other postretirement benefits are not funded in advance . employees hired after 2016 are not eligible for any postretirement health care or life insurance benefits. .
2018 2017 2016
Valuation date stock price $14.17 $14.17 $14.17
Expected annual dividend yield 1.4% 1.4% 1.4%
Expected volatility 39% 43% 52%
Risk-free interest rate 2.5% 2.6% 2.4%
Fair value of stock-based performance units outstanding $19.60 $19.45 $21.51
2018 2017 2016
valuation date stock price $ 14.17 $ 14.17 $ 14.17
expected annual dividend yield 1.4% ( 1.4 % ) 1.4% ( 1.4 % ) 1.4% ( 1.4 % )
expected volatility 39% ( 39 % ) 43% ( 43 % ) 52% ( 52 % )
risk-free interest rate 2.5% ( 2.5 % ) 2.6% ( 2.6 % ) 2.4% ( 2.4 % )
fair value of stock-based performance units outstanding $ 19.60 $ 19.45 $ 21.51
by how much did the fair value of stock-based performance units outstanding decrease from 2016 to 2018?