Random Feature (RF) models are used as efﬁcient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF model with P features, N data points, and a ridge λ, we show that the average (i.e. expected) RF predictor is close to a KRR predictor with an effective ridge λ˜. We show that λ˜ textgreater λ and λ˜ λ monotonically as P grows, thus revealing the implicit regularization effect of ﬁnite RF sampling. We then compare the risk (i.e. test error) of the λ˜KRR predictor with the average risk of the λ-RF predictor and obtain a precise and explicit bound on their difference. Finally, we empirically ﬁnd an extremely good agreement between the test errors of the average λ-RF predictor and λ˜-KRR predictor.