Jan Długosz provided the number of banners, the principal unit of each cavalry: 51 for the knights, 50 for the Poles and 40 for the Lithuanians.[38] However, it is unclear how many men were under each banner. The structure and number of infantry units (pikemen, archers, crossbowmen) and artillery units is unknown. Estimates, often biased by political and nationalistic considerations, were produced by various historians.[37] German historians tend to present lower numbers, while Polish historians tend to use higher estimates.[3] The high-end estimates by Polish historian Stefan Kuczyński of 39,000 Polish–Lithuanian and 27,000 Teutonic men[38] have been cited in Western literature as "commonly accepted".[5][10][37]