## 2 Materials and Methods  
Data from 525 rackets from 1874 to 2017 were collected and recorded in Excel(r) (Microsoft, Redmond, WA, USA) (see Table S1 in the Supplementary Material) and analysed in MATLAB(r) (Matworks, Natick, MA, USA). One hundred and eight rackets were characterised at the Wimbledon Lawn Tennis Museum, where it was possible to access old, rare and valuable samples, and one was from Manchester Metropolitan University. Measurements (and other records) of the other 416 rackets came from prior work [28; 29]. Of the 525 rackets, 417 (79.5%) were from the museum, 91 (17%) were from a brand's headquarters [28], 13 (2.5%) were from the university and four (1%) were from the ITF. Racket dating was principally carried out using a book [2] and the museum catalogue. If a racket featured in the book [2] and a range of less than ten years was given (135 (26%) rackets), the earliest date (year of release) was used. In 323 (62%) cases, dating was carried out using the museum catalogue, mainly (282 cases) because the racket was not in the book [2]. For racket models that were manufactured for more than nine years (17 models (e.g., Demon, Slazenger; Tournament, Spalding; Maxply, Dunlop) and 41 (8%) rackets), dates were taken from the catalogue to give the best estimation of the sample, as the design may have changed over time. The book [2] did not include rackets postdating 1990, and dates for 67 (13%) rackets (from the work reported in [28]) were obtained by consulting the manufacturer and websites [30; 31]. Some rackets may have been dated incorrectly (the catalogue stated \"circa\" before the date for 271 (52%) of the rackets), with errors estimated to be within five years in most instances, which was deemed acceptable given that \(>\)500 rackets spanning \(>\)140 years were characterised. Visual inspection identified racket materials, with cross checking against the book [2], catalogue, websites and graphics. No distinction was made between types of wood (ash, maple, mahogany, beech etc. ), grades of metal nor the constituent materials of a fibre-polymer composite (epoxy, glass,graphene, carbon, aramid etc. ), with rackets categorised as either, wood, steel, aluminium or composite, or a combination of two of these. Based on recommendations from previous work [28], string materials were not considered as it is challenging to identify them from visual inspection and the original strings may have been replaced. Figure 1a-c defines the racket measurements and Table 1 summarises the methods, which are detailed in [29]. Each racket was photographed, as were any distinguishing features (Figure 1d-g) (relative to a conventional modern racket) such as holes in the frame, extended string bed/no yoke, asymmetry, adjustable string patterns and unconventional yokes/throat regions. These distinguishing features were grouped in four categories: Head features, throat features, handle features and stringing patterns. For older rackets with wooden handles, grip length was identified using any grooves or engravings, a different wood/colour or polished coverings on the handle, as illustrated in [29]. A scale (Smart Weigh SWS1 KG Elite Series) and support were used to locate the racket's centre of mass (CoM) [29]. The racket was held horizontal with one end on the scale and the other the support, with the CoM location obtained from the product of its length and the ratio of the scale reading to the total mass. The method was compared to the more common approach of locating the 'balance point' for five rackets (1932 to 1987 with CoM locations from 321 to 335 mm), whereby the racket is balanced on a narrow support under the CoM [3; 28]: the largest difference between the two methods was 2 mm (\(<\)1%). Racket frame depth (Figure 1c) was estimated as the mean of the minimum and maximum depth measurements. Racket frame thickness (Figure 1c) was estimated as half the difference between the external and internal head width \(\left(\hat{l}_{w_{i}}\right)\) (Figure 1b). Head length was not used to estimate frame