How good is Tiger Woods?

A major objective of professional sport is to find out which player or team is the best. Unfortunately the structure of some sports means that this is often a difficult question to answer. For example, there may be too many competitors to run a round-robin league, whilst knock-out tournaments do not compare every player with every other player. The problem gets worse when one has to compare players whose performance varies over time. Fortunately mathematical modelling can help and in this article, we use the Plackett-Luce model to estimate time-varying player strengths of golfers. We use the model to investigate how good golf's current biggest attraction, Tiger Woods, really is

Passive tracers in a general circulation model of the Southern Ocean

Passive tracers are used in an o?-line version of the United Kingdom Fine Resolution Antarctic Model (FRAM) to highlight features of the circulation and provide information on the inter-ocean exchange of water masses. The use of passive tracers allows a picture to be built up of the deep circulation which is not readily apparent from examination of the velocity or density ®elds. Comparison of observations with FRAM results gives good agreement for many features of the Southern Ocean circulation. Tracer distributions are consistent with the concept of a global ``conveyor belt'' with a return path via the Agulhas retro¯ection region for the replenishment of North Atlantic Deep Water

The crystal structure of perdeuterated methanol hemiammoniate (CD3OD center dot 0.5ND(3)) determined from neutron powder diffraction data at 4.2 and 180 K

The crystal structure of perdeuterated methanol hemiammoniate, CD3OD center dot 0.5ND(3), has been solved from neutron powder diffraction data collected at 4.2 and 180 K. The structure is orthorhombic, space group Pn2(1)a (Z = 4), with unit-cell dimensions a = 12.70615 (16), b = 8.84589 (9), c = 4.73876 (4) angstrom, V = 532.623 (8) angstrom(3) [rho(calc) = 1149.57 (2) kg m(-3)] at 4.2 K, and a = 12.90413 (16), b = 8.96975 (8), c = 4.79198 (4) angstrom, V = 554.656 (7) angstrom(3) [rho(calc) = 1103.90 (1) kg m(-3)] at 180 K. The crystal structure was determined by ab initio methods from the powder data; atomic coordinates and isotropic displacement parameters were subsequently refined by the Rietveld method to R-p similar or equal to 2% at both temperatures. The crystal structure comprises a three-dimensionally hydrogen-bonded network in which the ND3 molecules are tetrahedrally coordinated by the hydroxy moieties of the methanol molecule. This connectivity leads to the formation of zigzag chains of ammonia-hydroxy groups extending along the c axis, formed via N-D center dot center dot center dot O hydrogen bonds; these chains are cross-linked along the a axis through the hydroxy moiety of the second methanol molecule via N-D center dot center dot center dot O and O-D center dot center dot center dot O hydrogen bonds. This 'bridging' hydroxy group in turn donates an O-D center dot center dot center dot N hydrogen bond to ammonia in adjacent chains stacked along the b axis. The methyl deuterons in methanol hemiammoniate, unlike those in methanol monoammoniate, do not participate in hydrogen bonding and reveal evidence of orientational disorder at 180 K. The relative volume change on warming from 4.2 to 180 K, Delta V/V, is + 4.14%, which is comparable to, but more nearly isotropic (as determined from the relative change in axial lengths, e. g. Delta a/a) than, that observed in deuterated methanol monohydrate, and very similar to what is observed in methanol monoammoniate

On the development of a soccer player performance rating system for the English premier league

The EA Sports Player Performance Index is a rating system for soccer players used in the top two tiers of soccer in England—the Premier League and the Championship. Its development was a collaboration among professional soccer leagues, a news media association, and academia. In this paper, we describe the index and its construction. The novelty of the index lies in its attempts to rate all players using a single score, regardless of their playing specialty, based on player contributions to winning performances. As one might expect, players from leading teams lead the index, although surprises happen