395 OSTEOPHYTES AND JOINT SPACE NARROWING ARE INDEPENDENTLY ASSOCIATED WITH PAIN IN FINGER JOINTS IN HAND OSTEOARTHRITIS

Objective To study the associations between structural abnormalities on ultrasound (US) or conventional x-rays (CR) and pain in hand osteoarthritis (HOA). Methods In 55 consecutive patients with HOA (mean age 61 years, 86% women) fulfilling the American College of Rheumatology criteria, pain in 30 separate hand joints was assessed upon palpation; osteophytes were assessed by US and CR and joint space narrowing (JSN) by CR. Associations between structural abnormalities and pain per joint were analysed using generalised estimated equations to account for patient effects and adjusted for age, sex, body mass index, US inflammatory features and other remaining structural abnormalities. Results In 1649 joints, 69% and 46% had osteophytes on US and CR, respectively and 47% had JSN. Osteophytes and JSN showed independent associations with pain per joint adjusted: OR for osteophytes: 4.8 (95% CI 3.1 to 7.5) for US and 4.1 (95% CI 2.4 to 7.1) for CR; for JSN: 4.2 (95% CI 2.0 to 9.0). Conclusions Osteophytes and JSN are independently associated with pain in individual HOA joints, taking into account patient effects

The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde