Ryder Cup Singles Ordering

SSRN Electronic Journal · 2026-01-01

On the structure of the Poisson trinomial distribution

arXiv (Cornell University) · 2026-03-09

We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the half-integers. Each part, when normalized, is a Poisson binomial distribution and hence log-concave with one or two modes. We also prove that each of the two conditional means (conditioning on being an integer or a half-integer) lies within $1/2$ of the unconditional mean. As a consequence, any two modes of the two conditional distributions are within $5/2$ of each other.

On the structure of the Poisson trinomial distribution

arXiv (Cornell University) · 2026-03-09

We study sums of independent random variables that take values $0$, $1/2$, or $1$. We show that the probability mass function of the sum splits into two interleaved parts: one supported on the integers and the other supported on the half-integers. Each part, when normalized, is a Poisson binomial distribution and hence log-concave with one or two modes. We also prove that each of the two conditional means (conditioning on being an integer or a half-integer) lies within $1/2$ of the unconditional mean. As a consequence, any two modes of the two conditional distributions are within $5/2$ of each other.

Validity and Reliability of the FlightScope Mevo+ Launch Monitor for Assessing Golf Performance

The Journal of Strength and Conditioning Research · 2023 · 11 citations

• Mathematics
• Statistics
• Psychology

ABSTRACT: Brennan, A, Murray, A, Coughlan, D, Mountjoy, M, Wells, J, Ehlert, A, Xu, J, Broadie, M, Turner, A, and Bishop, C. Validity and reliability of the FlightScope Mevo+ launch monitor for assessing golf performance. J Strength Cond Res 38(4): e174-e181, 2024-The purpose of this study was to (a) assess the validity of the FlightScope Mevo+ against the TrackMan 4 and (b) determine the within-session reliability of both launch monitor systems when using a driver and a 6-iron. Twenty-nine youth golfers, with a minimum of 3 years of playing experience, volunteered for this study. All golfers completed 10 shots with a 6-iron and a driver, with 8 metrics concurrently monitored from both launch monitor systems in an indoor biomechanics laboratory. For both clubs, Pearson's r values ranged from small to near perfect ( r range = 0.254-0.985), with the strongest relationships evident for clubhead speed (CHS) and ball speed ( r ≥ 0.92). Bland-Altman plots showed almost perfect levels of agreement between devices for smash factor (mean bias ≤-0.016; 95% CI: -0.112, 0.079), whereas the poorest levels of agreement was for spin rate (mean bias ≤1,238; 95% CI: -2,628, 5,103). From a reliability standpoint, the TrackMan showed intraclass correlation coefficients (ICCs) ranging from moderate to excellent (ICC = 0.60-0.99) and coefficient of variation (CV) values ranged from good to poor (CV = 1.31-230.22%). For the Mevo+ device, ICC data ranged from poor to excellent (ICC = -0.22 to 0.99) and CV values ranged from good to poor (CV = 1.46-72.70%). Importantly, both devices showed similar trends, with the strongest reliability consistently evident for CHS, ball speed, carry distance, and smash factor. Finally, statistically significant differences ( p < 0.05) were evident between devices for spin rate (driver: d = 1.27; 6-iron: d = 0.90), launch angle (driver: d = 0.54), and attack angle (driver: d = -0.51). Collectively, these findings suggest that the FlightScope Mevo+ launch monitor is both valid and reliable when monitoring CHS, ball speed, carry distance, and smash factor. However, additional variables such as spin rate, launch angle, attack angle, and spin axis exhibit substantially greater variation compared with the TrackMan 4, suggesting that practitioners may wish to be cautious when providing golfers with feedback relating to these metrics.

Monitoring Performance in Golf: More Than Just Clubhead Speed

Strength and conditioning journal · 2023 · 11 citations

• Computer Science
• Computer Science
• Simulation

ABSTRACT In the golfing literature, clubhead speed is the most commonly reported metric to assess golf performance. However, a rise in the availability and use of launch monitor technologies in recent years has gathered a wide range of metrics for any given golf shot. In addition, with distance and dispersion (accuracy) being the outcome measures of any given shot and of utmost importance in golf, launch monitors can provide an in-depth understanding of how a golf shot has been achieved. To date, very limited information offers practitioners working in golf an understanding of how these metrics interlink and relate to the outcomes of any given shot. Thus, we have created a deterministic model for the golf shot and provided an overview of the relationship between these launch monitor metrics and the outcome measures of distance and accuracy. This information will give practitioners a more detailed understanding of how golf shots have been achieved and help provide more methodical means of monitoring golf performance and providing feedback to players.

Impact of Distance Changes in Professional Golf, With a Focus on the ShotLink Era

SSRN Electronic Journal · 2023-01-01 · 4 citations

Practical Nonparametric Sampling Strategies for Quantile-Based Ordinal Optimization

INFORMS journal on computing · 2021 · 10 citations

• Computer Science
• Mathematical optimization
• Mathematics

Given a finite number of stochastic systems, the goal of our problem is to dynamically allocate a finite sampling budget to maximize the probability of selecting the “best” system. Systems are encoded with the probability distributions that govern sample observations, which are unknown and only assumed to belong to a broad family of distributions that need not admit any parametric representation. The best system is defined as the one with the highest quantile value. The objective of maximizing the probability of selecting this best system is not analytically tractable. In lieu of that, we use the rate function for the probability of error relying on large deviations theory. Our point of departure is an algorithm that naively combines sequential estimation and myopic optimization. This algorithm is shown to be asymptotically optimal; however, it exhibits poor finite-time performance and does not lead itself to implementation in settings with a large number of systems. To address this, we propose practically implementable variants that retain the asymptotic performance of the former while dramatically improving its finite-time performance.

Tractable Sampling Strategies for Ordinal Optimization

Operations Research · 2018-11-01 · 23 citations

In “Tractable Sampling Strategies for Ordinal Optimization,” D. Shin, M. Broadie, and A. Zeevi analyze a problem of ordinal optimization where the objective is to select the best of several competing systems, when the probability distributions governing each system’s performance are not known but can be learned via sampling. The objective is to dynamically allocate samples within a finite sampling budget to maximize the likelihood of identifying the best system. An exact solution to this problem over any finite time horizon is difficult to characterize. In lieu of that, we introduce a family of practically implementable sampling policies and characterize the set of problem instances over which their performance (over a long time horizon) is essentially the best possible. Furthermore, we show via numerical testing that the proposed policies perform well compared with other benchmark policies over finite time horizons.

Numerical solutions to dynamic portfolio problems with upper bounds

Computational Management Science · 2017-01-05 · 7 citations

Golf Analytics: Developments in Performance Measurement and Handicapping

2016-12-21 · 2 citations

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .443In principle, the scientific analysis of golf should be similar to baseball. As both games progress, competitors move from one discrete state to the next. But whereas modeling and measurement are well developed in baseball, that effort is just in its infancy in golf. It is only recently that golf has begun to record the data in a way that enables some useful modeling and analysis. The PGA Tour’s pioneering ShotLinkTM system∗ records data for each shot a PGA Tour player takes.† Basically,of Methods andthese systems record two critical items of information for each shot:1. The location of the shot 2. The condition of the current location (tee, fairway, rough, recovery, sand, green)The shot and hole locations allow the distance to the hole to be measured for each shot. At this writing, the PGA Tour’s ShotLink system has recorded data on more than 15 million shots.