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<b>Background and Purpose:</b> Post-stroke pneumonia is a feared complication of stroke as it is associated with greater mortality and disability than in those without pneumonia. Patients are often kept "Nil By Mouth" (NBM) after stroke until after receiving a screen for dysphagia and declared safe to resume oral intake. We aimed to assess the proportional contribution of stroke severity and dysphagia screen to pneumonia by borrowing idea from coalition game theory on fair distribution of marginal profit (Shapley value). <b>Method:</b> Retrospective study of admissions to the stroke unit at Monash Medical Center in 2015. Seventy-five percent of data were partitioned into training set and the remainder (25%) into validation set. Variables associated with pneumonia (<i>p</i> < 0.1) were entered into Shapley value regression and conditional decision tree analysis. <b>Results:</b> In 2015, there were 797 admissions and 617 patients with ischemic and hemorrhagic stroke (age 69.9 ± 16.2, male = 55.0%, National Institute of Health Stroke Scale/NIHSS 8.1 ± 7.9). The frequency of pneumonia was 6.6% (41/617). In univariable analyses NIHSS, time to dysphagia screen, Charlson comorbidity index (CCI), and age were significantly associated with pneumonia but not weekend admission. Shapley value regression showed that the largest contributor to the model was stroke severity (72.8%) followed by CCI (16.2%), dysphagia screen (3.8%), and age (7.2%). Decision tree analysis yielded an NIHSS threshold of 14 for classifying people with (27% of 75 patients) and without pneumonia (2.5% of 308 patients). The area under the ROC curve for training data was 0.83 (95% CI 0.75-0.91) with no detectable difference between the training and test data (<i>p</i> = 0.4). Results were similar when dysphagia was exchanged for the variable dysphagia screen. <b>Conclusion:</b> Stroke severity status, and not dysphagia or dysphagia screening contributed to the decision tree model of post stroke pneumonia. We cannot exclude the chance that using dysphagia screen in this cohort had minimized the impact of dysphagia on development of pneumonia.