{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T09:06:27Z","timestamp":1790672787241,"version":"4.1.0"},"reference-count":47,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T00:00:00Z","timestamp":1667433600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation (DFG)","doi-asserted-by":"publisher","award":["434\/8-1"],"award-info":[{"award-number":["434\/8-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With tracking systems becoming more widespread in sports research and regular training and competitions, more data are available for sports analytics and performance prediction. We analyzed 2523 ski jumps from 205 athletes on five venues. For every jump, the dataset includes the 3D trajectory, 3D velocity, skis\u2019 orientation, and metadata such as wind, starting gate, and ski jumping hill data. Using this dataset, we aimed to predict the expected jump length (xLength) inspired by the expected goals metric in soccer (xG). We evaluate the performance of a fully connected neural network, a convolutional neural network (CNN), a long short-term memory (LSTM), and a ResNet architecture to estimate the xLength. For the prediction of the jump length one second after take-off, we achieve a mean absolute error (MAE) of 5.3 m for the generalization to new athletes and an MAE of 5.9 m for the generalization to new ski jumping hills using ResNet architectures. Additionally, we investigated the influence of the input time after the take-off on the predictions\u2019 accuracy. As expected, the MAE becomes smaller with longer inputs. Due to the real-time transmission of the sensor\u2019s data, xLength can be updated during the flight phase and used in live TV broadcasting. xLength could also be used as an analysis tool for experts to quantify the quality of the take-off and flight phases.<\/jats:p>","DOI":"10.3390\/s22218474","type":"journal-article","created":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T04:00:51Z","timestamp":1667534451000},"page":"8474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["xLength: Predicting Expected Ski Jump Length Shortly after Take-Off Using Deep Learning"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5754-6985","authenticated-orcid":false,"given":"Johannes","family":"Link","sequence":"first","affiliation":[{"name":"Machine Learning and Data Analytics Lab, Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91052 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3967-2202","authenticated-orcid":false,"given":"Leo","family":"Schwinn","sequence":"additional","affiliation":[{"name":"Machine Learning and Data Analytics Lab, Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91052 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3617-8153","authenticated-orcid":false,"given":"Falk","family":"Pulsmeyer","sequence":"additional","affiliation":[{"name":"Machine Learning and Data Analytics Lab, Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91052 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Kautz","sequence":"additional","affiliation":[{"name":"Machine Learning and Data Analytics Lab, Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91052 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0417-0336","authenticated-orcid":false,"given":"Bjoern M.","family":"Eskofier","sequence":"additional","affiliation":[{"name":"Machine Learning and Data Analytics Lab, Department Artificial Intelligence in Biomedical Engineering, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg (FAU), 91052 Erlangen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,3]]},"reference":[{"key":"ref_1","unstructured":"Macdonald, B. (2012, January 2\u20133). An expected goals model for evaluating NHL teams and players. Proceedings of the 2012 MIT Sloan Sports Analytics Conference, Boston, MA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"514","DOI":"10.14198\/jhse.2017.12.Proc2.05","article-title":"An examination of expected goals and shot efficiency in soccer","volume":"12","author":"Rathke","year":"2017","journal-title":"J. Hum. Sport Exerc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"624475","DOI":"10.3389\/fspor.2021.624475","article-title":"A goal scoring probability model for shots based on synchronized positional and event data in football (soccer)","volume":"3","author":"Anzer","year":"2021","journal-title":"Front. Sport. Act. Living"},{"key":"ref_4","first-page":"38","article-title":"implementing the Expected Goal (xG) model to predict scores in soccer matches","volume":"4","author":"Umami","year":"2021","journal-title":"Int. J. Inform. Inf. Syst."},{"key":"ref_5","unstructured":"Bransen, L., and Davis, J. (2021, January 19\u201327). Women\u2019s football analyzed: Interpretable expected goals models for women. Proceedings of the AI for Sports Analytics (AISA) Workshop at IJCAI 2021, Montreal, QC, Canada."},{"key":"ref_6","unstructured":"Mackay, N. (2017). Predicting Goal Probabilities for Possessions in Football, Vrije Universiteit Amsterdam."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Decroos, T., Bransen, L., Van Haaren, J., and Davis, J. (2019, January 4\u20138). Actions speak louder than goals: Valuing player actions in soccer. Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA.","DOI":"10.1145\/3292500.3330758"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Robberechts, P., and Davis, J. (2020, January 14\u201318). How data availability affects the ability to learn good xG models. Proceedings of the International Workshop on Machine Learning and Data Mining for Sports Analytics, Ghent, Belgium.","DOI":"10.1007\/978-3-030-64912-8_2"},{"key":"ref_9","unstructured":"(2022, August 31). Expected Goals (xG) and Goal Probability Explained. Available online: https:\/\/www.bundesliga.com\/en\/bundesliga\/news\/expected-goals-xg-and-goal-probability-explained-13847."},{"key":"ref_10","unstructured":"Pingali, G., Opalach, A., and Jean, Y. (2000, January 10\u201315). Ball tracking and virtual replays for innovative tennis broadcasts. Proceedings of the 15th International Conference on Pattern Recognition (ICPR-2000), Virtual."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gomez, G., Herrera L\u00f3pez, P., Link, D., and Eskofier, B. (2014). Tracking of ball and players in beach volleyball videos. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0111730"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1007\/s11042-011-0833-y","article-title":"Ball tracking and 3D trajectory approximation with applications to tactics analysis from single-camera volleyball sequences","volume":"60","author":"Chen","year":"2012","journal-title":"Multimed. Tools Appl."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Badiola-Bengoa, A., and Mendez-Zorrilla, A. (2021). A Systematic Review of the Application of Camera-Based Human Pose Estimation in the Field of Sport and Physical Exercise. Sensors, 21.","DOI":"10.3390\/s21185996"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cao, Z., Simon, T., Wei, S., and Sheikh, Y. (2017;, January 21\u201326). Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.143"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Blank, P., Ho\u00dfbach, J., Schuldhaus, D., and Eskofier, B.M. (2015, January 9\u201311). Sensor-Based Stroke Detection and Stroke Type Classification in Table Tennis. Proceedings of the 2015 ACM International Symposium on Wearable Computers. Association for Computing Machinery, ISWC \u201915, New York, NY, USA.","DOI":"10.1145\/2802083.2802087"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1007\/s10618-017-0495-0","article-title":"Activity recognition in beach volleyball using a deep convolutional neural network","volume":"31","author":"Kautz","year":"2017","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"St\u00f6ve, M., Schuldhaus, D., Gamp, A., Zwick, C., and Eskofier, B. (2021). From the Laboratory to the Field: IMU-Based Shot and Pass Detection in Football Training and Game Scenarios Using Deep Learning. Sensors, 21.","DOI":"10.3390\/s21093071"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1080\/02640414.2018.1521769","article-title":"Machine and deep learning for sport-specific movement recognition: A systematic review of model development and performance","volume":"37","author":"Cust","year":"2019","journal-title":"J. Sport. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1186\/s40798-019-0202-3","article-title":"Current approaches to the use of artificial intelligence for injury risk assessment and performance prediction in team sports: A systematic review","volume":"5","author":"Claudino","year":"2019","journal-title":"Sport. Med. Open"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Elfmark, O., Ettema, G., Groos, D., Ihlen, E.A., Velta, R., Haugen, P., Braaten, S., and Gilgien, M. (2021). Performance analysis in ski jumping with a differential global navigation satellite system and video-based pose estimation. Sensors, 21.","DOI":"10.3390\/s21165318"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Elfmark, O., Ettema, G., J\u00f8lstad, P., and Gilgien, M. (2022). Kinematic determination of the aerial phase in ski jumping. Sensors, 22.","DOI":"10.3390\/s22020540"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"111139","DOI":"10.1016\/j.jbiomech.2022.111139","article-title":"Assessment of the steady glide phase in ski jumping","volume":"139","author":"Elfmark","year":"2022","journal-title":"J. Biomech."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1016\/j.jbiomech.2009.02.026","article-title":"Take-off analysis of the Olympic ski jumping competition (HS-106 m)","volume":"42","author":"Virmavirta","year":"2009","journal-title":"J. Biomech."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1123\/jab.11.2.224","article-title":"Techniques used by Olympic ski jumpers in the transition from takeoff to early flight","volume":"11","author":"Arndt","year":"1995","journal-title":"J. Appl. Biomech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1016\/j.jbiomech.2004.05.038","article-title":"Individual flight styles in ski jumping: Results obtained during Olympic Games competitions","volume":"38","year":"2005","journal-title":"J. Biomech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1080\/02640414.2011.624538","article-title":"Automatic measurement of key ski jumping phases and temporal events with a wearable system","volume":"30","author":"Chardonnens","year":"2012","journal-title":"J. Sport. Sci."},{"key":"ref_27","unstructured":"Schwameder, H., M\u00fcller, E., Lindenhofer, E., DeMonte, G., Potthast, W., Br\u00fcggemann, P., Virmavirta, M., Isolehto, J., and Komi, P. (2005). Kinematic characteristics of the early flight phase in ski-jumping. Science and Skiing III, Meyer & Meyer Sport."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1016\/j.jbiomech.2004.10.004","article-title":"Characteristics of the early flight phase in the Olympic ski jumping competition","volume":"38","author":"Virmavirta","year":"2005","journal-title":"J. Biomech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1016\/0021-9290(95)00169-7","article-title":"Dynamics of human flight on skis: Improvements in safety and fairness in ski jumping","volume":"29","author":"Platzer","year":"1996","journal-title":"J. Biomech."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/S0021-9290(02)00066-0","article-title":"The importance of being light: Aerodynamic forces and weight in ski jumping","volume":"35","year":"2002","journal-title":"J. Biomech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3130918","article-title":"Automated ski velocity and jump length determination in ski jumping based on unobtrusive and wearable sensors","volume":"Volume 1","author":"Groh","year":"2017","journal-title":"Proceedings of the ACM on Interactive, Mobile,Wearable\nand Ubiquitous Technologies"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Groh, B.H., Fritz, J., Deininger, M., Schwameder, H., and Eskofier, B.M. (2018, January 19\u201322). Unobtrusive and wearable landing momentum estimation in Ski jumping with inertial-magnetic sensors. Proceedings of the 2018 IEEE 15th International Conference on Wearable and Implantable Body Sensor Networks (BSN), Chicago, IL, USA.","DOI":"10.1109\/BSN.2018.8329669"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Link, J., Guillaume, S., and Eskofier, B.M. (2021). Experimental Validation of Real-Time Ski Jumping Tracking System Based on Wearable Sensors. Sensors, 21.","DOI":"10.3390\/s21237780"},{"key":"ref_34","unstructured":"Gasser, H. (2008). F\u00e9d\u00e9ration Internationale de Ski (FIS, International Skiing Federation): Skisprungschanzen Baunormen, Oberhofen, CH, International Skiing Federation."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_37","unstructured":"Chollet, F. (2022, September 20). Keras. Available online: https:\/\/keras.io."},{"key":"ref_38","first-page":"2079","article-title":"On over-fitting in model selection and subsequent selection bias in performance evaluation","volume":"11","author":"Cawley","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_39","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_40","first-page":"17","article-title":"Effect of kinaesthetic differentiation of the in-run position on the jump length in Polish national ski jumpers","volume":"10","author":"Wilk","year":"2018","journal-title":"Balt. J. Health Phys. Act."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"\u0160tepec, D., and Sko\u010daj, D. (2022, January 3\u20138). Video-Based Ski Jump Style Scoring from Pose Trajectory. Proceedings of the IEEE\/CVF Winter Conference on Applications of Computer Vision, Waikoloa, HI, USA.","DOI":"10.1109\/WACVW54805.2022.00075"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zecha, D., Eggert, C., Einfalt, M., Brehm, S., and Lienhart, R. (2018, January 22\u201326). A convolutional sequence to sequence model for multimodal dynamics prediction in ski jumps. Proceedings of the 1st International Workshop on Multimedia Content Analysis in Sports, Seoul, Korea.","DOI":"10.1145\/3265845.3265855"},{"key":"ref_43","first-page":"317","article-title":"Attitude estimation of skis in ski jumping using low-cost inertial measurement units","volume":"2","author":"Fang","year":"2018","journal-title":"Multidiscip. Digit. Publ. Inst. Proc."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Fang, X., Gr\u00fcter, B., Piprek, P., Bessone, V., Petrat, J., and Holzapfel, F. (2020). Ski jumping trajectory reconstruction using wearable sensors via extended rauch-tung-striebel smoother with state constraints. Sensors, 20.","DOI":"10.3390\/s20071995"},{"key":"ref_45","unstructured":"Schwinn, L., Raab, R., Nguyen, A., Zanca, D., and Eskofier, B.M. (2022, January 17\u201323). Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification. Proceedings of the Accepted at the International Conference on Machine Learning (ICML), PMLR, Baltimore, MD, USA."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Link, J., Perst, T., Stoeve, M., and Eskofier, B.M. (2022). Wearable sensors for activity recognition in ultimate frisbee using convolutional neural networks and transfer learning. Sensors, 22.","DOI":"10.3390\/s22072560"},{"key":"ref_47","unstructured":"Guyon, I., Luxburg, U.V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R. (2017). A Unified Approach to Interpreting Model Predictions. Advances in Neural Information Processing Systems 30, Curran Associates, Inc."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8474\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:10:14Z","timestamp":1760145014000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/21\/8474"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,3]]},"references-count":47,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22218474"],"URL":"https:\/\/doi.org\/10.3390\/s22218474","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,3]]}}}