Apex Risk Head Applies Quant Trading Models to MLS Roster Strategy

Apex风控主管将量化交易模型引入MLS阵容策略 美职联的工资帽限制促使俱乐部像评估多资产投资组合一样考量球员引援，以化解降级风险与财务尾部风险。 本期节目深入分析了足球数据分析如何超越基础事件指标，向高频追踪、人体姿态估计以及预期控球价值（EPV）等预测性建模演变。嘉宾们将足球运营与量化金融交易进行了直接类比，重点探讨了如何管理尾部风险、规避降级等灾难性下行可能，并应对MLS工资帽体系下的投资组合管理挑战。最后，他们还讨论了如何将球场上连续、混乱的移动离散化为微观序列，从而优化球员引援、战术制定以及球队阵容构建。 2026年美加墨世界杯预计将在104场比赛中产生超过90PB的数据，较2022年卡塔尔世界杯激增45倍；足球数据分析已从传统的离散事件记录，全面迈向10至25Hz的高频全场位置追踪与人体骨骼姿态识别。 (0:00) 足球量化分析与金融市场的波动率套利高度相似，本质都是在极度不确定与非正态分布下管理尾部风险；对俱乐部高层而言，其核心价值在于风险控制，例如规避代价高昂的转会失误与联赛降级威胁。 (7:00) 安德森与萨利提出的“短板理论”表明，提升球队最弱球员的水平比单纯升级明星球员能带来更高回报；而在遭遇红牌等极端异常比赛状态时，模型必须对数据进行审查与修正，以准确评估均势状态下的真实战力。 (10:00) 相比欧洲足球侧重引援与临场战术，美职联（MLS）严格的工资帽与特例规则促使数据部门将阵容搭建视为金融资产组合管理，在有限的薪资额度内权衡高薪巨星与高性价比资产的配置。 (40:00)

Soccer analytics increasingly operates like volatility arbitrage and quantitative finance, using continuous spatial tracking to manage tail risks, optimize roster capital, and price chaotic on-field outcomes. Risk Mitigation and Financial Parallels (0:07) Mike Treacy, former volatility arbitrage trader and risk head at Apex Fintech Solutions, explains that soccer analytics focuses heavily on avoiding catastrophic downside rather than merely pinpointing fair market values. In European soccer, the asymmetric financial risks of promotion and relegation mean a botched £30 million transfer can impair a club for years. Modeling soccer mirrors quantitative trading because decisions rely on non-normal distributions and noisy, continuous data with severe downside variance. High-Frequency Tracking and Discretizing Chaos Soccer was long viewed as resistant to statistical modeling due to its continuous flow and low-scoring nature, contrasting with discrete sports like baseball. However, positional tracking now captures the coordinates of all 22 players and the ball at 10 to 25 frames per second, with computer-vision pose tracking capturing up to 27 body joints. Law firm Morgan Lewis projects the 2026 World Cup's 104 matches will generate over 90 petabytes of data—a 45-fold increase over the 2022 tournament. Consultant Joris Bekkers notes that models tame this data firehose by segmenting continuous play into discrete micro-intervals of 2 to 3 seconds, measuring spatial control and actions that prevent events, such as closing passing lanes. Data Censoring and the Translation Barrier Raw match data can be distorted by extreme match conditions, requiring quantitative curation. Treacy highlights a fixture between Tottenham and Chelsea where Tottenham went down to nine men yet held a high defensive line; Chelsea striker Nicolas Jackson scored a hat-trick that comprised roughly 20% of his entire season goal haul. Leaving such game states unadjusted would severely skew baseline projections, so analysts censor non-standard states to project performance at equal strength (11 v 11). Advanced models calculate metrics such as Expected Possession Value (EPV) or Expected Threat (xT) over rolling 15-to-30-second windows. Because coaches cannot digest complex neural network outputs during matches, the primary operational bottleneck is translation: analysts monitor metric spikes and deliver filtered video clips rather than raw data matrices to the coaching staff. Roster Allocation as Portfolio Management (40:00) In Major League Soccer (MLS), analytics functions like financial portfolio management due to strict roster mechanisms and salary cap charges. Treacy notes that marquee players like Lionel Messi can earn upwards of $20 million in base compensation while incurring a standardized Designated Player cap hit around $750,000. Analytics departments must structure roster balance—deciding between three Designated Players or two DPs alongside four U22 Initiative slots—allocating cap capital much like a fund manager balances high-growth equities against stable, budget-friendly assets. Joe Weisenthal and Tracy Alloway caution that applying Goodhart's Law to sports analytics can incentivize game-theory-optimal styles that erode entertainment value. Just as mathematical optimization led to playstyle convergence in the NBA, hyper-conservative tactics such as playing strictly for penalty shootouts demonstrate that mathematically sound strategies can conflict with spectator appeal.

彭博节目讨论指出，现代足球数据分析正从棒球式的离散统计转向类似量化波动率套利的概率与风险管理体系，俱乐部不仅借此优化战术，更将其作为规避降级与转会尾部风险的核心工具。 量化套利逻辑与下行风险控制 前 Peak6 波动率套利交易员、现任 Apex Fintech Solutions 风险主管 Mike Treacy 指出，足球分析与量化对冲基金的运作模式高度相似，两者都必须在极端不确定性、非正态分布以及充斥噪声的不完整数据下管理尾部风险。在存在升降级机制的欧洲联赛中，球队面临着巨大的跨年度财务波动，因此分析的核心目标往往不是精确定价单项资产，而是降低运营下行风险，例如避免球队遭遇降级，或防止管理层在难以脱手的转会目标上浪费3000万英镑。Joris Bekkers 将现代足球分析的实际应用划分为引援与财务风控、场上战术策略以及媒体球迷互动三大支柱。这一领域的发展受到了 Chris Anderson 与 David Sally 在2013年出版的《数字游戏》（The Numbers Game）的影响，书中将足球定义为“短板游戏”，即提升阵容中最弱一环所带来的边际收益，远高于单纯升级队内明星球员。在此背景下，数据分析正在帮助管理层用概率分布模型审视引援与长线运营。 数据形态演化与离散化建模 主持人 Tracy Alloway 援引摩根路易斯律师事务所（Morgan Lewis）的数据预测，2026年美加墨世界杯的104场比赛预计将产生超过90PB的赛事实时数据，较2022年卡塔尔世界杯增长达45倍。Joris Bekkers 说明，分析界早期只能依赖记录传球、射门等触球动作与二维坐标的事件数据；而现代光学追踪与计算机视觉系统已能以每秒10至25帧（Hz）的频率记录场上全部22名球员及皮球的三维动态。目前的前沿技术甚至能捕捉多达27个骨骼关节点，通过身体姿态评估球员的防守重心与身体朝向。虽然足球看似连续且混沌，但分析师可通过将比赛切分为2至3秒的微观序列（如接球、盘带、压迫逼近），计算其对进球或失球概率的边际贡献。这类预期控球价值（EPV）和预期威胁（xT）模型能够以15至30秒为窗口连续推算攻防概率，从而将复杂的空间交互转化为战术视频分析师与教练组可消化的结构化指标。 异常样本审查与人机转译 在模型构建过程中，原始数据若未经修正可能会产生严重误导。以切尔西对阵托特纳姆热刺的比赛为例，热刺在遭遇两张红牌、仅剩9人应战的情况下依然保持极高的造越位防线，导致切尔西前锋 Nicolas Jackson 在开阔空间内上演帽子戏法。这3粒进球占据了 Jackson 该赛季总进球数的约20%，分析团队若直接采用未调整的每90分钟指标评估其基础能力，将引入巨大偏差。因此，量化模型必须对非均势状态（如红牌导致的人数差异）进行数据审查或情境调整。此外，深度神经网络等黑盒模型产生的概率矩阵无法直接与一线教练交流。顶级俱乐部通常由专业数据分析师充当“翻译官”，通过监测 EPV 等核心指标的异常波动，筛选并调取对应的比赛录像片段，向主教练呈现直观的战术漏洞与战术模式，而非堆砌未经处理的算法评分。 无球量化与比赛状态指标 现代追踪技术正逐步攻克“量化未发生事件”的难题。在传统球探观察与数据模型的交叉验证中，分析师通过追踪球员封堵潜在传球路线、压缩防守空间的移动，对球员的防守智商进行量化打分。例如在评估皇家马德里中场 Jude Bellingham 这类全能球员时，模型不仅审视其持球推进与创造得分机会的能力，更衡量其在无球状态下限制对手推进的实际贡献。同时，球员的拼搏精神（Hustle）和比赛态度也能够通过特定比分状态（Game State）进行数字化量化：当比赛进入大比分领先或落后（如净胜/净负3球），胜率已达98%的终局阶段，模型会持续监测哪些球员仍在坚持高强度冲刺、保持战术纪律并全力拦截传球路线。Treacy 强调，足球数据并非直接提供终极答案，而是为了提出更精准的业务问题。 MLS工资帽约束与组合配置 与欧洲足球主要聚焦于引援和战术准备不同，美国职业足球大联盟（MLS）的分析部门面临着类似金融投资组合管理的制度约束。由于严格的工资帽、指定球员（DP）以及 U22 倡议等名额限制，俱乐部必须对球员资产进行层级配置。例如，一位顶薪指定球员若表现平平可能严重拖累名额效益，但如果同样的产出发生在底薪合同球员身上，其性价比即可位居同级别前列。类似 Lionel Messi 这样的超级球星尽管实际薪酬超过2000万美元，但计入工资帽的限额仅约75万美元。因此，分析师需要权衡3名指定球员与“2名指定球员加4名 U22 球员”等不同名额组合，在核心高薪资产、高增长新秀与基础价值资产之间寻找平衡，奥斯汀FC（Austin FC）目前正在尝试通过这套组合管理逻辑提升联赛积分。 数据分析在推动理性决策的同时，也面临古德哈特定律（Goodhart's Law）的审视：当指标变成战术目标时，可能导致战术趋同或过度功利化（如弱队为追求点球决胜而全面死守），进而削弱比赛的观赏性；此外，拥有充沛算力的大俱乐部与中小球队之间是否存在技术鸿沟，仍是数据开源工具试图解决的长线议题。

## Background 本期节目由彭博社（Bloomberg）旗下的播客栏目《Odd Lots》于2026年7月16日发布于网络及RSS平台。节目由主持人 Joe Weisenthal 与 Tracy Alloway 主持，邀请了 Apex Fintech Solutions 风险主管兼奥斯汀FC顾问 Mike Treacy，以及资深足球数据顾问 Joris Bekkers。根据页面简介，本期对话探讨了足球如何从过去被视作过于混沌而无法建模的运动，演进为涵盖 xG、人体姿态追踪与时空数据的现代分析前沿，并深入探讨了波动率套利思维与足球战术运营的深层契合。 ## TL;DR 节目全面解构了现代足球数据分析的技术飞跃及其与量化金融的深层共通性。嘉宾指出，足球在欧洲升降级制度与低容错引援下本质上是一场管理极端下行风险的波动率套利，而在美职联（MLS）薪资帽体系下则演变为精密的资产组合管理与名额套利。技术层面，足球分析已从早期的持球事件与预期进球（xG），跨越至每秒多帧捕捉球员27个骨骼特征点的连续流离散化建模，并依赖分析师将神经网络黑盒翻译为主教练可落地的战术视频切片。最后，主持人和嘉宾共同反思了古德哈特定律对体育的负面侵蚀：当各队盲目追求博弈论最优解时，比赛战术的趋同与消极求生正在逐步破坏足球原生的艺术性与观赏体验。 ## Atmosphere & style 整期对谈在华尔街金融交易员的冷峻理性与铁杆球迷的澎湃热忱之间达成了绝妙平衡，语调严谨扎实却又穿插着极客式的幽默与行业内幕调侃。从在 Upwork 上联系乌克兰博彩黑客获取原始数据，到用“投资英伟达还是生物科技股”拆解美职联引援，嘉宾的讲述生动鲜活，彻底消解了大数据的晦涩感。最后阶段主持人面对“绿茵场终成二元计算题”所流露出的存在主义惆怅，更为这场高密度的硬核量化讨论覆上了一层富有温情的人文反思色调。 ## Bulletin - `00:00` 足球分析正经历向超高维度的技术跨越：2026年世界杯预计产生超90 PB数据（较2022年激增45倍），数据颗粒度已从起脚射门阶段的xG扩展至每秒捕捉27个人体特征点的全身体态骨骼追踪。 - `07:20` 足球运作与金融波动率套利高度契合，欧洲联赛的升降级制度放大了财务方差，而美职联（MLS）严苛的薪金帽规则则催生了类似“配比英伟达与沃尔玛”的投资组合管理与名额槽位套利策略。 - `22:30` 为解决深度神经网络的黑盒难题，数据工程将连续追踪坐标流离散化为2至3秒的微观事件片段，并通过战术结构分类与预期威胁模型精准匹配比赛视频切片，打通向教练席决策转化的流水线。 - `53:40` 数据过度优化正在引发古德哈特定律的反噬：如同NBA三分泛滥损害比赛多样性，足球追求博弈论最优解导致战术同质化与消极防守，在追求胜率的同时埋下了观赏性流失与商业价值损耗的隐患。 ## Key takeaways - `00:00` 传统观点曾视足球为过于流动、混沌而不可建模的运动，但计算机视觉与传感器技术正将连续比赛切片为离散数据，推动PB级量化分析革命。 - `07:20` 足球在本质上是概率分布与波动率管理：欧洲升降级机制带来不对称的财务风险，足球数据分析的首要价值往往是避免数千万英镑的引援灾难与降级深渊。 - `10:00` 传统转播指标如控球率在预测比赛胜负上几乎无信号价值，现代分析的核心已转移至无射门阶段的控球威胁积累（Possession Threat）与比赛势头（Momentum）。 - `12:35` 从仅能记录射门结果的xG，到每秒10至25帧的时空追踪数据，再到捕捉27个身体关节点的骨骼姿态分析，足球量化正向微观视线与躯干朝向纵深演进。 - `20:00` 严谨的模型必须进行数据审查与清洗：例如一方少打两人的非均势比赛会产生极端劣质数据，若不剔除将严重污染球员的真实战术均值评估。 - `22:30` 数据分析师的核心职能是“翻译”：深度学习模型输出的赢球概率无法直接指导实战，分析师通过结构分类模型锚定数据峰值，剪辑出对应时间戳的战术视频供教练决策。 - `25:00` 比赛战术推演契合衍生品交易逻辑，依赖赛前“预期”与赛中“实现”的动态校准，而官方补水暂停等规则让足球逐步“四节化”，提供了更多即时修正窗口。 - `27:30` 传统球探直觉与量化评估已深度协同，分析师借助净胜球分差（Game State）切分极端落后状态下的表现数据，使原本难以捉摸的“拼劲与意志”得以客观量化。 - `30:00` 现代追踪技术开启了对“未发生事件”的量化：以贝林厄姆为例，模型通过几何算法精确评估球员预先封堵传球线路、压缩空间的防守贡献。 - `35:00` 赛内实时胜率模型基于强大的赛前先验基准进行贝叶斯更新，开局前五分钟的短暂激烈或意外机会很难从根本上颠覆模型的胜负概率走向。 - `37:30` 美职联（MLS）的工资帽与指定球员（DP）规则催生了阵容层面的投资组合管理，球队必须在有限的薪资占用额度中追求每个名额槽位（Slot）的相对价值最大化。 - `40:00` 开源算法与神经网络工具虽然降低了中小球队的技术门槛，但从海量原始数据中提炼实战认知的专业人才缺口，依然是阻碍弱旅逆袭的深层壁垒。 - `50:00` 处理海量坐标流的关键在于离散化建模：将传球、接球、推进拆解为2至3秒的微观事件片段，以此计算球员每一次动作带来的增量进球期望价值。 - `52:15` 卖方金融机构的世界杯预测失真揭示了预测界的铁律：真正具备超额收益（Alpha）的量化胜率模型绝不会被公开分享，公开发表的研报主要用于眼球营销。 - `53:40` 古德哈特定律在体育界显现：当指标成为唯一追求，球员刷数据与极致防守等功利解法（如死守平局赌点球方差）泛滥，可能导致比赛观赏性退化并损害球迷基础。 ## Detailed walkthrough ### `00:00` 棒球记分册与足球的“不可量化”神话 Joe Weisenthal 和 Tracy Alloway 从儿时的棒球记忆切入探讨体育数据化。Joe 回忆起不到六岁时与祖父在底特律老虎队（Detroit Tigers）主场看球的经历，当时看台上总坐着相当数量的球迷，腿上放着特制的纸质记分册（scorebook），一丝不苟地手写记录每一次打席（at-bat）、出局方式、安打与保送。Tracy 也谈到自己年轻时曾在芝加哥看小熊队（Cubs）比赛，后来旅居日本期间更被当地棒球比赛无与伦比的现场狂热氛围震撼，两人甚至笑称如果未来去东京做播客现场秀，必须挑在棒球季。 棒球由无数高度离散的独立事件（discrete events）构成——投手与击球手一对一决斗、三振、四坏球保送、一垒安打——这使得数据记录极其直观，也奠定了《魔球》（Moneyball）革命的基石。但 Joe 发现去现场看足球（soccer/football）时完全无法套用这种方式。长期以来，体育分析界普遍认为足球具有极高的流动性（fluidity）与混沌性（chaotic nature），场上 22 人持续跑位，进球极少，且变量盘根错节，过去人们普遍坚信足球绝不可能像棒球那样被精确建模。然而如今格局已彻底颠覆，小型俱乐部依靠数据在转会市场上精准淘宝的《魔球》式案例屡见不鲜，伴随体彩与预测市场的井喷，足球数据分析正迎来爆炸式增长。 - 棒球的离散事件结构天然契合统计学，而传统观点视足球为过于连贯、低比分的无序运动。 - 据摩根路易斯律师事务所（Morgan Lewis）引用的数据，2026年美加墨世界杯（104 场比赛）预计将产生超过 90 PB（Petabytes）的比赛追踪与统计数据。 - 这一数据量相较于 2022 年卡塔尔世界杯暴增了 45 倍，反映出传感器、高速摄像机与计算机视觉在赛场上的全方位渗透。 ### `05:00` 连续流动能否切片？流动资产与足球分析的哲学交汇 随着数据体量呈指数级爆发，Joe 提出了一个深层的哲学与技术疑问：表面上连续流动的现实，本质上是否只是由微观离散事件构成的切片？正如极高帧率的高速摄像机能将任何看似连续的滑行分解为数以百万计的静止瞬间，计算机系统也正在打破传统界限。国际象棋是离散事件的极致，二十多年前已被深蓝等算法攻坚破局；而语言曾被视为人类最不可捉摸、最流动的艺术，如今大语言模型却展现出惊人的解析能力。尽管 Tracy 笑称自己内心深处的“卢德派”（Luddite）倾向仍执着于足球这项“美丽运动”（the beautiful game）中定有不可被算尽的人性火花与艺术灵光，但技术的发展正不断逼近建模的极限。 除了大众耳熟能详的“预期进球”（Expected Goals, 简称 xG），当下的足球分析技术已延伸至深层的人体姿态估计（body pose analytics）以及反映场上控制力波动的“势头图”（momentum charts）。这种在高度混沌与流动中寻找确定性的努力，与金融市场在波动中定价极其相似。 ```mermaid flowchart TD accTitle: 体育分析技术复杂度演进 accDescr: 展示从离散事件统计到高阶连续流建模的演进路径 subgraph Discrete["离散事件模型 (传统)"] A["棒球统计 (打席/三振/安打)"] B["国际象棋棋局推演"] end subgraph Transition["进阶统计层"] C["足球基础事件 (射门/传球/拦截)"] D["预期进球 (xG) 概率评估"] end subgraph Continuous["超密集连续流分析 (现代前沿)"] E["计算机视觉与人体姿态追踪 (Body Posing)"] F["动态控制力与势头图 (Momentum)"] G["90+ PB 级时空追踪切片数据"] end Discrete --> Transition Transition --> Continuous ``` 本期邀请到的两位对谈嘉宾恰好完美横跨量化交易与足球前沿数据两个领域： - **Mike Treacy**：曾任量化自营交易公司 Peak6 的波动率套利交易员（volatility arbitrage trader），现任 Apex Fintech Solutions 风险主管（Head of Risk），同时担任美职联奥斯汀FC（Austin FC）及某英超俱乐部的战术数据分析顾问。 - **Joris Bekkers**：专注足球数据工程与分析十年的资深顾问，曾为美国足协（US Soccer Federation）开发原始比赛追踪数据分析软件。 ### `07:20` 足球就像波动率套利：分布、杠杆与非完美信息 当被问及波动率套利与足球分析之间的共通技能时，Mike Treacy 指出，理解足球的核心在于**“赛场上的每一个维度本质上都是一个概率分布（distribution）”**。无论是球队在单场 90 分钟内的临场发挥、单个球员在不同战术体系下的状态波动，还是整整一个赛季的胜负积分，都不存在确定的因果线，而是一系列宽幅度的统计分布。 更关键的是，欧洲联赛特有的“升降级制度”（promotion and relegation）为俱乐部财务带来了极高的方差（variance）。一次保级成功或降级深渊，可能意味着数千万甚至数亿英镑转播收入的瞬间得失。Mike 强调，置身足球产业就如同在金融市场上进行高杠杆押注：决策者必须基于极不完美、不具备绝对预测性的信息去建立头寸。棒球的样本量大且事件可重复，而足球的低容错、强随机性与不对称风险收益结构，使得波动率管理成为统领球队运营、转会交易与战术决策的最底层思维。面对 Tracy 关于“足球数据分析终极目的究竟是类似价格发现（price discovery）的球员估值、优化战术训练还是胜负预测”的提问，Mike 直言，对于俱乐部投资者与管理者而言，其目标是全方位的渗透与覆盖。 ### `10:00` 足球数据分析的核心使命：从规避千万级引援灾难到战术重塑 足球数据分析在俱乐部与商业场景中的核心逻辑，往往首先不是为了创造奇迹，而是为了防范毁灭性的风险——避免球队不幸降级，或者避免斥资 3000 万英镑买来一个表现糟糕、两年内不得不赔钱清洗掉的水货球员。谈话中还穿插了一个幽默的插曲：节目制作人在聊天栏提醒主持人，按照彭博社（Bloomberg）的内部风格指南，这项运动应被称为“football”而非美式的“soccer”，两位主持人和嘉宾随即打趣要顺应这种企业规范。在被问及数据分析究竟是在帮助俱乐部物色人才还是服务于博彩机构时，足球数据分析顾问 Joris Bekkers 指出，这完全取决于机构的定位与诉求。 分析在足球产业中主要有三大落地切入点：其一是人事决策，帮助球队做出明智的雇佣与引援决策，防止数以千万计的英镑打了水漂；其二是战术优化，俱乐部通过挖掘比赛过程中的实时数据，推导传球路线该如何规划、球员站位该如何落位、采用何种战术打法能产生更高的预期进球（xG, Expected Goals）；其三则是球迷娱乐体验，市面上涌现了大量向大众普及深度比赛信息的数据应用与网站。回顾 20 世纪 90 年代，电视转播画面经常在屏幕下方悬浮角球数、黄牌数和控球率等图层，Joris Bekkers 直言这些传统指标“没有任何实际预测意义”，引发了主持人的追问。 - **引援与财务止损**：对中下游俱乐部而言，防范高达数千万英镑的引援失败是保住顶级联赛席位与财政健康的核心防线。 - **战术与站位推演**：利用场上数据寻找传球网络与跑位结构的最佳解，直接提升场上的得分概率与防守硬度。 - **低信号统计指标**：传统转播中展示的控球率（Possession %）几乎无法预测比赛的最终胜负；相比之下，角球数稍微更有参考价值，因为它能在一定程度上反映出哪支球队在比赛场面上占据压制性的主导地位。 --- ### `12:35` 从《数字游戏》到骨骼追踪：足球如何突破“过于复杂”的魔咒 在 2000 年代初《魔球》（Moneyball）彻底改变棒球界之后，足球长期被视作一种“变量过多、无法量化”的混沌运动——场上有多达 22 名球员争夺一颗球，进球事件极度罕见，随机性极高。相比之下，篮球每队只有 5 名球员，比赛场次密集，得分回合层出不穷，量化建模要容易得多。Mike Treacy 指出，足球分析在 2010 年代迎来了两大历史转折点：一是 2013 年克里斯·安德森（Chris Anderson）与大卫·萨利（David Sally）出版了具有划时代意义的专著《数字游戏》（*The Numbers Game*），该书证明足球从本质上是一项由“最弱一环（weakest link）”决定的运动；二是推特（Twitter）社区掀起的开源分析狂潮。 ```mermaid flowchart TD accTitle: 足球数据分析的演进路径 accDescr: 描绘从基础持球事件数据向高帧率追踪数据及全身体态数据演进的流程图 subgraph DataEvolution ["足球量化数据的技术演进"] A["持球事件数据 (On-ball Events)<br/>记录传球、射门与控球人<br/>缺陷：丢失其余无球人员位置"] B["时空追踪数据 (Tracking Data)<br/>10-25 帧/秒记录22名球员与球位置<br/>技术支撑：复杂深度神经网络"] C["全身体态追踪 (Full Body Pose)<br/>骨骼关节点与躯干朝向建模<br/>价值：捕捉微观阻截与造险动作"] A --> B B --> C end subgraph ConceptualShift ["认知与模型维度的飞跃"] D["预期进球 (xG) 普及<br/>量化每次射门期望值"] E["控球威胁与势头分析<br/>量化无射门的推进过程"] D --> E end A -.-> D B -.-> E ``` 在推特平台上，数据分析先驱 Michael Caley 扮演了至关重要的启蒙角色：每个英超比赛日周六通常会有 6 场激战，比赛结束仅仅 30 分钟后，Caley 就会在推特上连续刷屏发布各场比赛的预期进球（xG）图表。这些图表激起了广泛的行业争论：“这是否真实反映了场上本该发生的结果？”随着讨论走向深入，人们敏锐地察觉到了 xG 的天然缺陷——它只有在球员真正起脚射门时才会记录数据。然而一场足球比赛的绝大部分价值蕴含在射门之前：球权转换、每次控球推进形成的潜在威胁（Possession Threat）、比赛势头（Match Momentum）以及防守体系的变化。随着人工智能与算力的爆炸式增长，行业从只能记录“谁传了球、谁射了门”的持球事件数据，跨越到以每秒 10 帧甚至 25 帧同步捕获 22 人与足球位置的时空追踪数据，如今更是迈入了能够还原全部球员骨骼框架与身体朝向（Body Pose）的超微观分析阶段，借以评估微小肢体动作对防守空当与射门机会的深远影响。 --- ### `17:15` 控制能控制的：量化模型如何消化不可预测的哨声与 VAR 面对瞬息万变的绿茵场，数据分析师必须直面一个巨大挑战：如何量化那些纯粹的随机性，尤其是裁判判罚对比赛走势的巨大干扰？正如主持人所言，仅仅观察射门根本无法预料裁判是否会在整整一分钟后、退回到半个球场之外去重审一次争议判罚，进而彻底吹掉一粒精彩进球。对此，Joris Bekkers 给出了极为务实的量化哲学——“控制你能控制的（control the controllables）”。足球运动中固有的不可控与人为失误，本身就是该系统不可剥离的固定参数。 - **宏观对冲与统计抵消**：在单场甚至单个事件的微观分析中，争议红牌或点球错判确实会彻底扭曲局势；但在构建基础胜负预测模型时，若将时间跨度拉长到过去 10 年的成千上万场比分数据，不可抗力的随机扰动往往会在大数法则下互相抵消。即使模型完全不知道某场比赛是否存在红牌，依然能凭借最终赛果训练出强健的基线预测能力。 - **VAR 创造的全新数据维度**：被问及视频助理裁判（VAR）是否重塑了足球分析时，Bekkers 明确表示，VAR 不仅改变了判罚，更直接拓展了分析的数据资产库。每一次 VAR 介入、回看、改判本身都是可结构化记录并归类的关键事件，这为量化团队建立裁判行为模式、量化判罚对比赛动量与攻守转换的次生影响，提供了前所未有的全新研究窗口。 ### `20:00` 数据审查与清洗：剔除“劣质数据之源”的异常比赛状态 在处理足球原始数据时，分析师必须做出大量筛选：哪些数据该被纳入模型，哪些又必须被审查剔除（censor out）。例如，球员即使因手部微弱越过最后一名防守球员而被视频助理裁判（VAR）判定越位并取消进球，但从战术评估的角度来看，他能捕捉到极佳的机会、完成停球、转身并攻破球门，这种跑位与处理球的潜在能力本应在数据集中占有一席之地。然而，这类动作往往因为 VAR 的最终介入而在常规事件数据中被完全抹杀。 与此同时，非正常比赛状态（irregular game state）也会带来严重的统计扭曲。以大约三年前切尔西对阵托特纳姆热刺的一场名局为例：热刺在比赛中先后被罚下两人，仅剩 9 人应战。令人瞠目结舌的是，热刺非但没有龟缩防守，反而选择将整条防线压在半场附近的超高位，企图用越位陷阱抵挡切尔西的进攻。结果可想而知，切尔西在比赛尾声频频进球，前锋尼古拉斯·杰克逊（Nicolas Jackson）单场攻入 3 球。如果纵观他整个赛季的数据表现，这仅仅一场比赛的进球数就占到了他整季总进球的近 20%。如果直接将这场比赛纳入赛季统计，并在期末以“每 90 分钟产出（per 90 minutes）”的方式评估球员，整套数据集就会被极其糟糕的劣质数据严重污染。 这类比赛绝非预测未来的“数据富矿”，反而是一个“充斥着劣质数据的假源泉”。当出现红牌或悬殊人数差等不平等比赛状态时，理智的做法是对数据进行清洗和审查，剔除极端状态，从而还原双方在均势状态下的真实战术水准与球员实力。 - **红牌与极端状态清洗**：多数严谨的足球预测模型都会主动剔除红牌少打一人或两人的样本，防止异常的人数劣势扭曲战术常态。 - **样本偏误风险**：单场帽子戏法能瞬间拔高前锋在特定进攻指标上的赛季均值，若不进行数据审查，这种偶发数据将完全误导未来的转会或引援决策。 --- ### `22:30` 跨越“黑盒”鸿沟：将神经网络模型转化为教练看得懂的视频切片 随着计算机算力的飞跃，足球分析已逐步迈入由神经网络主导的新阶段：未来甚至可以做到捕捉场上每一名球员身体各部位的高频动作（每秒上百帧的姿态捕捉），并将海量数据喂入深度学习模型，直接推断赢球概率。但这引发了一个与国际象棋或围棋类似的经典困境——AI 模型虽然算力超群，却不会说人类的自然语言。对一线主教练或足球总监而言，一个只输出概率矩阵的“黑盒”毫无用处。 过去近八年间，足球分析领域公认的最大痛点正是“模型输出向主教练认知层面的翻译”（translation）。数据分析师的定位不再是单纯的模型搭建者，而是承担“同声传译”功能的专家。战术教练通常不会直接面对冷冰冰的原始数字，而是接收经过分析师消化提炼出的洞见。这种翻译过程往往建立在自下而上的视频切片联动机制上：分析师利用复杂的算法模型在海量数据中定位出关键时刻，再调出对应的时间戳视频片段，把具体的战术画面呈现给教练。 ```mermaid flowchart LR accTitle: 模型输出到教练决策的翻译流水线 accDescr: 展示从底层追踪数据与机器学习模型到高级指标再到视频切片和教练决策的完整流转过程。 subgraph RawData["底层计算层"] A["高频追踪数据<br/>& 姿态捕捉"] --> B["神经网络 / ML 模型"] end subgraph Metrics["高级指标提炼"] B --> C["战术结构识别<br/>(10-20秒窗口)"] B --> D["进球概率波动<br/>(xG / EPV / xT)"] end subgraph Translation["分析师翻译与输出"] C --> E["数据分析师<br/>定位数据峰值"] D --> E E --> F["精准匹配<br/>比赛视频切片"] F --> G["主教练制定战术<br/>& 人员调整"] end ``` 这种视频匹配并不是盲目翻找，而是依靠具有战术指向性的高级指标。例如： - **战术结构分类模型（Classification Models）**：以 10 秒、15 秒或 20 秒为一个时间窗口，自动分类对手当下的后场推进（build-up）方式与防守组织架构。 - **预期占优价值模型（Expected Possession Value, EPV）与预期威胁模型（Expected Threat, xT）**：量化预测在接下来的 30 秒或下一次球权转换中双方进球的概率波动。当概率曲线上出现异常峰值时，分析师能立即锚定“防线何时最容易丢球”或“何时最有机会撕裂对手防线”，并将这几秒的视频片段剪辑出来作为指导依据。 --- ### `25:00` 比赛节奏与时延：衍生品思维下的“预期”与“实现” 在探讨高频与延迟问题时，许多人会好奇足球分析是否能像金融高频交易一样，在几秒内吐出数据并让教练立刻做出换人调整。现实是，除极少数场景外，大部分高阶数据分析并不支持秒级的实时战术操作，真正的决策落地主要集中在赛前准备、半场休息以及赛后复盘。 足球比赛在战术推演上与金融衍生品交易有着惊人的异曲同工之处：核心逻辑在于**“预期结果（Expected Outcome）”**与**“实现结果（Realized Outcome）”**之间的动态对照。 1. **赛前预期**：球队基于对手以往的模型表现，计算市场隐含信息与预期产出（“对手会怎么踢，我们会怎么踢”）。 2. **赛中实现**：比赛哨响后的实时数据代表实际发生的实现结果。 看台上的分析团队不断监测赛场上的实时数据，并与赛前推演的预期模型进行校准。一旦发现实现结果与预期存在结构性偏差，分析师会在半场哨响前迅速整理好核心结论与支撑视频，直接下传至教练席，供主教练在半场 15 分钟的更衣室更动中调整部署。 随着现代足球规则的演变（如世界杯和高温赛事中频繁引入的官方补水暂停），以往“由上下半场构成的两幕剧（game of two halves）”正逐渐演变为更像美式橄榄球那样的“四节比赛（game of four quarters）”。这种比赛结构的离散化，不仅为主转播商带来了更多广告变现的时间窗口，客观上也大幅增加了战术团队利用数据进行中场乃至单节即时纠偏的频次。 --- ### `27:30` 传统球探对抗数据分析？以“分差状态”量化拼劲与态度 在《魔球》（Moneyball）式的故事中，人们常常津津乐道于老派球探与年轻数据分析师之间的文化冲突——老球探凭直觉和肉眼评判球员是否有“拼劲（hustle）”、是否有大心脏，而数据狂人只看上垒率。但在现代足球俱乐部的引援与球探体系中，这种水火不容的对立基本已经消弭，取而代之的是高度协同的复合评估机制。 主流俱乐部的常规流程是： - 资深球探现场考察球员，依据经验与直觉给出技术评级； - 数据团队基于内部模型对该球员进行纯量化评估； - 双方比对这两份结果之间的差值（delta）。一旦直觉评级与数据表现出现显著分歧，球探与数据分析师便会坐在一起深入复盘，拆解究竟是模型遗漏了视觉维度的盲点，还是球探的主观判断受到了认知偏差的影响。 甚至对于传统球探眼中最抽象、最不可言说的“拼劲”，数据分析师也能借助**比赛状态（Game State）**工具进行精准量化。所谓的比赛状态，即按照净胜球将比赛划分为 0、+1、-1、+2、-2、+3、-3 等不同情境： - 当比赛进入一方净胜 3 球（+3 / -3）、落后方胜率可能仅剩 2% 的垃圾时间时，整场胜负已定。 - 分析师可以单独切分并过滤出球员在净负 3 球状态下的表现数据：此时大势已去，该球员是在场上消极怠工、放弃防守选位，还是依然拼抢回防、保持战术纪律？ 这种利用数据交叉过滤出的极端比赛状态，为原本难以捉摸的职业态度与竞争意志提供了极具说服力的数字注脚。 ### `30:00` 数据眼中的“全能”：用量化框架解构裘德·贝林厄姆 传统球探往往喜欢用一些难以捉摸的主观词汇，比如称赞某个球员“极具坚韧品格（grit）”。但分析师们更倾向于把数据视作多功能的“瑞士军刀”——它或许不能直接给出绝对答案，但能精准提出关键问题。针对主持人提出“如何用量化分析框架去评判当今或史上最佳球员”这一重磅问题，嘉宾毫不犹豫地给出了一个具体人选：皇家马德里中场裘德·贝林厄姆（Jude Bellingham）。在现代足球中，大多数前锋都被死板地绑定在9号位角色上，而贝林厄姆却像是一本长篇故事书里的全能主角，能在每一个章节、每一幕场景中，以世界顶尖水平完成战术需要的任何任务；除了门将，他几乎能够胜任球场上的任何位置。 要量化这种“全能性”，数据分析团队主要从两个核心维度来切入：**控球时（In Possession）**与**无球时（Out of Possession）**。 - **控球分析**：衡量球员如何将球推进到极具威胁的区域，以及如何创造出高概率的得分机会； - **无球防守分析**：这在体育数据界是一个极具挑战性的前沿课题，因为分析师本质上是在“量化一件并未实际发生的事件的价值”。例如，当进攻方一名球员在边路持球、另一名队友在禁区前沿准备接应时，防守端的贝林厄姆总能在最精准的时机移动到传球路线上，像个“极其讨厌的幽灵”一样卡在传受双方之间。现代追踪技术能够实时计算球员封堵这些传球线路、压缩进攻空间的几何价值，并进一步结合他们脚下的实际技术动作完成全方位评估。 ```mermaid flowchart TD accTitle: 现代足球量化分析框架 accDescr: 展示控球与无球双维度的足球量化评估机制 subgraph Evaluation["球员表现综合量化框架"] direction TB subgraph InPossession["持球维度 (In Possession)"] A["推进传球与运球"] --> B["高危区域渗透"] B --> C["高概率进攻机会创造"] end subgraph OutOfPossession["无球维度 (Out of Possession)"] D["空间位置追踪"] --> E["传球路线封堵判定"] E --> F["阻断未发生威胁的量化价值"] end end ``` --- ### `35:00` 赛内实时胜率模型与前五分钟信息量 针对体育博彩与专业执教之间的模型差异，主持人提出了一个假设：分析模型能否仅仅通过一场比赛前五分钟看似势均力敌的0-0平局，就敏锐察觉出人类语言难以描摹的底层动能，进而断定某支球队其实有70%的概率取胜？ 专业数据分析顾问解释称，现代比赛中确实存在成熟的**赛内实时胜率模型（In-Game Win Probability Models）**，但其运作机理更偏向贝叶斯更新，而非五分钟内的剧烈反转： - **先验评估（Prior）**：系统在赛前会基于两队基础战力（类似国际象棋的 Elo 评分系统），生成两队各自的胜、平、负概率； - **动态更新（In-Game Updates）**：比赛开始后，模型会根据创造出的绝佳机会、预期控球价值（EPV, Expected Possession Value）或进攻势头实时修正概率。然而，仅仅前五分钟的场面——即便弱势队伍爆发出极高能量或创造了一两次意外机会——也很难彻底撼动赛前的强大先验基准，指针不会出现颠覆性位移。数据分析师会逐步根据涌入的比赛流信息微调对比赛走势的信念，而不是轻易被短暂的开局假象所误导。 --- ### `37:30` 欧洲联赛 vs. 美职联：从纯战术到“投资组合管理” 话题转向迈克·特雷西（Mike Treacy）正在提供咨询的美国职业足球大联盟（MLS）奥斯汀FC（Austin FC）。对比欧洲顶级联赛与MLS，两者在数据分析策略上展现出截然不同的面貌： - **欧洲足坛的分析范式**：欧洲缺乏严格的工资帽限制，且存在残酷的升降级制度，资金流动相对自由。其分析部门的核心任务通常高度聚焦在两大支柱：**引援招募（Recruitment）**与**一线队技战术表现分析（First Team Analysis）**； - **美职联的“投资组合管理”范式**：MLS取消了降级制，设置了指定球员规则（Designated Player）以及极其繁复的工资帽结构，旨在维持各队间的竞争均衡（Parity）。这使得MLS的分析团队必须引入第三个关键维度——**投资组合管理（Portfolio Management）**。 特雷西将MLS的阵容构建形象地比作金融资产配置：这就好比给你1亿美元预算，但硬性规定你必须将8000万美元配置在英伟达（NVIDIA）这种顶级高确定性资产上，1000万美元买入稳健的沃尔玛（Walmart），剩下的1000万美元去下注高风险高回报的未盈利生物科技股票。分析师不仅要衡量球员的竞技水平，更要从相对价值（Relative Value）的角度评估该球员在严密工资帽体系中的投资回报比。针对这种制度是否真的在大联盟各地球迷群体中建立起了平等的认同感，特雷西指出，奥斯汀FC在这一新管理框架下的尝试仅开展了九个月，期间体育部门也经历了人员重组，这种将投资组合理论深度整合进俱乐部运营、并转化为积分榜实际战绩的模式，目前仍在验证与探索阶段。 ### `40:00` 投资组合管理理论在 MLS 的实战：奥斯汀 FC 的阵容构建与薪金帽套利 作为一名拥有丰富波动率套利经验的前金融交易员，迈克·特雷西（Mike Treacy）将他在金融市场中积累的直觉与组合资产配置理念完整植入了美职联（MLS）奥斯汀 FC 的运营中。特雷西指出，美职联的薪资规则极其复杂，而正是这种复杂性为投资组合管理提供了绝佳的套利土壤。在联赛规则中，每个球员都对应着特定的名额槽位（Slot）。以“指定球员”（Designated Player，简称 DP）名额为例，如果一名球员以 DP 身份引进却表现平平，那就是一笔糟糕的交易；但如果同一名球员能以老将底薪（Senior Minimum）槽位签下，那么他在对应槽位的性价比百分位数中可能就会名列前茅。 在 MLS 的阵容构建战略中，各队拥有不同的组合路径：例如可以选择 3 名指定球员（DP），也可以选择 2 名 DP 搭配 4 名 U22 倡议球员（U22 players）。联赛虽然设有工资帽（Salary Cap），但核心逻辑其实是“薪水占用额”（Salary Cap Charge）。最典型的例子就是莱昂内尔·梅西（Lionel Messi），虽然梅西实际拿到的年薪可能超过 2000 万美元，但在规则限制下，他作为指定球员计入工资帽的实际占用额仅有约 75 万美元。该制度最初源于洛杉矶银河（LA Galaxy）引进大卫·贝克汉姆（David Beckham）时打破薪水限制的历史遗产。俱乐部必须在固定的总支出额度框架下，精算每一个名额槽位的占用额与产出，实现资本效率的最大化。 现代足球的一大通病在于顶级富豪豪门（尤其是欧洲五大联赛）能够依靠无限的资金垄断最顶级的球员，导致“强者愈强”。随着数据分析在比赛战术与引援中愈发关键，财力雄厚的俱乐部同样拥有更多算力、工程资源和顶尖分析师，这种技术军备竞赛可能进一步拉大贫富差距。然而，尤里斯·贝克斯（Joris Bekkers）长期致力于开发开源分析软件，试图通过开源工具帮助中小俱乐部构建图神经网络（Graph Neural Networks, GNN）与控球预期价值模型（Expected Possession Value, EPV），并处理门槛极高的追踪数据。尽管如此，贝克斯坦言，工具的平民化并不必然抹平鸿沟，因为中小俱乐部真正的瓶颈往往在于缺乏足够的数据科学人才，无法从浩瀚的数据中提炼出真正能够指导战术落地的核心认知。 ```mermaid flowchart TD accTitle: MLS 薪资帽结构与投资组合配置框架 accDescr: 展示 MLS 俱乐部在指定球员、U22 倡议与常规球员之间的薪水占用额与资本分配模式。 subgraph CapAllocation ["MLS 薪水占用额框架 (Salary Cap Charge)"] Budget["总薪金帽额度 (有限资本)"] DP["指定球员 (DP 槽位)<br/>实际薪资可达数千万美元<br/>工资帽占用额仅固定约 75 万美元"] U22["U22 倡议球员槽位<br/>年轻潜力股与低占用额"] SeniorMin["老将底薪 / 常规阵容槽位<br/>争取在同级槽位打出最高百分位产出"] end Budget --> DP Budget --> U22 Budget --> SeniorMin ``` - **指定球员政策历史**：源于当年洛杉矶银河签约大卫·贝克汉姆，允许球队在严格的工资帽限制下以天价高薪吸引世界级巨星。 - **名额套利的核心逻辑**：将阵容视为金融资产组合，不在于球员的名气，而在于该球员在其所占用的具体名额槽位（Slot）中所产出的超额价值（Alpha）。 - **开源软件对阵资源垄断**：贝克斯开发的开源工具降低了俱乐部接触前沿数据架构的门槛，但认知提炼（Distilling Knowledge）依然是阻碍弱旅逆袭的壁垒。 --- ### `45:00` 足球数据的进化链条：从乌克兰黑客的“草台班子”到骨骼姿态识别 谈及足球数据的来源与归属，特雷西分享了一段 2016 年他刚进入英超伯恩茅斯（AFC Bournemouth）建立模型时的奇特经历。当时他根本找不到正规的足球数据集渠道，于是他直接在自由职业外包平台 Upwork 上发布悬赏，寻求“有欧洲足球博彩建模经验的开发者”。一名来自乌克兰、名叫德米特里（Dmitri）的工程师回复了他，表示自己曾为大量专业博彩集团提供服务。在特雷西提出“把我能拿到的所有数据都弄来”后，德米特里通过某种极具极客与秘密实验（Skunkworks）色彩的方式，帮他调取到了当时全球范围内的全部持球事件数据（On-ball data）。 现代足球数据主要经历了解析维度的三次代际飞跃： 1. **持球事件数据（On-Ball Data）**：最基础、最通用的二维表格数据，可以用 Excel 轻松呈现。记录球场上按时间顺序发生的离散动作：传球、盘带、射门、进球、铲球等。每行数据包含发生时间、涉及球员、动作类型以及场上的 X-Y 坐标。分析师通过组合事件频次、动作速度和空间坐标，拼凑出比赛的大致马赛克画卷。 2. **追踪数据（Tracking Data）**：由安装在球场的专业摄像机阵列或广播电视转播画面（利用计算机视觉模型先识别球场边线标线与球门位置，再将球员相对位置解算为绝对坐标）提取。数据采样率通常为每秒 10 帧或 25 帧（fps）。在每秒 25 帧的格式下，单帧就需要记录场上全部球员及足球的 X-Y 坐标，包含大量复杂的球员/球队 ID 映射元数据。如果遇到不包含球权归属的原始数据，分析师甚至需要自行通过每名球员与足球的距离算法来计算谁在控球。 3. **骨骼姿态数据（Skeletal Data）**：数据密度相比追踪数据呈几十倍暴增。模型需要在每名球员身上捕捉 27 个身体关键特征点（涵盖鼻尖、左右耳、左右肩、脚踝与脚趾等）。这类数据规模迅速飙升至数百万乃至数十亿个数据点，直接将足球分析的数据体量推向了 PB（Petabyte）级别。 | 数据类型 | 采样率 / 维度 | 包含信息 | 数据体积与处理难度 | |:--- |:--- |:--- |:--- | | **持球事件数据 (On-Ball Data)** | 离散事件触发 | 传球/射门/过人、球员 ID、球场 X-Y 坐标、时间戳 | 轻量级，Excel 可直接打开查看 | | **球员追踪数据 (Tracking Data)** | 10–25 帧/秒 (fps) | 全场所有球员及足球的实时 X-Y 空间坐标、球队及球员 ID 映射 | 单场比赛数万行数据，需专用数据库管理 | | **骨骼姿态数据 (Skeletal Data)** | 25+ 帧/秒，人体 27 个关键点 | 头颈、肩膀、脚踝、视线与躯干朝向等高维空间形态 | PB 级别，极其依赖计算机视觉与密集算力 | 主持人和嘉宾随即打趣讨论起球员对被全方位监控的心理反应。主持人开玩笑称，如果自己录播客时一举一动、甚至脖子和手脚的细微摆动都被量化建模，心里肯定会感到十分怪异。但特雷西指出，大多数职业球员实际上对数据持开放和拥抱态度。在现代前沿应用中（例如纽约团队的研究），分析师正在利用骨骼数据与视线追踪（Eyesight）来分析球员的视野盲区与决策机会成本。当模型发现某次传球不是最优解时，教练组拿着数据去跟球员复盘，球员很可能坦诚解释：“我当时由于视线和身体朝向，根本看不见那个空档。”这种量化分析帮助战术指导脱离了毫无意义的事后指责。嘉宾最后感慨，三十四年前人们也曾坚信国际象棋是一门充满人类灵性与艺术美感、计算机绝不可能攻克的游戏，而今天足球分析的轨迹正展现出与棋类推演极为惊人的历史相似性。 ### `50:00` 足球是计算问题还是艺术：追踪数据的离散化建模 国际象棋曾长期被视作人类不可侵犯的智力艺术与直觉殿堂，但现代算力证明它归根结底是一个状态计算问题——只要拥有足够的数据和计算资源，游戏在某种意义上就能被穷尽与求解。主持人由此发问：看似连续、混沌且不可预测的足球，本质上是否也只是一连串人类肉眼难以逐一捕捉的离散事件？只要采集足够多的追踪数据、注入足够的算力，它是否也能像国际象棋一样被分解为无数微观的二元决策？世界与人生是否最终也是由计算构成的？ Joris Bekkers 坦言，刚接触海量球员追踪数据（Tracking Data）时，任何人都会感到不知所措，因为眼前展现的是一条无穷无尽的坐标流，很难立刻看清如何构建数学模型。但解决这一问题的核心逻辑正是“离散化”（Discretization）：将球场上发生的一切切分成一个个持续两三秒的微观事件片段。例如，将有球事件数据（On-ball Event Data）与位置追踪数据对齐，便能精准标定球员送出传球的瞬间，以及接球队员触球的下一瞬间。这构成了第一个历时约 2.5 秒的离散事件；紧接着，接球球员完成下一次持球推进或摆脱，又构成下一个 2.5 秒的微观片段。 ```mermaid flowchart TD accTitle: 足球追踪数据的微观离散化处理流程 accDescr: 展示从连续坐标流到离散微观事件，再到高层量化价值指标的处理链路 subgraph Input ["底层连续追踪流"] A["连续坐标数据流 (X, Y 坐标/帧)"] end subgraph Discretization ["事件离散化 (2-3秒片段)"] B["微观事件 1: 传球动作发起"] C["微观事件 2: 接球与停球控制"] D["微观事件 3: 持球推进与盘带突破"] E["防守方微观移动与防线反制"] end subgraph MetricAggregation ["高阶量化评估与应用"] F["增量进球期望价值 (Added Value)"] G["防守压迫与失球概率削减度量"] H["视频分析师战术切片与复盘"] end A --> B B --> C C --> D A --> E B & C & D --> F E --> G F & G --> H ``` 通过这一层层细分，球员的每一次微小变向、防守队员的贴身反制，都能转化为易于理解的高阶聚合指标： - **进攻贡献**：量化单名球员在特定推进或盘带动作中，为全队攻入进球所贡献的“增量期望价值”。 - **防守贡献**：追踪防守球员是否时刻保持在有效压迫距离内，量化其在阻止对手得分、化解威胁中的实际成效。 - **人机协同**：离散化后的数据切片与视频分析师的复盘工作流完美契合，使得庞大晦涩的数据可以直观转化为战术板上的调整建议。 --- ### `52:15` 卖方分析师为何预测不好世界杯与“绝不公开发表”定律 随着世界杯赛季临近，华尔街与各大券商的卖方研究部门（Sell-side Analysts）往往会扎堆发布世界杯预测研报。然而历史经验表明，这些研报的预测准确率通常非常糟糕，常常出现预测英格兰或美国队夺冠的偏颇结论。面对主持人“为何精通统计与数据建模的卖方机构每隔四年就足球预测集体翻车”的疑问，嘉宾们给出了犀利而真实的行业视角。 Joris Bekkers 直言，他并不清楚这类机构究竟采用了何种模型——是单纯的等级分排名（ELO Model），还是真正引入了逐球事件与追踪数据体系。但他送给金融分析师的建议非常直接：“各司其职，守好本分（Stay in your lane）。”卖方分析师就应该专注做好股票与市场的卖方分析，而不是跨界客串足球预言家。 主持人随之指出了交易与预测界永恒的博弈悖论：**如果你手里真的掌握了一套能够跑赢市场的顶尖预测模型，你绝对不可能把它写成研报免费公开发表**。真正的 Alpha 只会用来在博彩市场或预测市场中击败庄家闷声发大财；那些被拿来公开赚取眼球和营销声量的预测，本质上天然就缺乏可靠性。 --- ### `53:40` 赛后复盘：古德哈特定律、数据过度优化与体育观赏性的流失 在送别嘉宾后，主持人 Tracy Alloway 与 Joe Weisenthal 展开了赛后复盘。Joe 感慨，得知世界上大多数事物（包括运动）归根结底都能被芯片分解为二元计算问题，让人略感沮丧与虚无，因为人们总希望艺术、美感与直觉依然拥有不可替代的一席之地。 随后他们深入探讨了在体育分析革命中无处不在的“古德哈特定律”（Goodhart's Law）——**当一项指标变成目标本身时，它就不再是一个好指标**。 - **数据刷子现象**：当球队和教练开始迷恋特定高阶数据，球员便会针对这些指标调整自己的踢法以美化面板，教练也会倾向于挑选符合数据特征的球员。然而，个人数据的单点堆砌并不能保证稳定转化为球队整体的胜利。 - **多元目标的权衡悖论**：正如前文所提及的，特别是英超等高水平联赛中，俱乐部所优化的目标各不相同——有些在优化净利润，有些在优化保级概率，有些在优化争冠胜率。追求保级与追求争冠，在数据模型里得到的是两套完全相悖的最优解。 这种追求“博弈论最优解（GTO）”的过度量化优化，正在对体育的观赏性造成破坏： - **篮球的三分化退化**：早年 NBA 充满暴扣与对抗，极具观赏性；然而当数据分析证明三分球是数学期望最高的出手选择后，整项运动迅速被海量三分出手同质化，比赛流失了大量纯粹的视觉快感。 - **足球的战术趋同与消极求生**：世界各地的战术风格正日益趋同。例如在国际大赛中，像巴拉圭对阵法国时饱受批评的极致防守反击策略——全场彻底放弃进攻死守平局，纯粹依靠拖入点球大战后的巨大方差（Variance）来博取爆冷机会。从纯粹的博弈论来看，弱队选择这种极度难看的踢法完全是最优解。 二人总结道，为了赢球而优化、为了商业利润而优化、以及为了满足赌客而优化，指向的是截然不同的答案。如果过度追求量化最优导致比赛枯燥无味，最终虽然赢了球，却失去付费买票的球迷，这种优化本身也是一种危险的自限。尽管目前球迷仍愿意为足球比赛掏出天价门票，但过度分析化带来的隐忧已初露端倪。 ## Notable quotes > `07:20` 赛场上的每一个维度本质上都是一个概率分布（distribution） — Mike Treacy > `10:00` 没有任何实际预测意义 — Joris Bekkers > `17:15` 控制你能控制的（control the controllables） — Joris Bekkers > `20:00` 充斥着劣质数据的假源泉 > `22:30` 模型输出向主教练认知层面的翻译 > `30:00` 量化一件并未实际发生的事件的价值 > `45:00` 把我能拿到的所有数据都弄来 — Mike Treacy > `45:00` 我当时由于视线和身体朝向，根本看不见那个空档。 > `52:15` 各司其职，守好本分（Stay in your lane） — Joris Bekkers > `52:15` 如果你手里真的掌握了一套能够跑赢市场的顶尖预测模型，你绝对不可能把它写成研报免费公开发表 — Joe Weisenthal > `53:40` 当一项指标变成目标本身时，它就不再是一个好指标。 ## Mentioned Joe Weisenthal, Tracy Alloway, 底特律老虎队 (Detroit Tigers), 芝加哥小熊队 (Chicago Cubs), 《魔球》(Moneyball), 摩根路易斯律师事务所 (Morgan Lewis), 2026年美加墨世界杯, 2022年卡塔尔世界杯, Mike Treacy (迈克·特雷西), Joris Bekkers (尤里斯·贝克斯), Peak6, Apex Fintech Solutions, 奥斯汀FC (Austin FC), 美职联 (MLS), 英超联赛 (Premier League), 美国足协 (US Soccer Federation), 彭博社 (Bloomberg), 《数字游戏》(The Numbers Game), 克里斯·安德森 (Chris Anderson), 大卫·萨利 (David Sally), Michael Caley, 切尔西 (Chelsea), 托特纳姆热刺 (Tottenham Hotspur), 尼古拉斯·杰克逊 (Nicolas Jackson), 裘德·贝林厄姆 (Jude Bellingham), 皇家马德里 (Real Madrid), 英伟达 (NVIDIA), 沃尔玛 (Walmart), 莱昂内尔·梅西 (Lionel Messi), 大卫·贝克汉姆 (David Beckham), 洛杉矶银河 (LA Galaxy), 伯恩茅斯 (AFC Bournemouth), Upwork, 古德哈特定律 (Goodhart's Law) ## Video description <p data-prosemirror-content-type="node" data-prosemirror-node-name="paragraph" data-prosemirror-node-block="true" data-pm-slice="1 1 []">American sports fans have long been comfortable talking in the language of stats and analytics. Soccer embraced the 'moneyball' revolution later; the sport was once perceived as too complex to model analytically &mdash; there were too many players on the pitch, the game's progression was too random and chaotic to reliably predict. That's no longer the case, and soccer watchers are well aware of stats like xG (Expected Goals) and each match is an opportunity for a team to mine data, whether its tracking data, on-ball data, or even analyzing body poses and movement. Today, we speak with two soccer analytics veterans, Mike Treacy (head of risk at Apex Fintech Solutions) and Joris Bekkers (a soccer analytics consultant). Treacy's background includes a stint in analytics for a Premier League team and he's currently advising the MLS team Austin FC while Bekkers has built software that analyzes raw soccer data and he's worked with the US Soccer Federation. We talk to them about how VAR has affected the sport, how data analytics can capture ineffable things like hustle, how European leagues and the MLS differ in their analytics strategy, and why chess and soccer are not so dissimilar.</p> <p data-prosemirror-content-type="node" data-prosemirror-node-name="paragraph" data-prosemirror-node-block="true">Read more:<br data-prosemirror-content-type="node" data-prosemirror-node-name="hardBreak" data-prosemirror-node-inline="true"><a href="https://www.bloomberg.com/news/articles/2026-07-14/stubhub-world-cup-ticket-complaints-spur-legal-claims-from-fans?utm_medium=referral&utm_source=podcast&utm_campaign=odd_lots&utm_content=article" data-prosemirror-content-type="mark" data-prosemirror-mark-name="link">The Lawyer Taking On StubHub Over World Cup Ticket Sales</a><br data-prosemirror-content-type="node" data-prosemirror-node-name="hardBreak" data-prosemirror-node-inline="true"><a href="https://www.bloomberg.com/news/articles/2026-07-14/polymarket-partners-with-crypto-firm-during-world-cup-semifinals?utm_medium=referral&utm_source=podcast&utm_campaign=odd_lots&utm_content=article" data-prosemirror-content-type="mark" data-prosemirror-mark-name="link">Polymarket Partners With Crypto Firm During World Cup</a></p> <p data-prosemirror-content-type="node" data-prosemirror-node-name="paragraph" data-prosemirror-node-block="true">Only <a href="http://Bloomberg.com" data-inline-card="" data-card-data="">http://Bloomberg.com</a> subscribers can get the Odd Lots newsletter in their inbox each week, plus unlimited access to the site and app. Subscribe at&nbsp; <a href="https://www.bloomberg.com/subscriptions/oddlots?in_source=oddlotspodcast" data-prosemirror-content-type="mark" data-prosemirror-mark-name="link">bloomberg.com/subscriptions/oddlots</a></p> <p data-prosemirror-content-type="node" data-prosemirror-node-name="paragraph" data-prosemirror-node-block="true"><a href="http://bloomberg.com/subscriptions/oddlots" data-prosemirror-content-type="mark" data-prosemirror-mark-name="link">Subscribe to the Odd Lots Newsletter</a><br data-prosemirror-content-type="node" data-prosemirror-node-name="hardBreak" data-prosemirror-node-inline="true"><strong data-prosemirror-content-type="mark" data-prosemirror-mark-name="strong">Join the conversation:</strong> <a href="https://discord.gg/oddlots" data-prosemirror-content-type="mark" data-prosemirror-mark-name="link">discord.gg/oddlots</a></p><p>See <a href="https://omnystudio.com/listener">omnystudio.com/listener</a> for privacy information.</p> [Source](https://podtrac.com/pts/redirect.mp3/tracking.swap.fm/track/UVBrz8bN8aM2Xe47PEPu/traffic.omny.fm/d/clips/e73c998e-6e60-432f-8610-ae210140c5b1/8a94442e-5a74-4fa2-8b8d-ae27003a8d6b/4859579a-2313-42f7-9c12-b488014fc4d7/audio.mp3?in_playlist=982f5071-765c-403d-969d-ae27003a8d83)

[7:20] Mike Treacy: 赛场上的每一个维度本质上都是一个概率分布（distribution） [10:00] Joris Bekkers: 没有任何实际预测意义 [17:15] Joris Bekkers: 控制你能控制的（control the controllables） [20:00] 充斥着劣质数据的假源泉 [22:30] 模型输出向主教练认知层面的翻译 [30:00] 量化一件并未实际发生的事件的价值 [45:00] Mike Treacy: 把我能拿到的所有数据都弄来 [45:00] 我当时由于视线和身体朝向，根本看不见那个空档。 [52:15] Joris Bekkers: 各司其职，守好本分（Stay in your lane） [52:15] Joe Weisenthal: 如果你手里真的掌握了一套能够跑赢市场的顶尖预测模型，你绝对不可能把它写成研报免费公开发表 [53:40] 当一项指标变成目标本身时，它就不再是一个好指标。

[120:00] Mike Treacy: It was a rich fountain of bad data... when you look at his seasonal outputs for that entire season, that three goals was probably around 20% of his total goals. [122:00] Joris Bekkers: The coach isn't fed the data directly. The coach is fed just the information that the analyst finds from the data. And that... generally still boils down to having video clips. [128:00] Mike Treacy: Soccer data creates questions. It doesn't give us answers.

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When you're running a business, the best days are the ones where priorities stay on track. For midsize and large companies, risk can affect multiple parts of the organization at once, from property and liability to cyber and regulatory challenges. At that level managing risk becomes an ongoing discipline At the Hartford the focus is on helping businesses manage risk before it turns into something more disruptive And when losses do happen, that work is paired with insurance coverage shaped by years of underwriting, risk engineering, and claims experience. Learn more at thehartford.com slash risk mitigation. Policies provided by Hartford Fire Insurance Company and its property and casualty affiliates, Hartford, Connecticut. Bloomberg Audio Studios. Podcasts. Radio. News. Hello and welcome to another episode of the Odd Lots podcast. I'm Joe Weisenthal. And I'm Tracy Alloway. Tracy, I have a question. I know you spent a lot of your youth overseas. My youth. Did you ever go to many baseball games as a kid? yeah so i was in chicago for a few years so i went to the cups games and then i was in japan and the baseball scene in japan is amazing like the best vibes of a live sports event that i've ever ever witnessed or encountered i was just talking to someone about this last night i always wanted to go to a japanese baseball highly recommend that actually like if we ever do a live show in Tokyo let try to schedule it during baseball season Because that is like, I sort of think that's a bucket list thing. But anyway, the reason I asked this question is, I have this really vague memory as a child going to see Detroit Tigers games with my grandfather, like probably when I was like, maybe these memories are probably from when I was younger than like six or five. But there used to be a non-trivial number of people who would go to the games and they would keep score and they would write down every single at bat and the outcome of every single one. I'm pretty sure I've seen that, not in person, but like maybe in movies or something like that. It doesn't really happen anymore. Like I never see it. There may be a few like old timers who still as a hobby or habit do that. But it was like a non-insignificant number of people. And it's interesting to me, you know, I've been to a couple of soccer games this year. there is no equivalent way you could do that right because it's like baseball is filled with all of these discrete events the pitcher who is the pitcher who is the batter hit not a hit single not a strikeout walk etc like what would even be the equivalent in soccer so this has been a long running debate in soccer and i remember when money ball came out and you know sports analytics became a big thing especially for baseball because as you point out it these sort of discrete events that have a lot of statistics embedded in them A lot of people were saying that soccer you could never use data analytics in the same way for soccer. Like it's too chaotic. It's too fluid. There's too many variables. There's not enough goals. That complaint comes up a lot whenever we talk about, are we going to say soccer or football, by the way? You know what? Let's just say soccer. Okay. All right. I'll try. We can say football. I actually don't feel strongly about this one. But that said, we do see soccer analytics on the rise. Totally. Like now we get all these stories about like tiny clubs that are using data to source, you know, specific players in very moneyball style ways. We obviously have prediction markets. Yes. People are doing a lot of sports betting. And so all the analytics seem to be like becoming more important. And I will just say, I've read this crazy stat right before we came on from the law firm Morgan Lewis, and they were saying in the 2026 FIFA World Cup match based data is going to be something like. So it's 104 matches generating more than 90 petabytes of data. Yeah. Which is a 45 fold increase over the volume produced in the last World Cup. [5:00] in 2022. That's stunning. So this raises a question, and I know we're going to get to this in the conversation, and it almost is like a philosophical question, which is, okay, we see the game of soccer is like very fluid, right? There's no, we just said there's fewer discrete events. Like in theory, is something that's fluid a series of like microscopic discrete events, you know, could you get a million frames per second and actually turn it into discrete events? Like that is sort of like an interesting question to me. A parallel that I think of in this conversation is chess is like all discrete events. And that was seen as like a very difficult thing to crack. But then like over 25 years ago, it's like, yeah, of course they cracked it. But then you would think, OK, well, like what is the opposite of chess, which would be language? And you say, OK, you can't. That's fluid. That's all over the place. And yet computers seem to be understanding language pretty good. My inner Luddite says there must still be a secret like unmodelable thing. I can't talk when it comes to like football, the beautiful game. But you're right. That technology may prove me wrong very quickly. Well as you mentioned you know soccer analytics growing And obviously the interest now is for obvious reasons There all the betting on the World Cup People talk about the XG of like I don know a situation or a player the expected goals. Now we have body posing analytics as well, which blows my mind. And when our producer Kale introduced me, I hadn't seen them before earlier this year, like the momentum charts that show like, you know, how dominant a team is at any given moment. You see it going waves and stuff like that. So there clearly is a lot of work being done. I don't know how much it works. I don't know how much like momentum charts consistently predict who is going to be the winner. But just this question of like the ability to model deeply fluid things, the beautiful game, like it's an art, right? Like, can computers actually model this? And then like, if they can, what does that say about the ability to model a bunch of other things? Strikes me as just like a very relevant Question right now because it's the World Cup, but also relevant question in general about markets and finance for markets and finance. Exactly. So I'm curious to know, like how it works and how the moneyball revolution where we are in the arc with soccer. Anyway I really excited to say we really do have two perfect guests because they do sit right in this space and also at the intersection of everything that we talking about We going to be speaking with Joris Beckers He is a soccer analytics consultant a professional soccer analytics consultant for the last decade as well as Mike Tracy. He's the head of risk at Apex FinTech Solutions. He used to be a volatility arbitrage trader at Peak Six, and he also does soccer analytics for the club FC. So literally the two perfect guests to talk about some of these questions that are arising right now So Mike and Yoris, thank you both so much for coming on the podcast. Thank you for having us. This is a great introduction. Yeah, thank you. You know, Mike, let me start with you a question. A lot of people, I think, have, for good reason, an intuitive feel that sports analytics and trading markets are adjacent ideas. We know this. We know that a lot of the prop shops and market makers do both and so forth. How would you articulate based on your career, the sort of overlap between the skills and techniques you've developed as an arbitrage trader, a volatility trader, and the overlap of skills that they're like, okay this thing that we get into that we call soccer analytics Well soccer is unique because I say every aspect of the game is a distribution When you look at on pitch the performance by a team when you look at performance by an individual player, when you look at the seasonal outcomes and this unique component that is promotion relegation. So your finances are highly variant year over year. And so there's a lot of overlap between volatility trading and working in soccer in that you are making highly levered bets on often imperfect information that's not necessarily predictive like other sports such as baseball. Can I ask a very basic question, which is, what is the point of soccer analytics? So if we go back to the markets analogy, we talk about price discovery, right? Like you're trying to find the right price for a particular asset. With soccer, are you trying to price players, improve the training, make more successful predictive bets? I imagine it's a bunch of different things. Yeah, I'd say everything. I think you said, what are the things you're trying to do? And I think from an investor operator perspective, it's what do you... [10:00] trying to not do. You're not trying to get relegated and you're not trying to spend 30 million pounds on a player that is going to be terrible and you'll have to get rid of in two years. Yours, why don't you talk from your perspective? I mentioned you're a soccer analytics pro. Actually, our producer, by the way, just put it in the chat. The Bloomberg style guy does football, which is interesting. Maybe we'll just switch to, yeah, let's stay in a company style. You're a football analytics pro. Tracy asks, like, what is the point? Is it more on the team side of things in terms of identifying talent, et cetera? Or is it more on, I don't know, I guess, like the sort of the betting side? Like, what is the problem you and your professional capacity are trying to solve? So it highly depends on the organization. Some organizations might want to, like Mike said, make good hires, make sure that they don't lose millions of pounds. Some organizations might use soccer analytics to try and improve their strategy. So they might look at in-game data and try to figure out if there's some optimization that they can make based on where the passage should go or where players should be, what play styles make more sense or what yields more expected goals if you will And then I guess the third one is entertainment There are a lot of apps out there websites out there that provide fans with some sort of information And even back in the, let's say in the 90s, they would have these overlays on the TV where they show number of corners, number of yellow cards and possession percentage. I remember that. It doesn't mean anything, but it's interesting. So you can only imagine that you can go much deeper with that and people will still be engaged. Wait, actually, just say more on that. You said it doesn't mean anything. Is that something that has always been understood or is this something in 2026? We could say that a few of these stats that they like to put on the TV were just extremely like low signal data points. Yes. So when I when I say they don't mean anything, I don't think those were necessarily predictive of the outcome of the match. Got it. Corners might because it's an indicator of which team has the overhand in a game. But I'm quite sure most of the others like possession percentage don't mean all that much. I'm trying to look at game outcomes. Wait so we touched on this in the intro but like the perceived wisdom in the sort of early 2000s was that soccer was far too complicated to be given the baseball moneyball style treatment What actually changed to get us to this point where we not just talking about things like expected goals, but we're also talking about like body movements and posturing and things like that? You know, baseball had moneyball in 2003 and soccer had two things in the 2010s. So in 2013, Chris Anderson and David Sally published this book called The Numbers Game that distilled soccer down to more of a weakest link game. And then the other thing that happened was I would say we had a bit of this revolution on Twitter, which you kind of spoke about recently, Joe, where ideas were incubated. And I give Michael Cayley a lot of credit for this. He's been on the pod, but every Saturday in the Premier League, you'd have six matches and then you would wait 30 minutes and Kaylee would just post a stream of every expected goals chart. And it started to stimulate this discussion of does this represent what should have happened, what should have been the outcome? And I think it started to lead us down this path of where is XG flawed It only registers when you have a shot And so there is much more to the game than simply which shots occur There's possession and the threat of each possession. There's match momentum and there's changing styles. So it's evolved from on-ball data to tracking data to now we're going to that deeper layer of body pose and what movements can prevent or create opportunities to score i think what goes hand in hand with that is when i when i started 10 years ago soccer football was perceived as too complex there were 22 players there was a ball people were doing interesting analytics research and applied research already in basketball and what was said was well there's five players on each team so it's a lot less complex there's more games and we have more data and there's more scoring so you could derive metrics a lot easier and I think that the evolution in just how AI was applied in data availability so going from like Mike said only on ball events where we know which player made the pass which player made the shot [15:00] We always have to say, well, we don't know where all the other players are because those are not recorded. And now we have the ability to make highly complicated artificial intelligence neural nets with this positional tracking data where at 10 frames per second or 25 frames per second, we know where all the players are and we know where the ball is. And then additionally, at some point, we will get full body pose. So we know where the whole skeleton of all players are basically. like that sort of went hand in hand and it felt like it was inevitable but also the game is just more complex so it needed more compute it needed more data needed more knowledge Whether you're planning a big tech event, launching a new campaign, or just stocking up on team gear, finding the right promotional products makes all the difference. 4imprint offers thousands of options, from on-trend apparel and premium drinkware to tech, totes, and giveaways, so you can find the right fit for any audience, purpose, or budget. You can customize it all your logo your message your look and many items come with no setup charge to help you save And if you really watching the bottom line you find standout choices at every price point so you can make a real impact while staying on budget. Plus, you'll get expert help, fast turnaround times, and their 360-degree guarantee. So you can be 4imprint certain your order will arrive on time and look exactly right. Whatever your goal, 4imprint makes it easy to find your perfect promo match. Explore the possibilities today at 4imprint.com. 4imprint, 4certain. Support for the show comes from public.com. If you're actively involved in your portfolio, you probably catch yourself repeating the same actions. Buying the dip, manually sweeping idle cash, putting on a hedge. On public, you can now create AI agents that handle all these tasks on your behalf. Just describe what you want to do in plain English. Like, if the VIX hits 25, buy a put option on the S&P 500. or if my cash balance goes above $20,000, move the excess into my direct index. You approve of the workflow and your agent handles the rest. Monitoring the market, watching for your conditions and executing your strategies exactly as defined. An investing platform driven by your intent not just your clicks You can also get full read and write access to your account via the public API Go to public slash market and fund your account in five minutes or less That's public.com slash market. Paid for by Public Investing. Brokered services by Open to the Public Investing, Inc., member FINRA and SIPC. Advisory services by Public Advisors, LLC, SEC Registered Advisor. Complete disclosures available at public.com slash disclosures. So there's a lot of noise about AI, but time's too tight for more promises. So let's talk about results. At IBM, we work with our employees to integrate technology right into the systems they need. Now, a global workforce of 300,000 can use AI to fill their HR questions, resolving 94% of common questions. Not noise. Proof of how we can help companies get smarter by putting AI where it actually pays off, deep in the work that moves the business. Let's create smarter business IBM Tracy, Mike mentioned that Just looking at a shot on goal Is only going to tell you so much For example, it doesn't tell you If the referees are going to revisit a call Made a minute before the shot Halfway on the other half of the screen And take away the goal This was going to be my question Which we were talking about before the podcast recording But like how do you factor in let say the occasional randomness of the game and perhaps some erratic trying to be diplomatic here erratic decision making by referees and footballing bodies I think it's control the controllables. That's a fixed parameter within the game is that uncertainty that you can't control. and it's hard to predict there is human error obviously and it's impossible to isolate when that's going to happen in a match and how it will you just you just sort of play the game you also don't look at individual events per se you might from an analysis perspective but if you're building a basic predictive model for football outcomes you might just take all the the scoreboard results from the last 10 years and then all those things cancel out like if one team has a red card somewhere you wouldn't even know from these models but you can build some interesting let's say rudimentary predictive models with just the outcomes of games out of curiosity has var changed football analytics at all or presented new opportunities for data it presents new opportunities for data because that is an event that happens if a player has [20:00] fractionally offside because his hand is ahead of the last defender, that doesn't take away from the fact that he still got into a good opportunistic position, possessed the ball, turned and struck the ball in the net. And often that data is nullified because of the VAR, but in theory, it's something that you should consider in your data set. Within the raw data itself. There's tons of data that you could add or censor out. You know, yours mentioned red cards and a lot of our models, we censor that out of our data set. There's an infamous match from three years ago between Chelsea and Tottenham, where Tottenham went down to nine men and their response was to play a very high line, meaning they put all of their defenders up near midfield and tried to catch Chelsea off sides. And as one would expect Chelsea proceeded to score multiple goals later in the match And one player in particular Nicholas Jackson had three goals in that one match And when you look at his seasonal outputs for that entire season that three goals was probably around 20% of his total goals. So when something like that happens, when you have a irregular game state, it is wise to sort of manipulate your data and remove that to give you a full picture of what does this game look like at an equal game state. Oh, that's interesting. So it's not like that game in particular was a rich fountain of data. It's important to sort of like recognize that the data from this particular game is not going to be particularly predictive about other games and therefore you know a guy who scores three goals in that match is probably not going to continue to score three goals again for the rest of the it was a rich fountain of bad data okay and so at the end of the season when you see people analyzing the player they often analyze their season and what do they do per 90 minutes of And so you have this highly skewed data set by some really poor data And so there a lot of data mining involved in the process of building a model when you evaluate a team and individual players So here's a question I have, and you're talking about using neural networks, and it's like, eventually, we'll have the compute to have the position of every player's body flash maybe hundreds of images, frames per second, and so forth. And then you feed it all into a model. And then we learn something about who's more likely to win. But one of the things that happens in a lot of other domains, and here I'm thinking about chess or Go, for example, is that you can have these models that are extraordinary, but they don't speak English or they don't speak any human language. And so the transmission of what was learned from these events is something usable by, say a coach who's thinking about strategy or a general manager who's thinking about player selection. Talk to us about like when you think about these machine learning models that can't really communicate their findings in any way in a language that humans can understand, how you sort of bridge that gap to where this is useful information for a team or a manager This is generally be understood I think in the last couple of years or the last eight years as what the biggest problem You can build these models. These neural nets already exist. The main thing is the translation, like you said, from model outputs to coach. And I think in the last couple of years, most teams have found is that they need an expert analyst, the data analyst to do this conversion or this translation step where the coach isn't fed the data directly. The coach is fed just the information that the analyst finds from the data. And that could be, in the end, that generally still boils down to having video clips. So you can use the data to find video, and then you can show the video to the coach, which then from bottom up, you have this approach. That makes sense. But the part about, okay, we're going to use the data to find video. So all of this makes sense. You have the data specialist who translates, you have the video so that there's something tangible. But talk to us about that specific step where the data analyst sees some sort of model output and then is able to use that to find the relevant clip to show the coach something potentially instructive, because that seems like the hard part to me. Yeah. So the model output could be many things. It could be outputs from a class [25:00] model that says in this given 10 second or 15 or 20 second window this team played in this sort of build-up or they had this type of structure it could also be a little bit more advanced where you can simply say well in this instance we had a high probability of conceding a goal and that could be just from an expected goal shot if you're looking at only event data but you could also have model outputs from something we call an expected possession value model or an expected the threat model where you measure the chance that the team is going to score in, let's say, the next 30 seconds or the next possession. And then you can find the spikes there and either measure when your team is likely to concede or measure when the other team is likely to score. And you can use those kind of signals to boil it down to video. Yeah, this is something I wanted to ask, actually. So you mentioned speed just then. Like, what is the actual latency that we're talking about since we're using all these market Yeah. Like, are we talking about an insight that's actionable within seconds? Like you're going to sub a player on after your model spits something out like live during the game? Or is it more realistically that you reviewing the model and the analytics after a game and sort of tweaking I guess when when things have calmed down Apparently most of this does not happen live So most of it happens either pre or post but you can still do it. There's enough live data to make these instances worthwhile. Yeah, I'd say most of those types of adjustments based on data typically happen at halftime, or if you're in the World Cup, during a higher duration break. And in the derivatives world, I always think of expected outcome versus realized outcome. So what is the market implying? What do you expect? And then what is actually happening? And that is sort of the nexus of how teams prepare for matches. They come up with their own expected outcome. How is our opposition going to play? How are we going to play? And then that live in-game is your realized outcome. And so you're receiving that data and it's being transmitted to analysts who can then communicate it down to the bench to discuss with the manager who can then make those changes at halftime. It interesting The game of two halves Joe is now the game of four quarters offering up more opportunities to make model based adjustments That right We have we used to have two discrete events in a game The first half of the second And now we have at least four So I guess that, yeah, that that creates more data as well as maybe more ad adjustment as well as as well as more ad revenue. You know, obviously in baseball, at least according to Michael Lewis, right, that there was this period where, you know, you had the old time scouts and they're like, oh, this guy has good hustle, right? Or this guy has a good heart. There was like no data behind any of it. He may just sort of had the, you know, the swagger of someone who looked like maybe a star player. And then it's like, oh, no, but look at his like on base percentage or that's his or whatever. And then they get promoted. But it was like a culture thing. Has there been a similar cultural clash within sort of soccer scouting where what the data says about what constitutes a player does not map to traditional intuitions? I think a lot of clubs look at it from two perspectives. I don't think there's this old school scouts versus the data guy mentality. I think it a very collaborative I think what a lot of clubs do is they have an individual scout who will go watch a player and give his assessment and his rating And then they will have their own internal model with data and they will look at the deltas between those two different models And if something seems off, you often have collaboration between the data person and the scout and they figure out who's right, who's wrong. And then to your point about hustle, let's call it. Yeah. There are Swiss Army knife ways to quantify that in soccer in certain instances. If you look at game state, say the game state, you know, game state is essentially zero plus one minus one plus two minus two plus three minus three. And so say you're in a plus three, minus three game state and win probability for one team is 98%. You can manipulate the data and only look at how players are performing in that game state. You're out of the game. Are you still competing? Do you still care? Are you in the right position? Now, that may not align with... [30:00] the old school scout saying, you know, this guy has grit. But again, there's Swiss Army knife ways to give some type of indication. You know, I like to say soccer data creates questions. It doesn't give us answers. Wait, just to better understand this. Can you give us like an analytics framework if you were trying to judge the best? This is a loaded question, but it comes up on every discussion. But you're trying to judge the best soccer player either of all time or currently like what would the analytics framework for that actually look like jude bellingham okay let me say more yeah yeah like really no seriously this is a great question like walk us through what the math says about jude bellingham and how you would derive that well jude bellingham can play four or five different positions right most players they have the number nine and their role is number nine. But if you think of the game as this book with different chapters within the story, Jude Bellingham can perform whatever task he needs to perform at every single chapter throughout the book. And he does it at the highest level He could play any position on the pitch besides goalkeeper And just sorry like how is this established Like someone could say oh this guy they say this in baseball, too. He's a good all around player, whatever we can see. But like, what is the data that actually establishes that Jude Bellingham can play at high levels in a wide range of position? How do you derive that conclusion quantitatively? So from a data lens, we think of it in two fronts, in possession and out of possession. OK, so in possession is how you're progressing the ball into threatening areas, obviously creating high probability opportunities. Then then out of possession is how are you preventing a team from moving the ball into threatening areas? It's a very tricky question, sports, because you're trying to quantify the value of an event that does not happen. so let's say Joe you have the ball out on the wing Tracy you're right in front of the box Jude Bellingham he would be always always moving into that passing lane he's right in between you guys at the right moment Jude guy so annoying and we have the ability to to quantify the value of of those movements and the closure of of these lanes as players move out on the pitch And then you obviously get to the next phase where it how do they do this with their feet Whether you're planning a big tech event, launching a new campaign, or just stocking up on team gear, finding the right promotional products makes all the difference. 4imprint offers thousands of options, from on-trend apparel and premium drinkware to tech, totes, and giveaways, so you can find the right fit for any audience, purpose, or budget. You can customize it all, your logo, your message, your look, and many items come with no setup charge to help you save. And if you're really watching the bottom line, you'll find standout choices at every price point so you can make a real impact while staying on budget. Plus, you'll get expert help, fast turnaround times, and their 360-degree guarantee. So you can be 4imprint certain your order will arrive on time and look exactly right. Whatever your goal, 4imprint makes it easy to find your perfect promo match. Explore the possibilities today at 4imprint 4imprint 4certain Support for this show comes from public If you actively involved in your portfolio you probably catch yourself repeating the same actions Buying the dip. Manually sweeping idle cash. Putting on a hedge. On public, you can now create AI agents that handle all these tasks on your behalf. Just describe what you want to do in plain English. Like, if the VIX hits 25, buy a put option on the S&P 500. or if my cash balance goes above $20,000, move the excess into my direct index. You approve the workflow and your agent handles the rest. Monitoring the market, watching for your conditions, and executing your strategies exactly as defined. An investing platform driven by your intent, not just your clicks. You can also get full read and write access to your account via the public API. Go to public.com slash market and fund your account in five minutes or less. That's public.com slash market. Paid for by Public Investing. Brokered services by Open to the Public Investing, Inc., member FINRA and SIPC. Advisory services by Public Advisors, LLC, SEC Registered Advisor. Complete disclosures available at public.com slash disclosures. So there's a lot of noise about AI, but time's too tight for more promises. So let's talk about results. [35:00] At IBM, we work with our employees to integrate technology right into the systems they need. Now, a global workforce of 300,000 can use AI to fill their HR questions, resolving 94% of common questions. Not noise. Proof of how we can help companies get smarter by putting AI where it actually pays off, deep in the work that moves the business. Let's create smarter business. IBM. Yeah. We started talking about this sort of translation from what the model says to a coach or something like that. And that still seems tricky. For a better, someone who's betting on sports, that might be totally irrelevant. Like they're just like, the model says this, this team is better. The line doesn't match up with this. Therefore, we're going to bet on this team. I don't know why the model says my model says this team is better, but it does. So the translation is unnecessary if you're just betting. Like, are we at the stage where we get in close to the stage where you could, for example, feed a model the first five minutes of a game, scoreless zero, zero. And to all the players like, oh, this looks like a competitive match. It's going to be good, both sides. But models are able to detect something that we can't articulate that says, oh no this team is playing And even though it looks like a tie game and a competitive one actually for reasons that we can put into English put into language this team looks like they going to win the game They have a 70 chance Is that a thing or is that a phenomenon or is that a realistic thing to expect? There are in-game win probability models, which start with just a pre-game team strength. So both teams have some value. Perhaps you can think of an ELO rating. and they boil down to a win, a draw, and a loss percentage. And then those percentages can in-game be updated, but they won't swing all that much because you have this prior information. So maybe after the first minute, one team has some energy, or maybe after the first five minutes, let's say, some team has created some high probability chances and that team might be the underdog team. This was highly unexpected, I guess, since the ELO rating said that the other team would be at the overhand. So you can slightly update your beliefs there. I don't think it's like changing the needle or moving the needle all that much, given that it's just five minutes of information, but you can definitely update your beliefs throughout the game, given a chance it's created, expected possession value, as we just talked about, or momentum or something in between depending on the data you have available to you Mike I wanted to ask you given your involvement with Austin FC we know that there are obviously differences between Major League Soccer and European leagues. And some of those are, you know, things like salary caps, designated players, roster rules. Lack of relegation. Lack of, yeah, that's a big one. Does that actually make soccer analytics and MLS like a little bit cleaner? in some ways in the sense that like in the European leagues, the money is, again, trying to be diplomatic here, but it's very free flowing. There's a bit of rule stretching going on at times when it comes to salary restrictions and things like that. Like compare MLS analytics versus European analytics for us. So in European analytics, you have essentially recruitment and then first team analysis. In MLS, you have recruitment, first team analysis, but you have this third vector that I call portfolio management, right? This cap structure in the MLS is put in place with the intention of creating parity. And as you mentioned, it highly complicated The best way for you to understand it would be like me saying Tracy I going to give you million You can spend million on NVIDIA million on Walmart and million on a speculative biotech stock And so you have to think of each player from a relative value perspective based on where they slot in your cap structure. But has that worked? I mean, with MLS. So it's like, I understand you have this new league that's, you know, you don't want some really rich team to win all the time. And then, I don't know, only Miami wins and then fans lose interest in the rest of the country. I'm just I don't know what the actual I think my understanding is Austin in particular is a very big fan base. But has that worked in practice to sort of create an equal level of like fan affinity that's geographically distributed? Well, at Austin, we're only nine months into our project here, and we just had some turnover with our sporting department. And so I would say that we have yet to integrate and prove this portfolio management theory and the impact on success and points in the table. [40:00] As a market participant, when I read these rules, my brain immediately goes to the markets and portfolio allocation. OK, so we have to watch Austin FC as a test case for the portfolio management thesis in football. But wait, just to be clear, so this portfolio management thesis, which you obviously have a strong intuition for having traded volatility for a long time, this is the framework that you're bringing to your work in Austin. Yeah, correct. Every player has a designated slot. So a player that could come in as a DP could be terrible. But if he's going to be a designated player, but that same player, if he is going to be a senior minimum salaried player, could be in the top percentile of talent for that specific slot and then within the league itself you you know you have different roster construction strategies you can either have three designated players or you could opt for two designated players and four u22 players And the way the league works is they have a salary cap but it more of a salary cap charge So whilst Lionel Messi may be making over $20 million in salary, his salary cap charge as a designated player is going to be much lower than that. It could be $750,000. Wait, I don't understand that. Yeah, it's confusing. There's a salary cap charge based on these roster designations. So every slot has a dollar charge associated with it. So you have to work within that framework of what is the charge for each player and your finite amount of capital you're allowed to spend. So the designated players are the ones you're allowed to pay more. Got it. Because this is the legacy of like LA Galaxy getting David Beckham and wanting to pay him lots and lots and lots of money. This is helpful. Okay. So one of the criticisms of modern football, I guess, is that it's dominated by the wealthiest clubs. Like whoever has the most money can buy the best players certainly in Europe And so the big just kind of get bigger And I could certainly see an argument where if analytics becomes more important to actually playing the game then whoever has the most resources the most compute the most engineers I guess nowadays is going to have an edge here But on the other hand, we have had technology before that has a sort of democratizing effect. That was the Moneyball store. Yeah, we have open source models, all of that. And I think there have been some instances of the smaller clubs actually like using this technology to perform better. But which way are we going to go? Is it the big get bigger or maybe we see some smaller clubs level the playing field here? I hope it's the latter. Yeah, same. So you mentioned open source models actually build open source software to help these smaller clubs. I guess it's also helping the bigger clubs. but it allows them to build these graph neural nets and these expected possession value models and then also load this these tracking data this tracking data which has been a big task just in general because of the data structure and the data size and the software that i that i work on helps clubs any club basically get get started so i hope by doing that it will help the smaller clubs help data providers I guess provide better insights to level the playing fields But I'm not sure that it is working out necessarily because getting the knowledge, like we talked about before, actually distilling the knowledge from the data is still, I think, one of the bottlenecks. Oh, yeah. So this reminds me, I wanted to ask as well, who actually owns the data here? Where does the data come from? It depends. And I think some of it is a gray area. There are a lot of data providers. Some have licenses, some don't. Yeah, it's a big question mark in some instances. I'll tell you a story about when I first started building models for AFC Bournemouth back in the Premier League in 2016. I had no idea where I could find the data. And so I went on Upwork and I posted an ad and I just said, I need a developer who has worked with European football bettors. and a gentleman named Dmitry in Ukraine replied to me and he said, yeah, I've worked with many professional bettors. And I said, give me all the data that you can find. And so it was like, [45:00] very skunk works, but Dimitri was able to find a way for me to get access to all of the on-ball data across the world at the time to start building my models. What is the data? So it's like, okay, you find some data provider or Dimitri in Ukraine collects data. Is this numerical data? Is this a series of frames? When you say, okay, you need to go out and get the data. What form are you getting it? What does that mean? Like, what does it look like? So it's varied throughout the years, but the most prevalent generic data out there is on-ball data. And on-ball data, if you're just to put on your Excel hat, think about what it looks like in an Excel spreadsheet, has every single event tagged. So you have, it just goes down a series of events, pass, pass, pass, dribble, shot, goal, pass, pass, dribble, tackle. It has the event. It has the player or players involved. It has the XY coordinate on a pitch and it has the time And so when you have these raw data points you can conditionally put together a mosaic of what is happening on the pitch because you can measure the events, the speed, and the location. Tracking data is a bit more nuanced. I'll let yours touch on that. So you can still imagine an Excel spreadsheet, but I don't think your Excel spreadsheet would like it very much if you try to load in this data. It's basically a player identifier, a team identifier, and then X and Y coordinates for all players at 10 or 25 frames per second. So that means, I guess, 25 rows for a single frame. And we never really touch, let's say, the raw data in the sense that we don't get the pictures of the game and then try to figure out ourselves where the coordinates are or what the coordinates are. So there are a lot of data providers out there that either put cameras in the stadium or use the broadcast footage to extract this data. So they will have different models One of the models would be first identify where all the pitch markings are so they have a way to understand where all the players are relative to the pitch markings Then they know where all the players are and you can convert all of that into coordinates They know where the goals are obviously And then you'll get that in a single file for a single game. Some providers might give you one file per minute. They might give you one file per half. And then that's just the raw data with the identifiers in the coordinates. They might get an additional file that has all the metadata that says, this identifier belongs to this player, this identifier belongs to this team. if you're lucky and you're tracking data you get an identifier that says which team is actually on the ball because that's highly relevant but some sometimes it's not included and you have to figure it out yourself by calculating the distance to the ball for each player and then obviously you have skeletal data which is i guess 27 times more dense or maybe even more because you have 27 coordinates one for each body pose point so or body point so you might have one for your left shoulder for the tip of your nose for your left ear for your right ear for your right foot for your ankle and that gets into the millions and millions of data points so when you talked about in the introduction about these petabytes of data i assume it's gonna be mostly skeletal data because that data is incredibly rich how do players actually feel about all of this because you know like if people were watching me do my job and monitoring like my neck movements They are That the thing They are Tracy All right But no one no one modeling like what I doing with my hands or my feet at all hours of this particular recording I would have mixed feelings about it. Right. Like, do you have any color on how players actually feel about, I guess, the rise of statistical analysis in football? I think they find it useful. I think something that New York has worked on this specifically is is eyesight. What can they see and what they cannot see? And so when you look at the data and you think about opportunity cost decision making and you make a suboptimal decision, when you go and talk to the player, they might just simply tell you I couldn't see it. And then you move on to you move on to the next. So it's it's very complex. I find most players to embrace the data. There's curiosity around it, but, you know, they likewise know the limitations. You know, we started this talk about, oh, soccer is fluid. It's a beautiful game. It's an art. I totally agree. But like people actually did say this about chess 30 or 40 years ago. And there was actually some people who held out the belief computers will never be able to beat humans in chess. [50:00] because it is an art. And it almost seems hilarious that like this view held on for as long as it did. But it turns out that no chess is just a calculation problem. And when you have enough data and compute, you can solve the game kind of. Is soccer in the end like, is it just a series of lots and lots of discrete events that our eyes are not capable of? But at the end of the day, with sufficient compute and data collection? Is it just like chess and that it's just a lot of micro binary decisions that can all be summed up? And is this therefore how life is? When you work with this data as long as I have and with this tracking data specifically, in the beginning, it seems very overwhelming because it's just an infinite stream of coordinates. And so I struggled with that a little bit in the beginning. I was wondering what I should do with this. How are you going to model any of this? But I totally agree with you. You can discretize this. So you can discretize it into, let's say, very minor events where we use the on-ball event data. And if we align that with the positional tracking data, we might know every single moment where a player makes a pass. And then you might know the next moment where a player makes a reception So that could be discretized into one event that might last two and a half seconds or three seconds the next step would then be the player receives the ball they make an on ball action that also lasts two and a half seconds that would then be your next discretized event and then you have all these small events which are micro movements by players counter movements by defenders and if you go these let's say sequences one at a time you can still make aggregated metrics from this but using all the tracking data that you have at your disposal but it's actually still understandable for you and so you might say well this player made this many dribbles and it gained the team this much in terms of added value to scoring a goal and you can do the reverse for defenders where you can say well this defender was always close to the ball so he was hoping not concede a goal. And if you go back to the analysis part where you want your video analysts to look at this, you cannot they also do this, just discretized, discretizing it like this will help significantly. So I have one more question, which is it is obviously World Cup season which means it is also a sell side analyst publishing World Cup prediction notes and research season And in my experience they tend not to be very good Like often they will publish that England or the USA are going to win whatever World Cup Does the numero strategist predict Japan? That not to my knowledge, but, you know, they often get it wrong. If we think about statistical modeling data, I mean, the sell side firms, they should be pretty good at this. And yet, do you have a take on why they seem to struggle with soccer predictions every four years? Honestly, for them, I have no idea what data they're using, whether they're using an ELO model, whether Nomura has on-ball event data, tracking data. There's different ways that you can come up with these predictions. But I think, you know, I like to say stay in your lane. And I think sell-side analysts should stick to sell-side analyzing. Isn't that simply the age-old problem of if you have a good model, you wouldn't publish it? Yeah. You would just beat the bookies? Right. Yeah. There's often criticism of people who publish things for a living. Mike and yours, thank you so much for coming on OddLots. Learned a lot there. And I really appreciate your time. And enjoy the rest of the World Cup Thank you Thank you Tracy, I have to admit, I find it a little depressing that probably most things in life are probably just computation things. You know what I'm saying? It's like I want to think that like that there is something called art and beauty and intuition and something. It's probably just computers all the way down. binary events that can be chunked and analyzed by microchips oh you know the question i would have asked yeah but we ran out of time was the idea of like good art's law which is like once you have a measure like the measure yeah because you see this criticism of sports analytics which is like players start focusing on their stats coaches are focusing on the player stats and then they get the players with the good stats and then they just focus on improving their stats more but the stats don't necessarily translate into like wins all the time. Yeah. You know, I was thinking something that Mike said in the beginning, which is that like a particularly like an English Premier League team, there's multiple things they could be optimizing for. So they could be optimizing for profit. They could be optimizing for avoiding relegation. They could be optimizing for avoiding relegation. [55:00] optimizing for wins. Those are all distinct things. But you see this when a sport gets over-optimized. It didn't come up. A good example is like basketball. When I was younger, it was like the game was fun because there were lots of slam dunks. And then everyone realized that three-point attempts were not being taken enough. And so suddenly the game is dominated by three-pointers, which may be a better way to play, but it's not necessarily a more fun fan experience than watching a dunk so you think like okay could the game get better formally but it becomes less entertaining there's a lot of criticism i think that's a possibility because people are already talking about convergence and like actual football play style totally and you see this like you know there was a lot of criticism in the like people were very critical of how paraguay played right like play to just survive into penalty kicks then hope that the variance of the penalty kick period allows you to beat france but it's like no that's like the the game theory optimal or just the game optimal play if you considered to be the weaker team So it does feel like there all different things you know again going just to the core of the question stats like what are you solving for Solving for winning is very different from solving for profit, is very different from solving for a gambler. And there are different answers to each one. Yeah, you win, but no one's paying for it or happy about it. This is plausible. Although for now, people are paying crazy amounts of money still to go see a soccer game. All right, Shall we leave it there? Let's leave it there. This has been another episode of the Odd Thoughts podcast. I'm Tracy Alloway. You can follow me at Tracy Alloway. And I'm Joe Weisenthal. You can follow me at The Stalwart. Follow our producers, Carmen Rodriguez at Carmen Armand, Dashel Bennett at Dashbot, Kale Brooks at Kale Brooks, and Kevin Lozano at Kevin Lloyd Lozano. And for more Odd Thoughts content, go to Bloomberg.com slash Odd Thoughts where we have a daily newsletter and all of our episodes. And you can chat about all of these topics 24-7 in our Discord, discord.gg slash Odd Thoughts. 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