Game theory/ baseball question
Posted by Sean Fri
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Sean Fri
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Game theory/ baseball question
I was reading the following article in the Washington Post today:
In it, the columnist is talking about the advanced stats in baseball, and how they can tell us that a teams chances of winning a game can change drastically on certain plays, while other plays affect those chances hardly at all. The paragraph in question:
"But other plays are cataclysmic by comparison. Daniel Descalso’s single off the Washington Nationals’ Drew Storen in Game 5 of the 2012 National League Division Series increased the St. Louis Cardinals’ chances of winning from 13 percent to 50 percent.
In the legendary Game 6 of the 2011 World Series, four key plays from the ninth through the 11th innings changed the probability of a victory by 54, 47, 43 and 37 percent. “Winning” one such play matters enormously while the outcome of a dozen other plays combined may hardly matter at all."
But this doesn't seem right to me. This seems like someone complaining about losing on the river in a pot that was all-in pre flop. Sure, you were 95% on the river the way the first four cards were dealt, but if the money went in pre, it never matters what order the cards come in, you were always flipping to begin with. You can never really say you were a 95% favorite. To me, in a baseball game, the money goes in on the first pitch. The resulting sequence doesn't really 'change the odds' of your winning - your odds stay the same as they were when you started playing. Obviously it's not as purely mathematical as that given that human beings are involved, but isn't the concept of the odds of winning 'changing' like that pretty much game theory nonsense?
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Um... a poker hand isn't a good analogy for a baseball game imo given there aren't sufficient opportunities to influence the outcome (especially if we're talking AIPF at which point there is no chance to influence things).
A better way to look at this is (perhaps, if we must look through a poker lens), a HU freeze-out. Winning the "key plays" (big pots) can dramatically change the likelihood of you winning whereas the outcome of many of the "smaller plays" (tiny pots) doesn't matter nearly as much.
FWIW, I think the idea that "big plays" matter more than most of the others is as true as it is obvious. This is true for many sports (goals in soccer, wickets in cricket, break points in tennis etc.).
"baseball match"....made me cringe....it's a game
Agree with the rest of ^. The AIPF seems like a bad very bad analogy as there are many more actions, judgements and decisions still to be made.
Well, Tom, that's certainly true. But in situations like that, you have information before you decide to take the risk and put in money on every hand of the tourney. In this situation, you 'decide' to take the risk when the game starts. You can't get more than one win out of a game. You can't shovel money in after you've hit a grand slam. You can't risk your previous wins, nor can you get a shot at your opponents wins.
That's why I'm saying it's more like a pre-flop all-in hand. There, you have your hand (the team) which you think is stronger, and you have the stake (a win) that you hope to win. And then the cards gets dealt. Although there's a reliance on ability in sport, there's a lot of randomness too, and in baseball, even the very best teams at best a 60/40 favorite over the field. (A .600 winning percentage usually gets you close to the playoffs.) I'd say having the better team is akin to having the better hand, but even aces get cracked by randomness.
Having a particular event happen in a game, although obviously it's going to have a huge impact on the actual outcome, doesn't actually change the odds of one team's winning when the risk was taken, i.e. when the game started. Because you don't decide to restart the game after the event occurs. Or decide the game is going to be worth more wins.
Big plays matter in many sports, yes. But a five on the river matters a lot when it gives you a set to beat my pocket kings. Still, if the money all went in pre-flop, it doesn't really matter what order the events happened in - I was still a favorite to win.
As for your apparent point about the odds at the start being all that matters, I don't agree. Indeed, this is an argument which suffers when taken to its logical conclusion: no part of any journey matters. At the start of the season, team A are 5% to win the World Series. No game matters. To make this logically absurd: when they are born, person Y has a 0.001% chance of becoming President of the United States, their personal, academic, and professional lives don't matter - they graduated Harvard Law summa cum laude and became Governor of Pennsylvania, doesn't matter, they were only 0.001% when they came into this world kicking and screaming. I fail to see the value in this observation.
Either your point is that, when a team is 3-0 up in the World Series, well, they were 5% at the start of the season which seems kinda irrelevant, or you are so pessimistic about the human condition that you don't believe we can influence events as they pass, thus making our actions somewhat pointless.
If your point is that we should only focus on the odds when we start, I disagree because this shields us from taking responsibility for our actions. Unlike in an all-in, where I have NO CONTROL over the outcome, in most other scenarios, including a baseball game, I can have an influence which makes them inherently different.
Indeed, in my HU match analogy, I am x% at the beginning depending on my opponent, but this % changes as the match progresses and I am capable of influencing the result to some degree through the quality of my play same as in a baseball game.
I'm honestly expending a lot of energy trying to find the kindest way to reply to this, but rhetorical underhandedness really steams me. The reductio ad absurdum isn't relevant, because not every baby born in the US is automatically entered into a contest to be President, so his chances at birth don't matter. Every baseball team that plays a game though, has to finish it, and the value of victory is decided at the start: one win. So I fail to see the value of your failing to see the value in an observation that I never made.
Then the false choice of two other things I never said. The first part I don't even understand. The second is pointless. I honestly don't see how you got out of my discussion that I think we can't influence events or that our actions are pointless. Please show me where I said that.
What I was attempting to ask, and forgive me if I failed to ask it clearly enough, is - Isn't it pointless to ascertain a chance of winning at a point where there is no opportunity to decide whether or not you want to play? It's a meaningless stat. To everyone, including, I suppose gamblers, unless someone is stupid enough to book action in the middle of a game.
Once the game starts, it has to be completed. Yeah, the players influence it - that's why you hired them. You tried to get an edge so that your team has (have) the best chance of winning before the game begins and random events start to introduce themselves. (They're not NOT controlling the outcome, but the outfielder I hired because he catches 99.9% of fly balls might find himself in a situation with the sun in his eyes today. I still hired the right outfielder.)
If a team comes back to win after being down 7 runs, isn't it the same as a team jumping out to an 8 run lead and holding on for a one run victory? Who cares when this stuff happens? Yes, some weak willed players might be affected by 'momentum' but almost all of them were weeded out before they got to the major leagues.
I'm just asking - once you've started playing the game - isn't it just as stupid to check in on a team's 'chance of winning' at any particular time as it is to worry about a street by street rollout on an AI pot?
(And, as already stated if you bothered to read it, I understand that it's a little more complicated since humans are involved. But honestly, not much.)
1) As our likelihood of winning or losing alters, so too our strategy could change. I don't know baseball as well as most sports (being British), but I do know that many sports require substantial tactical alterations as our chances of winning increase or decrease (bringing on a defender in soccer to protect a lead, pulling the goalie in ice hockey when behind late etc.). Having a rigorous, quantifiable way of measuring this can increase the quality of the decisions we make.
2) Post-game analysis and tactical decisions going forwards can be hugely aided by this information. Understanding the value of a certain play in terms of fractions of games won (that play increased us form 55 to 70% to win, thus earning us 0.15 games) will allow players and coaches to better identify not only which plays are best to make, but also which ones to practice and which to protect against.
3) People betting sports gain information from this statistic. You say, "unless someone is stupid enough to book action in the middle of a game," but in-play betting is currently a huge part of the sports market (at least in England it is - for example, during our televised games, numerous adverts run at half-time with updated odds). So this certainly is of use to gamblers.
4) Entertainment value. Many statistics in sport exist in part to aid the understanding and enjoyment of the audience. Whilst an experienced expert may intuitively know the importance of any given moment, this allows the less knowledgeable spectator to accurately appreciate the importance certain actions. Given increased enjoyment likely boosts viewing figures, this cannot help but benefit the sports providing those statistics (see for example the vast increase in statistics being shown in soccer, such as shot-conversion and passing accuracy, born in part from the public's desire to better understand the styles of top sides such as Barcelona and Bayern Munich).
As for your dislike of my rhetorical style, I understand your complaint re: the Presidency argument, but the season of baseball remains true: a team is entered at the beginning of the season with the desire to win the title. They have a certain% chance of winning and, although this alters throughout the year, it began at some undefined figure which changes as games pass. How this changes is, as with the likelihood of a team winning a game, of value for various reasons. The significance of continued opportunities to influence the outcome is what makes both the game and the season dramatically different to the all-in hand.
"I'm just asking - once you've started playing the game - isn't it just as stupid to check in on a team's 'chance of winning' at any particular time as it is to worry about a street by street rollout on an AI pot? "
if you really feel this way, then I will happily set up bets with you on games but we bet on the outcome at various points of the game.
but yeah, like Tom said, if you dont know how the actions in the game have effected the potential outcome, you cant make the most +EV decisions going forward. (which you cant do once AI, because you no longer have the chance to make strategic decisions. Which is why toms HU sng is a much better analogy)
This is much more cogent and reasonable reply, so thanks for taking the time. You often do, and that's part of why I respect you. You haven't convinced me that the stat is particularly useful, except in one sense, though. Maybe because you're misreading what the stat actually is. Quickly, point by point:
1) Yes, and it does alter strategy, often. But there's already an easy rough stat that tells us our likelihood of winning: the score. Most managers have been in the game long enough to have an intuitive understanding of their chances of winning one run, two run or blowout games in late innings, and having an actual number stated in terms of percentages likely wouldn't alter their understanding of the situation, nor their actions in them.
2) Sabermetrics are indeed valuable in choosing players and/ or choosing pre-game strategies for those players, but THIS statistic doesn't tell you how your chance of winning or losing increased or decreased based on a DECISION you made. It tells you how that chance increased or decreased following a RESULT that occurred. In the example from the article, Descarlo's single off of Storen increased the chances of winning from 13 to 50 percent, but the decision the manager made wasn't for him to hit a single. It can't be. The decision was to send him up to bat, and that results in a single about 25% of the time. The event that occurred - an actual single - increased the chances of winning, yes, but only because of the result. This is why I relate it to watching the cards roll out and change winning percentages in an all-in hand after you already can't take back the decision. (The more useful stats in this situation would be what Descalo's late inning batting average against right handed pitching is, and his history with Storen. Knowing that you only have 13% chance of winning in this situation late in a game and trailing is as obvious as it is useless. You're still sending a guy up hoping he gets a hit, and you use stats to figure out who that guy on your bench is. This stat isn't one of them. This stat just tells you that if you're losing late in the game, you'll likely lose the game. But if you string together some hits, you have a better chance of winning.)
3) Yes. Granted, though I think this type of betting occurs a lot less with baseball than it does in other sports. I think it's more useful for the oddsmakers to set the correct line for the house, but again - the score of the game does that roughly and quickly, and I would suppose fairly accurately for people who have been around the game enough. So, it WOULD be useful if you could use a model to generate a number quickly enough to set a line before a new event changed the situation, but I don't think it happens often. Also, the article wasn't talking about betting.
4) Yes, just like the numbers going up and down in all-in pots in televised poker! Which was what brought to mind the analogy I started with, while admitting it was an imperfect analogy. And again, the article was concerned mostly about in-game strategy, not the fans. Which is why I related the two and asked the question in the first place: this is an entertaining stat, but not one that's of any particular use to a manager in a game.
And in re: the season thing - you're certainly not wrong, but with baseball, you're not as right as you think. Baseball guys use a LOT of useful stats to choose a team and select a strategy, then send them out and hope they stay healthy. There are trades, there are injuries, there are promotions and demotions. People's cats die and it might affect their play. But the die are cast to a large extent when the season starts, and you have to weather the variance. But again - that was an aside. The article was talking about single games. Actually, it was talking about instant replay, and how important big plays are, so you want to make sure the referees don't fuck up. (Astounding! Big plays are... bigger... than little plays! Who knew? SO glad we have statistical proof!)
MEA CULPA (for the tl;dr crowd):
To be honest, and as critical of myself as I was of you, I could very easily avoided most of this by being hyper specific and pointing out from the beginning that a 'play,' in the way the columnist was using it, was actually 'the results of a play.' In other words, not so much the decision as the thing that ended up happening. This information doesn't tell us how many EVgames we gain when we tell a good runner to steal with two outs and a slugger at the plate. This stat tells us merely that our chances of winning go up when that gambit works. But we knew that already. I wasn't suggesting that stats are useless (I feel the opposite.) I was just asking, isn't THIS stat a bullshit stat in-game?
And to Toothpaste: Yeah, ok, we can use his analogy, it doesn't change the question 'isn't this stat game theoretical nonsense?' (Maybe should have said 'useless' or 'redundant, since we keep score and we all know what that means') My question wasn't 'What's the best analogy we can use to point out this is nonsense?'
I do think there are similarities, though the HUSNG might be a level deeper. If you're a stronger player, you can still get beat by randomness, but you can't change the stake once you start. Yes, you can tell yourself that you have more control - and you DO - over how things go, but you're still subject to variance. The fact that you have control over how things go is, in fact, what GAVE you the edge to start. You're just zooming out a level, saying you were 75-25 to win the match based on skill, then you had to play the hands. That's not a ton different from saying you were 75% pre, then the cards got dealt. But either way - doesn't matter. I'm just saying this is a results stat, not a decision stat.
Hope no one got bent out of shape. Next time I make a non-poker post I'll work even harder to make sure my meaning is clear so that we don't waste our time again. Love to all.
maybe a little off topic but - if you like baseball and stats your should read Trading Bases by Peta
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