I'm writing this because I think it's an issue that underlies a lot of the complaints we get about game balance-- the most recent log about a Legacy being one of many things that reminds me of it. Some of this is obvious to most people, but I know from reading that I'm talking about some common mistakes in places.

There was a study published about 25 years ago by Daniel Kahneman (who won the Economics Nobel in 2002 for this and related studies) about what basketball fans call the "hot hand". (Logicians tend to call it the "Gambler's Fallacy".) I ran across a layman's version of it in a Steven Jay Gould essay about Joe DiMaggio a while back, and it's stuck with me. (link)

Short version: You usually cannot watch more than 10 minutes of broadcast basketball without an announcer crowing about what player has the "hot hand". You see a guy make 4 shots in a row, and everyone's trying to force that guy the ball, the crowd boos if the coach takes him out, etc. Quoting Gould here: "Everybody knows about 'hot hands'. The only problem is that no such phenomenon exists." Basically, the chance Dwyane Wade (or whoever) will hit a shot is statistically unrelated to the chance they hit their previous shot. This isn't merely a textbook theory-- some sad-ass interns got stuck crunching every shot by every player for season after season, and that's what the numbers say. Similar studies have shown in baseball that there is either no such thing as a "clutch hitter", or else the effect is so small as to be unmeasurable. (I've seen estimates that "clutchness" could impact a player's batting average by no more than .002 or .003, which is insignificant in terms of a manager deciding who to put in, compared to many other factors. See this for more.)

Now, most people can process why CF's code (generating near-random series of ones and zeros) should be more random than hitting a basketball shot. The code isn't "pumped up by the crowd", "gaining confidence", "taking advantage of a rattled defender", or whatever other rationalization people are using to explain a favorable streak. Yet people often interpret logs as if the unusual is commonplace, or else as if they are studies rather than anecdotes.

What's interesting is why most people (myself included) have to consciously fight the tempting idea of a "hot hand", and it's also why the CF forums make me think of this topic so much:

A) Selective memory: Streaks and extremes stand out: You're not so likely to remember the time when you tried 10 dirt kicks and 5 of them landed, even though that may have happened a lot. You're much more likely to remember the time you missed 10 in a row, and you accused Nepenthe of setting your "Dirt Kick luck to zero" or something else Hasturian. Teleport is the best example of this-- even after the changes, your chance of dying to a Teleport is fairly low, yet most people would guess higher, because they remember the times it got them killed better than the times it landed them on some random road.

B) Memetics: People prefer talking about the unusual: The above is amplified by the circulation of logs-- comparatively rare streaks seem more common because people are more likely to post fights where something really unusual happened. Also, these logs generate more discussion. The simplest example of this is people posting logs where they improved on a skill 3 times in a row or whatever. (Seeing enough of these logs might make you think the RNG is streaky like that. It's not-- see below also.) Another example is: If you went only by logs, you'd assume that most CF fights end in a PC death. The reverse is true-- the loser usually escapes, and defense has the upper hand.

C) Perspective: It's only a streak to you: Going back to the log of 3 skill improvements in a row, while that may look like a streak to you, it's not a streak as far as the RNG is concerned. The RNG has probably output tens of thousands of random numbers in between those skill improvements-- while you were waiting for that combat round, it's been taking care of all the swings and misses for you and everyone else in the world, and each swing generates tens or hundreds of accesses to the RNG. So even if the RNG is imperfect (ours was chosen more for speed than for pure randomness), any actual (local) streakiness has long since washed out. This perspective can show up in many ways, thanks to our brains' ability to cluster information-- witness the people that swear that you get more skill improvements right after a death. (The improvement code has no idea if you're a ghost.)

D) Internet Tough Guy Syndrome: A lot of anecdotal information gets amplified, intentionally or not, thanks to what we'll charitably call the "artistic license" of making a better story, or advocating a specific position. If someone thinks X is overpowered (correct or not), they'll probably only post the log where X worked really well. Not everyone can test everything, so most people rely on word of mouth, and the voice of one loud person too often ends up as "what everyone says".

Anyway, the next time you're claiming that Skill X sucks (or is overpowered), make sure you've guarded against the above. Check it yourself if you can. Make sure you've seen something a bunch of times. If your evidence is on the shaky side, it's very rare that something is so broken that it can't wait another day or week, especially for an ability that's been in for a long time already. Take the long view.

valguarnera@carrionfields.com

People see a skill failing 10 times in a row and say the RNG is broken, but the thing is, the nature of randomness is such that streaks like this must occur from time to time. If they are NOT occuring THEN the rng is broken.

It's funny how selective people's memory is sometimes. One time when I played on PokerStars a guy there was trying to convince me that card dealing there was screwed up in such a way that if two people went all in pre-flop and both had a pair, the one with the lower pair had a higher chance of winning =)

I've already commented on it, but I've come across this before. It is truly a serious mind #### until you can wrap your head around it. So I'm going to *attempt* an extremely condensed version for those people who aren't getting what it is saying, or are disagreeing with the research based on personal experience.

Basically here's the deal (as I understand it). If you are flipping a coin, you know that 50% of the time it's going to come up heads. That is if you keep flipping forever you'll have and equal number of heads and an equal number of tails results. This is intuitive.

However, if you flip the coin the first three times and come up with heads all three times, you *might* be inclined to believe that you are affecting the outcome somehow, or that this coin is more likely to come up heads. This is false and I think we can all agree on that.

If you are good with statistics you can predict just how likely any given streak is. In a 50/50 toss up, a streak of 5 might have a likelyhood of 1 in 100. This isn't exactly far fetched. It's unlikely, but given enough tries, it'll happen 1 in 100 times.

Now lets pretend like instead of a coin, it's a 50% field goal shooter. He makes 5 consecutive shots. You say, "He's got a hot hand tonight." However, just like the coin he does this with a specific regularity, in fact 1 in 100 times he makes 5 consecutive shots. *IF* the "hot hand" actually existed, then he'd have more 5 consecutive shot streaks than the statistics predict (he's a streaky player). But he doesn't. Not over his season, or career, or anything. Not only has he not done it, no one has. They've looked at ass loads of data, searching for just such an occurance, and why not? Everyone knows it exists. Our player can feel it when he plays, but the fact of the matter is that regardless of how he feels, his streaks happen with exactly the frequency of that coin flip.

Now, his streak might come at an opportune time, so it is remembered. That means he's clutch, right? No, because he isn't having those streaks in "clutch" situations any more than he should. He's having them at essentially random intervals, and we are only remembering those clutch streaks, but not all the other times. It really is that simple, but the unintuitiveness is mind boggling.

What if our player is only a 40% shooter next year? Well then next year he won't have as many 5 hit streaks. If over his carreer he's 45% then he won't have quite a 1 in 100 rate of 5 hit streaks. You might think that he would, I mean what about that season when he was shooting lights out at 60% and seems like he couldn't miss in the playoffs? Sorry no, he's a 45% career shooter and his 5 hit streaks occur at the below 1 in 100 rate. For that season they are higher, but overall they are as predicted.

But what about the other factors? Apparently they all cancel out, just like a coin flip, it is totally predictable. It's that simple, but it's very difficult to believe.

I believe, and agree with you, that there exists an extreme Selective Memory Syndrome when it comes to posting and reading logs.

I'll forego my many examples I have of such because I think you covered it very well. To concur, I've got hundreds of logs of my own sweet victories and ill begot defeats on my hard drive, but probably four of when the dude got away. Check.

However, being the sports fan that I am, I can't help but argue with the "hot hand" thang being non-existant in sports.

You quote and comment:
>>"Everybody knows about 'hot hands'. The only problem is that no such phenomenon exists." Basically, the chance Dwyane Wade (or whoever) will hit a shot is statistically unrelated to the chance they hit their previous shot.

Ok, you are correctly stating a valid argument, but relating it misleadingly to the overall argument (in my opinion) based on an irrelevant premise. Sure, one shot has no bearing on the next shot-- in and of itself. But, what about the factors contributing to the streakiness of the player? Is he rested, not injured, and generally prepared for the defense layed out? Are his teammates setting picks, running his favorite plays, wearing down their defense? I've watched enough (and played) basketball to know that there ARE certain times when the "streakiness" can be embraced. The caveat here, is that this streakiness could probably be attributed to any number of real factors, and not to the outcome of the prior shot- as the premise you put forth. How did Kobe score 81 that one game? He was predominately manned up against an inadequate defender, was in good health, and his teammates and him wanted him to keep making the shots. I could break that game down six ways from Sunday, and probably convince you that the dude was indeed "hot" in his shooting, but I won't now. Let's keep in mind overall shot percentages might not be as impressive as they otherwise would because of some of the absolute ridiculous attempts he was taking, okay, everyone? (though 81 points at a 60% clip ain't poor).

Now, clutch hitting? Sheesh. There are hitters that are streaky. I won't even bust any stats here, but I've seen enough and played enough to know that it's true. Sometimes you feel it all through yourself that you can hit the thing. You know it. Sometimes you can't see the ball for the life of you. Usually in sequential days/games, for whatever reason. Your stance is right, your in tip top shape, your vision is better because you ate so many carrots, I don't know why- a combination of mental/physical factors. Anyways, my dogs are hungry and bothering me and I am digressing, so I'll discontinue myself....

Keep in mind all that you can prove, disprove almost anything with statistics. It's the scope of the stats that matters. The scope.

Again, though, I like the argument man. It's easy for us to counter with such nice ammo . Let's not just argue the stats for global warming and I'm cool.

Ok, you are correctly stating a valid argument, but relating it misleadingly to the overall argument (in my opinion) based on an irrelevant premise. Sure, one shot has no bearing on the next shot-- in and of itself. But, what about the factors contributing to the streakiness of the player? Is he rested, not injured, and generally prepared for the defense layed out? Are his teammates setting picks, running his favorite plays, wearing down their defense? I've watched enough (and played) basketball to know that there ARE certain times when the "streakiness" can be embraced.

I know I feel it when I play. It's very intuitive, yet completely wrong. That's why the field is interesting to me.

See my response to Dwoggurd for more detail, but the basic point is that I'm not proposing a hypothetical about what I think would happen. I'm explaining what rigorous studies have observed when objectively looking at what happens during professional basketball games.

Now, clutch hitting? Sheesh. There are hitters that are streaky. I won't even bust any stats here, but I've seen enough and played enough to know that it's true.

If you can bust those stats, you can resolve one of the thornier issues among baseball stathead geeks. Basically, the argument is about whether "clutch hitting" exists at all, with the two sides settling somewhere between "utterly undetectable" and "very minor".

Again, though, I like the argument man. It's easy for us to counter with such nice ammo . Let's not just argue the stats for global warming and I'm cool.

I guess I didn't figure that a published, peer-reviewed economist's study counts as "nice ammo".

Feel free to bring global warming to the off-topic board. I know a thing or two about it.

Keep in mind all that you can prove, disprove almost anything with statistics.

Which is why reputable publications use a peer-review process to evaluate the validity of methods.

valguarnera@carrionfields.com

>I know I feel it when I play. It's very intuitive, yet
>completely wrong. That's why the field is interesting to me.

I'd have to look at the research, but I can think of a number of mundane reasons why players might be more "streaky" than random chance would dictate. For instance, if a player believes he's on a cold streak then his performance may decrease purely on the basis of that (incorrect) belief. Sort of like a psychosomatic illness- it happens because he believes it's already happening. If a player believes he's on a hot streak, that belief might cause him to modify his style of play (regardless of the sport) in such a way that he becomes more effective.

Think of it this way. Your point is based on the idea that a player has a fixed skill level. Maybe he's a 0.333 hitter. Every time he steps up to the plate there's a 1/3 chance he'll get a hit. Given that, over the course of a season you'd expect there to be any number of hot and cold streaks just based on chance. If the guy happens to hit 0.800 over a two-week span, he's still just an 0.333 hitter for the next game.

Where this breaks down is when you consider that the player's attitude may make him more or less than an 0.333 hitter at any point in time. Maybe the belief that he's on a cold streak modifies his technique, his concentration, you name it, such that he becomes a 0.200 hitter. Maybe when he's on a hot streak, pitchers become intimidated and pitch to him differently so that he gets better balls to hit. I'm just not sure it's accurate to treat human beings as if they were perfectly random variables.

I tend to agree. A human being is not a pair of dice. If someone comes back from injuries, for instance, he may play poorly. If someone on the other hand is having a great year, they may have improved confidence or simply hit their stride and play better. The thing is, what is this study determining as a cluster? A single game or a single season? Because its not uncommon at all to have great seasons followed by poor seasons. I don't think its a case of 'hot hands', but human beings are affected by a large number of variables so its only natural to assume the stats they produce are non-random.

>and play better. The thing is, what is this study determining
>as a cluster? A single game or a single season?

My impression was that it's shot by shot. So obviously a player might do better from one season to another. But one shot is no more or less likely to hit than the one immediately preceeding it, statistically. Obviously in the real world something or other may affect a shot. A minor hand injury, for example.

>I don't think its a case of 'hot hands', but human
>beings are affected by a large number of variables so its only
>natural to assume the stats they produce are non-random.

Interestingly, if you add enough variables the system becomes chaotic and the results become as unpredictable as the weather. It's not quite accurate to say that it's random (I don't think... could be wrong), but chaos and randomness are often indistinguishable.

My impression was that it's shot by shot. So obviously a player might do better from one season to another. But one shot is no more or less likely to hit than the one immediately preceeding it, statistically. Obviously in the real world something or other may affect a shot. A minor hand injury, for example.

Yup. It's shot by shot, but for large sample sizes. As a fan or coach, the take-home message is that whatever is going on, you can safely treat the "hot hand" as irrelevant or absent. Give the ball to the guy who looks open, not the guy who hit the last shot. (The broader take-home is that your intuition is often wrong.)

Interestingly, if you add enough variables the system becomes chaotic and the results become as unpredictable as the weather. It's not quite accurate to say that it's random (I don't think... could be wrong), but chaos and randomness are often indistinguishable.

This is probably how I'd try to explain the observations. I mean, a coin flip isn't truly random either. What side lands face up is affected by the imparted torque, the air density, the precise angle of contact between the coin and the surface it hits, etc. Precisely-calibrated coin flippers operated in a vacuum could, with sufficient engineering, (nearly) always toss a heads. But as far as the coin flips you've done, it's random and uncorrelated, just like how you should treat CF's RNG.

valguarnera@carrionfields.com

Ok, I misunderstood what you were saying then. Thanks for the clarification.

I'd have to look at the research, but I can think of a number of mundane reasons why players might be more "streaky" than random chance would dictate.

Also tested-- Gould covers this in great detail. Players generate the expected normal distribution of results for a random variable with success rate X (X being shooting percentage or batting average in the studies I've read). Despite all the real variables you discuss, they perform as if each attempt is statistically independent. They've also been unable to identify individuals who perform outside the bounds of probability during a large enough number of attempts-- it isn't that equal numbers of "hot" and "reverse-hot" (players who tend to miss after a hit) exist.

A "streaky" player would be easy to measure-- the width of the distribution would change, the frequency of runs of length X would be higher than anticipated, etc. Doesn't happen. I'd have totally backed your ideas before seeing the results, but we'd both be wrong.

A "clutch" player would also be easy to identify. They'd pass statistical tests showing a greater propensity for success in pressure situations. There's literally dozens of writeups on this available on the web, and based on the definition of "clutch" they either:

1) Can't find anyone who passes certain tests.
2) Can find a few people, but the effect is so small as to be negligible.
3) Find a few people, but different people show up from test to test, suggesting low reliability.

They all seem to agree that it's not a real important factor at the professional levels.

Basically, as a fan or coach, you should:

1) Don't force the ball to the "hot hand". Use your usual strategy regardless of recent shooting success.

2) Don't allow reputations like "clutch hitter" to influence who you sign or for how much.

Michael Lewis's Moneyball and The Blind Side have some great discussions of how professionals (notably the A's GM, Billy Beane) have been using these sorts of tests and metrics to make decisions. Both are great reads. If you've suddenly noticed an interest in OBP during baseball coverage, Beane is why.

valguarnera@carrionfields.com

Alright, I've had some free time to look into stats on "clutchiness". And, I have to humbly agree with you. For the most part, clutchiness seems to exist only in our minds.

Specifically, I looked at stats of RISP, RISP2 (avg w/ runners in scoring position, and avg w/ runners in scoring position and two outs, respectively) for hitters I thought were exceptional "clutch hitters". Although I did find a few statistics to support my belief that clutch hitting exists, I became tired and worn from finding waffling counter examples for the same player. I.e., a player who has a +.25% increase in RISP one year, will have a -.25% RISP the next. Et cetera. Quite frustrating, I've got to say, as I found no silver bullet which I thought would present itself piece o' cake. Ugh.

However, I did come across an interesting set of team statistics. Which at first glance might be a start to back the elusive clutch factor.

Again, mainly I'm looking at the difference between None on/out, and Scoring Posn, ScPos/2 Out data. The average league data represents little "clutchiness", the Yankees represent a negative "clutchiness" (who needs it with such a stacked lineup), and the Angels representing an extreme clutchiness:

Total stats for the all 2005 teams:

               AVG   AB   R    H  2B 3B  HR RBI  SB  CS TBB   SO  OBP  SLG
Total         .268 5586                                      983 .330 .424
None on/out   .272 1396 ---  380  73  8  47  47   0   0 100  230 .326 .437
Scoring Posn  .272 1485 ---  404  78  8  46 582  23   5 179  269 .347 .428
ScPos/2 Out   .248  644 ---  160  33  3  19 213   9   1  84  123 .342 .398
Close & Late  .254  867 ---  220  40  4  22 112  14   4  86  175 .325 .385

And here are the numbers from a good offensive team, the 2005 Yankees:

               AVG   AB   R    H  2B 3B  HR RBI  SB  CS TBB   SO  OBP  SLG
Total         .276 5624 886 1552 259 16 229 847  85  27 637  989 .355 .450
None on/out   .288 1356 ---  390  66  5  57  57   0   0 134  230 .359 .470
Scoring Posn  .272 1490 ---  406  63  6  67 623  31   8 203  288 .360 .458
ScPos/2 Out   .233  679 ---  158  24  2  23 216  10   1 107  138 .344 .376
Close & Late  .260  734 ---  191  35  3  25 121  10   0 107  142 .357 .418

2005 ANGELS:

               AVG   AB   R    H  2B 3B  HR RBI  SB  CS TBB   SO  OBP  SLG
Total         .270 5624 761 1520 278 30 147 726 161  57 447  848 .325 .409
None on/out   .263 1402 ---  369  74  6  41  41   0   0  97  201 .315 .412
Scoring Posn  .296 1400 ---  414  70  7  37 566  39  13 159  198 .361 .435
ScPos/2 Out   .279  663 ---  185  35  3  14 232  25   5  85  103 .364 .404
Close & Late  .270  923 ---  249  36  3  22 115  30   3  88  154 .336 .387

>> Ok, you are correctly stating a valid argument, but relating it misleadingly to the overall argument (in my opinion) based on an irrelevant premise. Sure, one shot has no bearing on the next shot-- in and of itself. But, what about the factors contributing to the streakiness of the player? Is he rested, not injured, and generally prepared for the defense layed out? Are his teammates setting picks, running his favorite plays, wearing down their defense? I've watched enough (and played) basketball to know that there ARE certain times when the "streakiness" can be embraced.

I know I feel it when I play. It's very intuitive, yet completely wrong. That's why the field is interesting to me.

Really, my point was not to confuse "streakiness" with what is going on in a situation to cause an observed streak. Let's not even consider previous successes/failures counting towards our successive attempts, but look at the situation affecting the outcome(s). Are they favorable? Then you're probably going to see a positive affect on our "streak". This is different from looking at the shots as a sequence of unrelated events, but rather as a product of an external, reproducible factor(s). That is all.

If you can bust those stats, you can resolve one of the thornier issues among baseball stathead geeks. Basically, the argument is about whether "clutch hitting" exists at all, with the two sides settling somewhere between "utterly undetectable" and "very minor".

"if I want to know one hitter's batting average on grass fields, during the day, with a runner on second and 1 out, I can get it." (sorry from other post)

No stat-busting now, sorry, but... yes, and I'd define a "clutch" hitter as someone who's better at hitting in this situation than the average, or even decent hitter in similar situations. There's some players who excel at this. Due to hand eye coordination and the ability to know where to hit the ball where the defense isn't for that particular situation. There are hitters who are better at this than others. Usually you'd bat them in the third or fifth place if you were even a mediocre manager. Better managers have a greater tendancy toward figuring this out on a day-to-day basis than others. 2002 Angels. 'Nuff said* . Someone such as Barry Bonds may or may not be this sort of hitter but the point is moot when you have other skills, namely the ability to hit the ball over the fence or off the first baseman's skull if he has to. Heehee.

In any case, this sort of statistic is still moot to our point; specifically, in that "streakiness" is not necessarily tied to "clutchiness". A reasonable manager would realize that his hitter is hitting well, or not, and choose the correct hitter accordingly. Sure you can take a stat over a given period and claim it as an absolute, but really, there's an integral summation of specific at bats for which a hitter is more or less effective. Averaged out over the entire scope you get your statistic. But real people will see the streaks involved, and I'd argue this is why good managers are good managers.

I guess I didn't figure that a published, peer-reviewed economist's study counts as "nice ammo".

Yep, that was a bad choice of words by me. I suppose I should have used the term "cool points to discuss". Because they are .

Feel free to bring global warming to the off-topic board. I know a thing or two about it.

Maybe I will. I, on the other hand, don't know too much about it. But would REALLY enjoy hearing intelligent discussion without any pulling of heartstrings or discussion of dead dolphins and such. Which is what my virgin ears are getting this year about the subject.. for whatever reason.

* The 2002 Angels had arguably the most mediocre team ever, but were uncanny in having the right people hitting in the right places at the right times. Really fun stuff to watch. I am redeemed from twenty something years of frustration even though I have little hopes for them this next.

P.S. Apologies for this not being even slightly related to gameplay. Your first post on the topic was spot on, well put, and relavent-- and this is not. Please do other importatnt things than respond to this guy's post, Valg.

I'm writing this because I think it's an issue that underlies
a lot of the complaints we get about game balance-- the most
recent log about a Legacy being one of many things that
reminds me of it. Some of this is obvious to most people, but
I know from reading that I'm talking about some common
mistakes in places.

I haven't played for a while, but looking at the said log I believe people call that legacy overpowered not because it happens to work in this log but because it does too many nasty things to an opponent at once.
If a such thing is possible it may be a balance issue, though not necessary it actually is.


There was a study published about 25 years ago by Daniel
Kahneman (who won the Economics Nobel in 2002 for this and
related studies) about what basketball fans call the "hot
hand". (Logicians tend to call it the "Gambler's Fallacy".)
I ran across a layman's version of it in a Steven Jay Gould
essay about Joe DiMaggio a while back, and it's stuck with me.
(link)

Short version: You usually cannot watch more than 10 minutes
of broadcast basketball without an announcer crowing about
what player has the "hot hand". You see a guy make 4 shots in
a row, and everyone's trying to force that guy the ball, the
crowd boos if the coach takes him out, etc. Quoting Gould
here: "Everybody knows about 'hot hands'. The only problem is
that no such phenomenon exists." Basically, the chance
Dwyane Wade (or whoever) will hit a shot is statistically
unrelated to the chance they hit their previous shot. This
isn't merely a textbook theory-- some sad-ass interns got
stuck crunching every shot by every player for season after
season, and that's what the numbers say.

But, nevertheless, "hot hand" thing exists.
Regardless of what some sad-ass intern may try to prove.
And it is not necessary mystic (though, who knows, maybe mystic helps). Morale bonus, confidence, feeling an opponent's weakness, etc, greatly raises the hit rate.
Basketball shot is not a dice throw.
From my own experience I can tell, for example, that in european football (in a certain county it's called soccer) there are days when almost every hit ends with a goal and there are days when you miss all the time. Many experienced players feel such days before they actually know the final score.

There are such "mystic" things in chess team tournaments as well.
When one of team members gets a bad position or loses a game, the rest of his team get often into troubles as well.
Thus, there is "a rule" among experienced chess team players. If you have bad position, never surrender. Sit, walk, do nothing, don't move pieces, waste your time but don't resign as long as possible.

Yet people often interpret logs as if the unusual is commonplace, or else as if
they are studies rather than anecdotes.

This part made me chuckle.
They don't do that often, you just tend to remember the cases when they actually do.

your chance of dying to a Teleport is fairly
low, yet most people would guess higher, because they remember
the times it got them killed better than the times it landed
them on some random road.

Still, you end up in Whitecloaks way to often.
I don't know what is the reason, number of teleport rooms in that area or evil Nepenthe's code.
But I certainly find myself in Whitecloaks after a teleport more often than in any other area, not that I die there too often. And there are areas where I landed maybe once in several years.

But, nevertheless, "hot hand" thing exists.
Regardless of what some sad-ass intern may try to prove.
And it is not necessary mystic (though, who knows, maybe mystic helps). Morale bonus, confidence, feeling an opponent's weakness, etc, greatly raises the hit rate.
Basketball shot is not a dice throw.

You might expect it to (I would), but people have spent a lot of time looking for it in multiple sports and it doesn't seem to show up. Basketball and baseball are easy examples because they're so easily quantified and extensively documented-- if I want to know one hitter's batting average on grass fields, during the day, with a runner on second and 1 out, I can get it. A few possibilities:

1) The "hot hand" exists, but it's miniscule. Still, if it can't be provably measured with multiple seasons of data, it's not really worth talking about.

2) It exists, but is canceled by everything else going on. If you have the "hot hand", maybe you feel confident, but the other team is also paying more attention to you. Maybe you feel an opponent's weakness, but your opponent is now conscious of it and protects it.

3) Maybe confidence is actually a neutral factor-- you don't hesitate, but you also underestimate your opponent.

From my own experience I can tell, for example, that in european football (in a certain county it's called soccer) there are days when almost every hit ends with a goal and there are days when you miss all the time. Many experienced players feel such days before they actually know the final score.

My point is that your experience (and mine) is deceptive. A lot of gamblers swear by hot and cold streaks based on personal experience. They're entirely wrong. It's exactly my point about how people read logs, credit the skill code with non-existent rules, etc.

If you have a good, measured counterexample from football/soccer, chess, or another sport, please provide it. It's entirely possible it exists in some competitions but not others, but I haven't seen it, and my last stats professor swore the absence of a "hot hand" was surprisingly universal.

valguarnera@carrionfields.com

in the "hot hand" phenomenom.

I can't speak about baseball, but in basketball hitting streaks exists.
I don't know exactly what your professor or the sad-ass intern studied, but I believe they mistaken because they simply can't estimate all factors (nobody can). And very likely they replaced a reason with a consequence.

Even simply hit rate is different for various players.
It can't be said that better players have more/longer hitting streaks because their average hit rate is higher. In reality, their average hit rate is higher because they have those hitting streaks

Also, when a player and his team feels that he is "hot handed" in a certain game he takes more chances. Trying hard shots, leads the game, etc. Under "normal" circumstances he wouldn't even try to throw from the center but being "hot handed" he may try.
Keep in mind, that 1 basket out of 2 is easier than 10 out of 20 because defenders (as you also noticed) will pay additional attention to you and, in general, it is harder to create 20 shot-attempt situations for yourself than just two. In practice, that means you will take more risks and shoot from not-so-good-positions more often.

They explain some of what you are talking about. Basically everyone has good streaks (even crappy players) but great players have longer and more memorable streaks.

The studies in question asked: Given a successful shot N, does the probability of success for shot (N+1) increase, decrease, or stay the same?

The answer is "stays the same" in any sufficiently large sample set. This isn't in the realm of opinion-- it's a simple observation of real data. (That paper has since been expanded to larger studies in multiple sports, as I mention above.)

"I can't speak about baseball, but in basketball hitting streaks exists. I don't know exactly what your professor or the sad-ass intern studied, but I believe they mistaken because they simply can't estimate all factors (nobody can). And very likely they replaced a reason with a consequence."

The professor who did the initial basketball study in question (Amos Tversky) would have shared Kahneman's Nobel for Economics in 2002 for exactly this type of work had he not died beforehand. (A pretty good summary of the study, cribbed from the Boston Globe, is here.) The full study is here: Gilovich, T.; Vallone, R.; Tversky, A. (1985) "The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology, 17, pp. 295–314. Kahneman got the Nobel precisely for showing how otherwise intelligent people perceive randomness in a highly irrational manner.

The good news is that if you can prove they're mistaken, you can probably get a cover article in a nice economics journal. It's not every day you get to shoot down a Nobelist in his primary field!

"Also, when a player and his team feels that he is "hot handed" in a certain game he takes more chances. Trying hard shots, leads the game, etc. Under "normal" circumstances he wouldn't even try to throw from the center but being "hot handed" he may try. Keep in mind, that 1 basket out of 2 is easier than 10 out of 20 because defenders (as you also noticed) will pay additional attention to you and, in general, it is harder to create 20 shot-attempt situations for yourself than just two. In practice, that means you will take more risks and shoot from not-so-good-positions more often."

Another interesting theory shot down by inelegant facts.

Some good books in related fields, if anyone's interested:
Prisoner's Dilemma, William Poundstone.
Full House, Stephen Jay Gould.
The Strategy of Conflict, Thomas C. Schelling.

Gould's the best pure author IMO, but the other books are more strictly about game theory. Poundstone's the more accessible of the two-- he's writing for a layman browsing the bookstore, whereas Schelling's book is basically an intro-level college textbook.

valguarnera@carrionfields.com

First of all, I've glanced through the links you pointed.
But they don't have the studies themselves, they just refer to some "studies".

The studies in question asked: Given a successful shot N,
does the probability of success for shot (N+1) increase,
decrease, or stay the same?

The answer is "stays the same" in any sufficiently large
sample set. This isn't in the realm of opinion-- it's a
simple observation of real data. (That paper has since been
expanded to larger studies in multiple sports, as I mention
above.)

As I said, there is more than just probability in succesful shots.
When you flip a coin then yes, those studies would be applicable.
As an ultimate example: you would never train if your consequent shot has the same probability of success.
But, nevertheless, people become better with shots as they are training hard.
Or become worse as they stop training, getting old or tired.

These "studies" operate with average hit percentage, but that percentage already includes hitting streaks of different players.
A "hot hand" player makes a succesful shot not because his previous shot was successful, but because he's feeling good and unstopable today (which includes a number of factors).
And a "cold hand" player misses his shot because it is not his day, not because he missed his previous shot (he is sick today, for example).
The trick is that the average hit ratio of that player already includes his good or bad streaks and thus will certainly "confirm" that their streaks are nothing and are within the probability based on their average hit ratio.

The good news is that if you can prove they're mistaken, you
can probably get a cover article in a nice economics journal.
It's not every day you get to shoot down a Nobelist in his
primary field!

I should find time and point that their studies are misguiding.
However, the good thing is that real sport managers don't really use those studies in making their teams successful.

>First of all, I've glanced through the links you pointed.
>But they don't have the studies themselves, they just refer to
>some "studies".

They do explain the real life application of those studies though. Specifically this portion:

"Of course Larry Bird, the great forward of the Boston Celtics, will have more sequences of five than Joe Airball—but not because he has greater will or gets in that magic rhythm more often. Larry has longer runs because his average success rate is so much higher, and random models predict more frequent and longer sequences. If Larry shoots field goals at 0.6 probability of success, he will get five in a row about once every thirteen sequences (0.65). If Joe, by contrast, shoots only 0.3, he will get his five straight only about once in 412 times. In other words, we need no special explanation for the apparent pattern of long runs. There is no ineffable "causality of circumstance" (if I may call it that), no definite reason born of the particulars that make for heroic myths—courage in the clinch, strength in adversity, etc. You only have to know a person's ordinary play in order to predict his sequences. (I rather suspect that we are convinced of the contrary not only because we need myths so badly, but also because we remember the successes and simply allow the failures to fade from memory. More on this later.) But how does this revisionist pessimism work for baseball?"

>The studies in question asked: Given a successful shot N,
>does the probability of success for shot (N+1) increase,
>decrease, or stay the same?
>
>The answer is "stays the same" in any sufficiently large
>sample set. This isn't in the realm of opinion-- it's a
>simple observation of real data. (That paper has since been
>expanded to larger studies in multiple sports, as I mention
>above.)
>
>As I said, there is more than just probability in succesful
>shots.
>When you flip a coin then yes, those studies would be
>applicable.
>As an ultimate example: you would never train if your
>consequent shot has the same probability of success.

This is a logical fallacy. If you improve, your average (or field goal % or whatever) improves. The point is that if your average is already at a highly defined number, then your misses/makes and runs can be accurately guessed. You are right in that it is not a coin flip, but player skill is reflected in their averages.

>But, nevertheless, people become better with shots as they are
>training hard.
>Or become worse as they stop training, getting old or tired.

Of course they do, but their average also decreases or increases appropriately.

>These "studies" operate with average hit percentage, but that
>percentage already includes hitting streaks of different
>players.

Nope, just the player themselves. It includes *that* players hitting streaks, but those, again, can be predicted and fall in the expected realm.

>A "hot hand" player makes a succesful shot not because his
>previous shot was successful, but because he's feeling good
>and unstopable today (which includes a number of factors).

What they are saying is that the cause and effect are the opposite of what you claim (I think). He feels unstoppable because he's on a streak, but the streak is basically a random occurance based upon his skill level.

>And a "cold hand" player misses his shot because it is not his
>day, not because he missed his previous shot (he is sick
>today, for example).

I've always been under the impression I play better when I'm sick. Logically I know this probably isn't true, but the times when I wasn't feeling well and performed average or poorly aren't remembered like the times when I felt crappy and played extremely well.

>The trick is that the average hit ratio of that player already
>includes his good or bad streaks and thus will certainly
>"confirm" that their streaks are nothing and are within the
>probability based on their average hit ratio.

This is some sort of circular logic. Thats like saying that because flipping a coin already includes streaks of heads or tails that the frequency and length of them are somehow independant of the fact that it is a 50/50 chance. What the study is saying is in the quoted block above.

>The good news is that if you can prove they're mistaken,
>you
>can probably get a cover article in a nice economics journal.
>
>It's not every day you get to shoot down a Nobelist in his
>primary field!
>
>I should find time and point that their studies are
>misguiding.
>However, the good thing is that real sport managers don't
>really use those studies in making their teams successful.

Real sports managers probably buy into the "hot hand" thing, but that mean it has any scientific basis. Real people buy into the earth being 6000 years old, but I bet you don't think they're smart to think that way because it isn't the way you think. This case is even more extreme since literally everyone thinks this way because of the way our brains are wired as a species.

>>The studies in question asked: Given a successful shot N,
does the probability of success for shot (N+1) increase,
decrease, or stay the same?

>>The answer is "stays the same" in any sufficiently large
sample set. This isn't in the realm of opinion-- it's a
simple observation of real data. (That paper has since been
expanded to larger studies in multiple sports, as I mention
above.)

> As I said, there is more than just probability in succesful shots.
When you flip a coin then yes, those studies would be applicable.
As an ultimate example: you would never train if your consequent shot has the same probability of success.
But, nevertheless, people become better with shots as they are training hard.
Or become worse as they stop training, getting old or tired.

> These "studies" operate with average hit percentage, but that percentage already includes hitting streaks of different players.
A "hot hand" player makes a succesful shot not because his previous shot was successful, but because he's feeling good and unstopable today (which includes a number of factors).
And a "cold hand" player misses his shot because it is not his day, not because he missed his previous shot (he is sick today, for example).
The trick is that the average hit ratio of that player already includes his good or bad streaks and thus will certainly "confirm" that their streaks are nothing and are within the probability based on their average hit ratio.

Without having read the studies, I dare guess that Valg simplified it a bit. The reasonable way to study something like that would be to analyze a large sample of shots and see if the hits/misses on a per-game basis match a normal distribution... I.e. that hot-hand days and cold-hand days would just be statistical fluctuations.

There is a perfectly logical and reasonable explanation as to why you THINK you end up in the Whitecloak Encampment far more often than you most likely do.

That encampment is by far the most recognizable high danger area which you can teleport into freely. I personally don't believe I end up there any more than I end up in Arboria, Mortorn, Whistlewood, ect. ect..

The one place I cannot remember landing in, however, is the Eastern Road. The reason for this is likely explained by the same logic as above.

If you've played sports all your life, you probably realize that there seems to be varying types of muscle memory. There's the overall muscle memory which allows you to do pretty much what you've done before. And then there's the muscle memory you have when you do something to perfection, or close to it. There's a reason why every golf ball hit by a pro isn't perfect... muscle memory isn't perfect either. But if you stroke a few beautiful shots in a row in basketball, let's say. You get a certain feeling... wow, that's exactly how it should be. That doesn't mean it will last forever, or you'll hit every shot, it just means your mind knows that you're doing things absolutely correct, even if the results aren't always positive.

I'd agree that such things as 'clutch' hitters are highly overrated, and would agree that it's mere percentage points difference. I more believe in streaks, most of which I again attribute to muscle memory. Your mind is telling your body exactly how that last shot/hit was done, and you're copying it. But, of course, muscle memory falls apart at times, then comes a slump, where you forget what it was you were doing right, and have to relearn.

This is, to me, a better explanation of what the 'hot hand' is. It's purely physical, with psychology playing a very, very minor role.

Just my opinion, I have no stats to back it up, except a lifetime of playing sports.

I agree the effects are probably very subtle. The books I've read on this all dealt with professional athletes, since accurate statistics and opinion polls were available. So we're only talking about people who have probably taken over a million shots or swings in their life. If they were easily rattled, or had serious consistency problems, they wouldn't be professional athletes.

Gould talks about this in light of the disappearance of the .400 hitter in Full House. Basically, the worst guy in MLB used to be some shlub (and probably on the Phillies). Nowadays, the worst guy in MLB is an amazing athlete who has the misfortune of being around roughly 1,000 slightly more amazing athletes (and probably is still on the Phillies). As human performance approaches its limits like that, everyone loses the ability to "take over" a game, and trends like "clutch hitting" or "hot hand" wash out.

valguarnera@carrionfields.com

The Phils will make the playoffs this year. Granted, I say this every year, but this year I'm 100% certain.

Baseball is where researchers tend to get most statistics on consistency from, and that makes a certain sense. But also, so much is hidden and obscured when going through anywhere from hundreds to thousands of at bats. Over that period, one percentage point makes a huge difference. Not so as much in something like football. A kicker will never kick as many field goals in his life as a starting position player in baseball will have at bats in one season. That's why things like Vanderjagt vs Vinatieri are so interesting and you can make a semi-valid 'clutch' argument.

It's also one of the reasons sports is infinitely fascinating. Everyone see's statistics the way they want to see them. In baseball statistics are God... in football, they're often dismissed as meaningless. In Carrion Fields numbers aren't always impressive. You've got know the total situation for every pk to give a true picture of it. That's impossible to record in a statistical way. That's why trends are ultimately far more important than numbers or individual instances.

In summation, Phillies 2007 World Champions, they'll sweep the Pirates in the World series, six games to none.

Everyone sees statistics the way they want to see them. In baseball statistics are God... in football, they're often dismissed as meaningless.

I know you're a football guy, so I'd recommend The Blind Side by Michael Lewis. I haven't finished it yet, but he makes the argument that football is in the middle of this sort of economic/stats revolution, which is part of why teams have started to pay their often anonymous left offensive tackle top-of-the-league kinds of dollars over the last decade or so. Lewis mostly talks about how teams learned to respect the LT position, but there's an undercurrent that football has always been dominated by "go with your gut" guys who are doomed to be usurped by the Bill Belichicks who are hoarding and microanalysing draft picks. If you've read Moneyball, it's essentially the same thesis.

I think CF has a similar problem in that the oft-cited statistics might not be the best ones. (I don't claim to know the best ones.) There's a culture, but some characters and players are definitely over- or under-appreciated. PK ratio, kills/hour, gank-o-meter, etc. are all good starts, but I wouldn't trust any of that over the opinion of a couple veterans who had fought the character in question a lot. Kills/hour is useless if you're comparing a guy who does nothing but fight with a guy who spends a lot of time exploring and RPing. Etc.

And don't get me started on why average yds/carry is much less useful to a coach than median yards/carry.

valguarnera@carrionfields.com

>And don't get me started on why average yds/carry is much less
>useful to a coach than median yards/carry.

I don't know...seems like mode yds/carry could be rather useful as well. But yeah, simple fact of those random 80yrd runs are so going to skew the average, whereas they're going to have much less an effect on median or mode.