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thoralf



Joined: Mar 06, 2008

Post   Posted: Nov 17, 2017 - 16:29 Reply with quote Back to top

Endzone wrote:
What I like best in the 'to kick or not to kick debate' for the bash v agility match up, are coaches who say it's best to kick with the agility team but best to receive with the bash team, not spotting the contradiction!


It's not a contradiction if it's the best strategy for the two parties, and if reversing their strategies hinder both parties equally. It's some kind of mutual equilibrium.

It'd be really surprising that there's an equilibrium for all combinations of bash vs elf games, and all the various situations. So "it depends" should win.

I told ya. Time for some game theory.

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Purplegoo



Joined: Mar 23, 2006

Post   Posted: Nov 17, 2017 - 16:43 Reply with quote Back to top

Licker - apologies if I incorrectly remembered you as a RO5 chap. My bad.
licker



Joined: Jul 10, 2009

Post   Posted: Nov 17, 2017 - 17:19 Reply with quote Back to top

Purplegoo wrote:
Licker - apologies if I incorrectly remembered you as a RO5 chap. My bad.


No need to apologize. I don't think there is anything wrong with Ro5, so I may have discussed/denfended it in the past, I just don't adhere to it (other than as dictated by nuffle...) personally.
mrt1212



Joined: Feb 26, 2013

Post   Posted: Nov 17, 2017 - 18:21 Reply with quote Back to top

licker wrote:

It is good fun, other than a couple people here who seem to want to throw insults my way, I think it's just a spirited discussion. And where's the fun in just agreeing with everyone and saying 'but in some cases...'. Since in this particular discussion, the people who think other things are being illogical Wink


Well I dont think you're being illogical but I think you found a 'best solution' and stopped there because it was 'obvious'.

If we had access to the data and could really mine it we could flesh out a picture based around game state and win probabilities at that game state.

Basically we could look specifically at the 2nd half kick off and work out the population win rates based on a few different game states

1: Kicking off 2nd half up 2-0
2: Kicking off 2nd half up 2-1
3: Kicking off 2nd Half up 1-0
4: Kicking off 2nd half tied 0-0
5: Kicking off 2nd half tied 1-1
6: Kicking off 2nd half down 0-1
7: Kicking off 2nd half down 1-2
8: Kicking off 2nd half down 0-2
9: Receiving 2nd half up 2-0
10: Receiving 2nd half up 2-1
11: Receiving 2nd half up 1-0
12: Receiving 2nd half tied 0-0
13: Receiving 2nd half tied 1-1
14: Receiving 2nd half down 0-1
15: Receiving 2nd half down 1-2
16: Receiving 2nd half down 0-2

Your hypothesis suggests that 1-3 have the highest win probability at half. In fact you are living your hypothesis! 1 is especially hard to deny as possibly being highest win probability except for perhaps 9.

But what if we found out that 4-7 are in fact a lower win probability than 10-13?

Also what if we started qualifying each of those gamestates by how often they are achieved? What if 1 and 2 are much less likely to happen than 3 and 3 is less likely to happen than 11-13? Or what if we found that 3 and 5 are equally likely but 5 has a much lower win probability?

What if we then started comparing global stats to individual coaches?
What if some coaches could achieve the 9-13 gamestates more often than the 1-5 game states and shows a higher win probability in 9-13 gamestates than 1-5 gamestates?

So what I'm getting at and what I have always kind of maintained is that 'logic' might dictate one mode of action when we are filling in what we think is axiomatically true for variables we are kind of familiar with but not might be true when we actually have the numbers or when we look at individual cases, especially where coaches self select to receive in the 2nd half or are forced to by the other coach winning the toss.

Again, I don't think your stance is illogical, I'm saying there might be more to it than what you believe is an underlying fact - that state 3 is both the most achievable AND gives the highest win probability for every coach, every time.

Also as a philosophical sidebar:

What if through all this analysis we found that 53% of coaches do better when receiving first and 47% did better when kicking. Is the takeaway from that difference really going to be "receiving first is obviously better". What's the threshold for determining best practices between two disparate groups that both enjoy success?


Last edited by mrt1212 on Nov 17, 2017 - 19:07; edited 2 times in total
The_Murker



Joined: Jan 30, 2011

Post   Posted: Nov 17, 2017 - 18:33 Reply with quote Back to top

"So, in order to get to 2-0, you have to first get to 1-0. Kicking first makes getting to 1-0 less likely. Because, again, if you are such a pro at stealing the ball and scoring anyway, why would you not want to steal the ball and score when you are already ahead?"

Well, that's the trick, isn't it? Not too many experienced coaches here are so bold or disillusional as to say they are really "pro" at stealing the ball, or even preventing a good coach from scoring. If anything, the "Kick First" camp probably acknowledges that EVERYTHING in Blood Bowl at the higher levels is difficult, with the exception of scoring quickly with elves at times. "Kicking first is easier" because NOT having to stop an enemy touchdown, ever, and still win the game is often very doable. It's called an elf-stall. It's a thing. (Dangerous, but real)

It is you who seems to indicate defending, and scoring, and Blood Bowl in general is easy. Maybe that's why your views are so powerful.. the game at Cyanide is just.. easy.

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happygrue



Joined: Oct 15, 2010

Post   Posted: Nov 17, 2017 - 18:52 Reply with quote Back to top

Endzone wrote:
What I like best in the 'to kick or not to kick debate' for the bash v agility match up, are coaches who say it's best to kick with the agility team but best to receive with the bash team, not spotting the contradiction!


Laughing

That is amusing, though it's not a true contradiction - receiving first with a bash team against another bash team seems very different than bash vs. agility...

I'm in the "kick with everything, almost always" camp. I think that puts me in a minority. I have 3 main places where I would opt *not* to kick to the other team if I could choose:

1. The matchup appears to be one where I would like to score early, or have the option to score early.

2. The matchup appears to be one where my best chance to win is via attrition. This is quite common for some folks, but based on the types of teams I usually play, it's pretty rare for me to think that my *best* strategy is to play for straight damage and hope to remove players as *the* path the victory.

3. Weapons. Which is really just a sub-case of #1. Playing against gobbos Or a deathroller? Might be nice to score early if you can stick those weapons on the line, or at least make them squirm regarding if they put said weapons on the line or not.

Unless one of those three things is happening, I would prefer to kick. Maybe there are a few other odd cases but not that seem "normal" to me.

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Throweck



Joined: Feb 23, 2013

Post   Posted: Nov 17, 2017 - 19:00 Reply with quote Back to top

I have found this interesting as I always receive if I can as I think my offence is much worse than my defense so I like to try and score and hopefully score on defense 2nd half. I never really think too much about it but now I am!

I shall soon be up there with Harad and Endzone. Very Happy

It's an important choice for sure and, for me, it has become habitual like the choosing of heads on every coin toss.

Thank you for helping me reflect on my coaching.
Sp00keh



Joined: Dec 06, 2011

Post   Posted: Nov 17, 2017 - 19:08 Reply with quote Back to top

I always click heads

mrt1212 wrote:

If we had access to the data and could really mine it we could flesh out a picture based around game state and win probabilities at that game state


Nahhh just need to know both races, who kicked, who won. for as many games as possible
That would let u find which is best option for each type of matchup

Half time score doesn't matter because the decision is made at the start and the result of interest is at the end


Last edited by Sp00keh on Nov 17, 2017 - 19:16; edited 1 time in total
MattDakka



Joined: Oct 09, 2007

Post   Posted: Nov 17, 2017 - 19:12 Reply with quote Back to top

I toss a real coin, see if it's Heads or Tails, then I choose the same in the client.
That way I don't have to decide. Smile

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mrt1212



Joined: Feb 26, 2013

Post   Posted: Nov 17, 2017 - 19:36 Reply with quote Back to top

Sp00keh wrote:
I always click heads

mrt1212 wrote:

If we had access to the data and could really mine it we could flesh out a picture based around game state and win probabilities at that game state


Nahhh just need to know both races, who kicked, who won. for as many games as possible
That would let u find which is best option for each type of matchup

Half time score doesn't matter because the decision is made at the start and the result of interest is at the end


I was using half time as an easy frame of reference for candlejack to scrape the replay files.

But I would argue that taking the pulse of the game at half could go a long way towards validating or invalidating some of the premises we see in this thread to justify either option.

Like it's great theorybowling to say that going up 1-0 creates a game long advantage that leads to higher win probability but...

How often does a 1-0 lead turn into a 2-0 lead versus a 1-1 tie? Why isn't the half a good inflection point to measure the game?

One of the stumbling blocks for me with licker's hypothesis is the assumption that 2-0 and 1-0 are much more likely outcomes at halftime than 1-1 when receiving first and scoring early.

What if that isn't the case? What if we could determine that scoring on turn 2 of the 1st half while receiving as X team actually leads to more half times that are 1-1 globally or for a significant portion of individual coaches? And what if we could show that a 1-1 gamestate at half for the team receiving first had a lower win probability than being up 1-0? What if scoring turn 3 cut that probability of that 1-1 outcome at half by a significant amount and followed a linear distribution for each turn you delayed scoring? That'd be a pretty important confounder, wouldn't it?

Looking at the gamestate at half gives us an inflection point to prove or disprove specific theoretical frameworks of how a game flows and what is the best decision, something that just looking at the start of the game and the end doesn't.

Like, don't you kind of want to understand the why of methodologies working?
Sp00keh



Joined: Dec 06, 2011

Post   Posted: Nov 17, 2017 - 20:46 Reply with quote Back to top

Ok half time would be relevant to find the 'why' of one option is better than the other

I mainly care about the actual answer tho:
Team that kicks gets x% more wins or losses, etc.
Or maybe it's got some race-based subtlety. That's what I want to know. It doesn't need half time theories for that
mrt1212



Joined: Feb 26, 2013

Post   Posted: Nov 17, 2017 - 20:52 Reply with quote Back to top

Sp00keh wrote:
Ok half time would be relevant to find the 'why' of one option is better than the other

I mainly care about the actual answer tho:
Team that kicks gets x% more wins or losses, etc.
Or maybe it's got some race-based subtlety. That's what I want to know. It doesn't need half time theories for that


Well the top level question is certainly easy enough to find out if you build a query that looks at halftime splits as well - you simply can ignore that halftime part of the query for those top level purposes.

In chatting with Christer he actually thought he could go even more granular but when I first came up with the idea I was assuming any process would require a lot of manual work on candlejack's behalf, which he said was the case.
mrt1212



Joined: Feb 26, 2013

Post   Posted: Nov 17, 2017 - 22:12 Reply with quote Back to top

And to be honest, I think licker just fundamentally disagrees with the premise that a coach receiving with a tied score in the 2nd half might have an equal or higher win probability than a coach who scores at any point on offense in the first half - not because he has the numbers to rule it out but because he doesn't see any logical explanation as to why this could happen. He already distilled it down into the following statement:

Quote:
Do you want to play for the best chance at being up 1-0 or not?


The assumption licker is making that all things being equal for how a coach plays defense, you should be able to defend a 1-0 lead as capably as a 0-0 tie, so why elect to not have the points on the board right off the bat and protect that lead that has to be reckoned with by the opposing coach?

And I just don't think he has enough information to base an entire dogmatic prescriptive action on that assumption though. He's basically saying it's very unlikely for a coach to do their defense differently enough between the two situations to think that a coach could significantly do better playing defense right off the bat versus scoring and playing defense quickly.

What if the global data sets showed coaches receiving in the second half with a tie had a near equal win probability as someone receiving in the first half and going into half with a 1-0 lead? How would licker's logical framework account for this? It wouldn't because a central assumption is that playing with a lead is always better than not. And while that is hard to argue against in a hypothetical space, what if we did indeed find that both scenarios have an equal win probability? And what if the biggest correlative factor to winning overall was then how often you achieve either of those two states at halftime when put into those positions?

Further, what if individual data sets showed a coach wasn't quite capable as going into half with a 1-0 lead after receiving as they are going into half with a tie or better kicking? licker's logical framework suggests that a scenario like that is really really unlikely or near impossible. It just doesn't follow that a coach like that should exist and yet if they do...there's nothing in licker's hypothesis that could explain it since one of the central assumptions he makes is you play defense like you play defense like you play defense. If we found that globally a significant portion of coaches in fact follow this pattern of not being able to maintain leads when receiving first but can consistently keep the score tied or better when kicking, we would be inclined to discount that central assumption of how coaches be or play defense situationally.

But again, if we accept lickers assumptions to be true, of course his logic is ironclad. I just suggest, maybe his assumptions aren't entirely correct given the absence of information and the self reporting of coaches doing the opposite and finding success.
licker



Joined: Jul 10, 2009

Post   Posted: Nov 17, 2017 - 23:33 Reply with quote Back to top

That feels like a lot of 'what ifs' to me.

But hopefully you can get your hands on the global data, I admit, I only have my own data to base my opinion off of (and some additional from a couple other elf coaches I follow, but I haven't looked at all their matches, just the ones I watched).

Still, I'm really not sure why the defense would be any different up 1-0 on turn 2/3/4/... as opposed to tied 0-0 on turn 1. Indeed if you are ahead you can likely play more passively if you think it possible to deny the score, if tied you may feel the need to play more aggressively to actually steal the ball.

It's all dependent on the in game situations of course, but logic will still suggest that you should have more options with a lead than without. Assuming you are playing to win (and not assuming overtime as a possibility though I haven't decided how overtime affects it, don't think it does too much).
Harad



Joined: May 11, 2014

Post   Posted: Nov 18, 2017 - 00:16 Reply with quote Back to top

We've been through this before so I will try to be brief:

It's a bit more complicated than this but...

In any match-up there is a probability to score on offence without leaving time for the counter score [P(A)] and a probability to stop the opposing score on defence [P(B)]. If you achieve both these things you win [P(A AND B)] (there are obviously more complicated scenarios but hopefully one can see that much of the following logic still holds - one such complication is that as Purplegoo excellently noted, the weight we each ascribe to winning vs drawing may be different).

Depending on the amount of relative player attrition those probabilities will vary and so will be different in the two halves [P(A1), P(A2), P(B1), P(B2)]. The relative player attrition varies depending on the match-up (and I accept that this also varies depending on who kicks or receives).

So, by analysing this we can arrive at the optimal solution and decide on P(A1 AND B2) or P(B1 AND A2).

I posit that the optimal solution is not to always kick or always receive. Let's take a simplifcation, P(A1) = a and P(A2) = a +x, P(B1) = b and P(B2) = b+y. Why would a(b+y) always be bigger or smaller than b(a+x)? Or more simply, why would bx always be bigger or smaller than ay? To me it's quite clear that the probability of scoring and stopping the score vary significantly with teams and with relative deterioration of player numbers to the extent that there is unlikely to be a relationship which defines a rule.

As I've noted before, I find it interesting that different people have different heuristics and that they often vary according to the environment in which they play. This makes sense to me as in some situations the relationship between bx and ay is likely to be more similar.

I've tried to lay this out with some maths which I think is not very rigorous to illustrate the point. So please pick holes in this if there are mathematical deficiencies which matter but I think there is scope to get lost on quibbling on points of maths which are correct but which don't aid the understanding of the issue. It's also been a long day and I may be being very stupid.

I also think there can be value in knowing what one has to do to achieve one's desired outcome e.g. knowing you need to score twice to win or knowing your opponent has to score twice for you to lose. This depends on how valuable each outcome is to you.
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