Risk management: easy vs. important

[mattgslater]

I'm not going to go into new terms here. My objective is to open up the discussion of probability, importance and contingency, ideally to put a bug in somebody's ear to get started on a Benthamic-style calculus for Blood Bowl action prioritization.

Meditation I identifies three skills that are important for the BB coach: risk, space and resources. In that meditation, I identify space management as the final bit of uncharted ground (cue Star Trek jokes), but the truth is, there is one more bit of ground in risk management. It's a subset of a larger subject that can mostly be addressed in terms of mathematics and ground rules which all good coaches know. But the relationships between the odds of turning over/re-rolling/getting hurt, the value of the rest of your turn, the rewards for success, and the impact of your action (or non-action) in the face of an unlikely turnover, these things bear further discussion.

Obviously, the free-and-obvious stuff like standing up comes first. What I'm really thinking of (though not the whole of the story) is the relationship between easy and important. How do we identify the balance? Because we're talking about a lot of situational stuff, we'll have to play a bit of an analogical game at first, discussing particular scenarios or talking in broad generalities and leaving room for exceptions. After that, we can eventually work out a quick calculus involving actions risked, potential knockdowns (on your own turn or the opponent's), scoring odds, etc.

[mattgslater]

For instance, is there some kind of calculus we can work out that factors in the relative value of a turnover, a blown action, an injury roll, a knockdown, a loose ball, etc. for any given situation?

For example, if a Skaven team kicks off to you and the ball goes deep, you had probably best deal with it quickly, or you run huge risks. However if it's Dwarfs kicking off to you and landing the ball deep, you might play a little looser, no? The difference can be expressed to percentage of a TD allowed and percentage of a TD scored. This may not be easy to figure out. Both of those chances play into your chance of winning or tying the game, but the latter is also expressible as a fraction of 3 SPP, or 4 if you were going to chuck it. If you were planning on picking up, GFI'ing or otherwise rolling dice, the relationship between your failure chance on that action and the actions you may not have taken is also expressible in TD terms, as well as in actions on both sides of the ball.

What's a block worth? I mean, there's a chance of a knockdown, which may be a blown action. There's the chance of a push, which may mean a blown or redirected action, or another burned action on your part for a secondary block. There's a fraction of a lost action and/or of a lost TRR, and there's the same fraction for each player who has yet to take a valuable action. There's a fraction of a block against, too, potentially yielding injury. On top of this, there's a chance for SPP, which has an independent value.

Eventually, if you humor me, we'll be able to boil it down to a formula that can be worked with, which in turn will lead to some general rules of thumb, much as we did with AC/CLs. This venture is exponentially harder, but it's also one of the more important "gray areas" in the game. One potential obstacle is that wins, SPP and injuries all have semi-independent values, so we're dealing with multiple currencies that play into each other.

[B SIDE]

I think it's possible. In chess, a game in which the only random element is whether you will play as black or white pieces, advantages are often measured in fractions of a pawn (impossible of course), and expressed as "winning chances". How much more fitting might these expressions and concepts be to a game where pieces really do have chances, and where a goblin essentially is a fraction of an orc?

To begin, we must agree upon a concept of value. Generally, the aim of a BB coach is to score the W. That failing, a draw is preferred to a loss. One might immediately suppose that a simple numeric system- by which, for example, a W is worth 1, a tie 1/2, and a loss 0- could quickly be agreed upon by all parties. But as you point out, the issue of value is complicated by such considerations as player advancement, permanent injuries and playoff standings. Is it more important to win, or to advance your players on their skill paths early in the season? To stop the tying TD, or avoid a blitz that exposes your star to the sidelines?

I posit that, to begin, each game ought to be considered independently, without regard to league strategy. SPP's are an important (and fun) part of BB league play, but if each game is to be considered separately, even the slightest chance of dropping the ball ought to be avoided if it has the chance to interfere with the immediate goal of winning the game (or half-winning it). It seems to me that in most league formats, winning has advantages (cash for the treasury, boosts to FF, better placement in the playoffs, etc.) that more than make up for the handful of SPP's you might gain from tossing the ball around in the backfield on turn one. But that is a digression. Regardless of what we eventually discover to be the most significant factors in determining relative values of actions in league play, I suggest that we ought to consider the game before the meta-game. In this instance, we must endeavor to understand the value of actions before we explore the opportunity costs associated with those actions' alternatives. After all, even when a coach isn't too concerned about winning this game, it's always because he wants to win the next one.

[mattgslater]

Okay, so we have two sides of the equation, carrot and stick. I think we should look at the downsides of any given action first.

What can go wrong?

* You can burn a TRR. If you have three left on T6 and it's the end of your turn, this has no value. If it's the first action of the turn and your last TRR on T4, it's a big deal. This is expressible in "winning chance" but is a big variable. It's also expressible in TV as half TRR cost or as 50k if you induced (or forwent inducing) a TRR.

* You can fall down. If your man falls (even with Wrestle), you blow 0.5 to 1 actions. If he's stunned, you blow another one. If he's KO or Regen, you burn the rest of the drive. If he's KO, you burn up to half of the rest of the match after the drive. If he's BH (or ejected), you burn the rest of the match, unless you have a reserve or successful Apo use, and then you get a player replacement (probably a downgrade if a reserve) after the drive. Then there are missed games and deaths.

* You can turn over. The value of a turnover is expressible as the sum of the value of each remaining action. But this is harder to calculate than it sounds. Because each action has a value depending on its ease and importance. If you were planning on moving one player to a new position, and moving another, similar player to man that one guy's old spot, you're really only wasting one action by turning over before you do it, even though you were planning on moving two guys. If the second guy is also in a good spot as-is, but the new spot for the first guy is a little better, you're wasting only the difference. If the first move had a 1/6 chance of turning over and ruining your setup, you are actually wasting 5/6 actions and gaining 1/6 of an advantage on that front by turning over before you take the action sequence. If you have no TRR and throw a 2d skilled block, then a 2d unskilled block to set up a 2d skilled block on a rookie, your first block is "wasting" 17/324 actions (1/36 to skull, times one action (the unskilled block) plus 8/9 action (the skilled block after the unskilled one), resulting in 11/324 knockdowns lost (1/36 x (5/9+(8/9x3/4)) and 1/36 x 11/81 = 11/2916 of a saved turnover on a later block. Obviously, you'd not be daunted by those odds if that's all you have left in the turn.

* You can suffer a situational disadvantage. This is one of those places where we'll have to do a lot of thinking to boil out a formula that works, but when we do it'll probably be pretty simple in practice. I'm not ready for this one yet. One thing to note is that there's often a relationship between blown actions and situational advantage, and that relationship can go either way. Sometimes, a blown action leaves you with a situational disadvantage, such as if you fail an easy action before a harder, more important one that might free up a key player. Sometimes, taking a free action may leave you with a situational disadvantage if an easy action intended right after it fails. This means we need to account for the value of "contingent" actions, easy actions that you have a reason (other than turnover odds at action priority) to hold off until after hard actions. For example, you are trying to form a screen, you may want to race a player into position. But if the block intended to free up his fellow screener skulls out, "in position" might be a terrible location.

What else?

[mattgslater]

Hey, I'm editing a PowerPoint presentation on FMEA (Failure Modes and Effects Analysis). It's very clear that this discipline would apply directly to BB play-planning. Does anybody here have any professional experience with FMEA?

... crickets. Guess not.