The value of a turnover

[mattgslater]

What's a turnover worth? These are the factors that occur to me off the top of my head.

1) The knockdown, if any, expressed in injuries, lost TZs, lost actions and burned MA on future turns. This is the easiest to calculate. This decreases the turnover value for pickups, passes and catches, and increases the turnover value for blocks against Mighty Blow or GFIs into multiple TZs against a foul-intensive opponent.

2) The failed action, if relevant, including any loose balls, standing/unmoved opponents, or failed Move actions (Dodge/GFI). There is a reduced penalty here for a both-down, for instance, for a failed dodge or GFI if the occupied square is the main objective, or for failed catch inside a good formation. Similarly, a skull-out or failed AG roll on a key blitz has an increased value, as would a fumbled pass from the backfield.

3) The lost actions on the remainder of the turn, including the difference between your opponent's position now and what the opponent's position would be had your turn concluded (what with pushes/knockdowns/injuries, covered routes, etc). This includes turnover odds on successive actions. A turnover on an early action or an action with important contingencies will have an increased impact.

Am I missing anything? Once we have this, we can figure out the relative value of a TRR counter on any given turn, thereby providing assistance to coaches who would like to use TRRs more efficiently.

If it's just these three factors, I'll start calling them Knockdown, Failure and Burn, respectively, expressed by the variables K, F and B.

I'll start with Knockdown, and we'll go from there.
Knockdown: The factors in a knockdown are:
* Lost action or movement, unless KO/Cas'ed
* Lost TZ for one or more turns
* The downside of the square he occupies while prone, less the upside of same
* Any change in priority for the now-prone player's action on a consecutive turn
* The chance of a stun times the value of a stun
* The chance of a KO times the probable number of lost turns
* The chance of a Cas times the number of turns remaining in the game
* The chance of a death or retiring injury times the value of the player, less the value of the lost TV
* The chance of a statloss times its on-pitch value in future games
* The chance of a MNG times the value of the player in the next game, less the value of his replacement (reserve or JM), less the value of the lost TV in the next game, plus the odds that his absence will deplete your bench and cause you to set up short men.

Man, that's a lot. Fortunately, most of it's based on constants, which will let us boil it down to a simpler formula: the value of the lost action (ActV, on a scale of 10) on the next turn times times the chance of remaining on-pitch (OnP, or 100%-KO/Cas chance, expressed in increments of 1/13 perms), plus chance of AV penetration (AVP, expressed in 1/36 increments) times the value of an injury roll (InV, which has an expression in lost actions, lost gold, and lost player value), plus the value of the player's TZ in the opponent's turn (TZV).

So... K = (ActV x OnP) + (AVP x InV) + TZV.

ActV and TZV are highly situational, and will have to be covered by rules of thumb.

AVP is as follows, with -1 AV vs. MB opponents (and treated as AV7 vs. Claw; PO does not apply)
AV: AVP
10: 3
9: 6
8: 10
7: 15
6: 21
5: 26
4 (Snotling vs. MB): 30

InV is Act+TZV (guaranteed stun or worse), plus 1/4 the value of a KO and 1/6 the value of a Cas. The value of a KO is worth (Act+TZV) times the number of turns remaining in the drive (estimated) or half, plus the value of the player's loss on future drives, which is kind of sticky when one considers reserves, future injuries/ejections and the open questions of drive length and KO rolls. The value of a Cas is the value of a KO without considering recovery odds, plus 1/6 of the sum of the value of a MNG, a permanent injury (in the aggregate) and a death. Obviously, that too is kind of ephemeral and hard to reduce to a hard formula. Still, it can be said that:

InV = Act+TZV+KOV/4+CasV/6+(MNG+PermInj+Death)/36, where KOV is the (Act+TZV)x(remaining turns -1)x(turns in next drive/2 plus turns in following drive/4 (if applicable), plus turns in the next drive/8, etc.), and CasV is (Act+TZV)x(14-Turn #).

OnP will approach 100%, as it's usually 1-(5/12 x AVP/36). It's 1-(7/12 x AVP/36) if you're Stunty, and somewhere in between vs. Mighty Blow.
Halfling: 95/144 ~ 2/3
Goblin, Skink or AV6: 109/144 ~ 3/4
AV7: 119/144 ~ 5/6
AV8: 195/216 ~ 9/10
AV9: 67/72 ~ 13/14
Tree: 139/144 ~ 29/30
So depending on your tolerance, you can ignore OnP if you're AV9, AV8 or even AV7, but not if AV6 or stunty.

Anybody want to double-check my formulae?

[Ullis]

I think the main thing you should look at is on how the turnover will affect the ball. If the turnover would lead to your opponent having a free blitz or even a block at the ball carrier, you reroll. If the turnover would almost guarantee a TD for the opponent and by not turning over you have a much better chance at stopping him, you reroll. If the ball is on the ground and the turnover would give your opponent a chance to snatch it, you generally reroll.

If none of the above holds true, then you can look into other stuff. If you have lots of rerolls left, you can generally reroll. If it's your last reroll and there's important turns left, you should aim to hang on to the reroll (I think it's best to try and finish any half with one reroll left).

Worrying about your player dying or getting hurt is about the last thing you should take into account (the git failing at something probably deserves any punishment coming his way). However, that's also probably the easiest to express in a numerical format, so trying to put this into numbers will probably lead into a wrong direction.

[mattgslater]

Understood, and probably agreed in principle. The first goal is to break down all the various factors. I'm not so interested in ascertaining what's important until everything is laid out. After that, we can start talking about conclusions.