Why Even A Bad System Is Better Than No System At All

I love the ideas here, but I have some pretty major quibbles.

When Renney says “bad strategy”, he doesn’t really mean a bad strategy. He means a very good strategy that isn’t quite perfect. A bad strategy would be to, say, pass the puck to the other team every time you get possession. The Sabres’ strategy you described is obviously nothing like that—I’d call it a very good strategy that isn’t quite perfect.

The other problem is that you really have to define what “no strategy” means, because I don’t think it really exists. Even if you define it as each player randomly choosing what to do at any time, you still need to assign a list of possible actions and a probability for each of those—and that sounds a lot like a strategy to me. What I think Renney means by “no strategy” is “each individual player following what they believe to be the optimal strategy”. And obviously that might end up really badly, but it could also work out very well, if every player has the hockey sense of a Crosby or Lidstrom.

This was meant as sort of a trial run at analyzing hockey using higher level math concepts. I deeply appreciate the comments and will try to take them all into account in my next post, such as Matt F’s suggesting I should include hyperlinks. For now I thought I would try to clarify my thinking a little based on what has been said in these posts.

I meant here, as I think Renney did, to have strategy stand as a near perfect synonym for plan. When I say no strategy I mean no plan. If it helps I took no strategy to be having no plan, nothing that has been communicated to the players. I took a bad strategy as one that is communicated to the players but that has the primary attribute of being worse than that employed by an average team in the league. A good strategy is one that is better than the league average. (Now observant readers will say to themselves how the heck is he measuring the quality of the plan so he can place various teams approaches on a line. For now, lets accept that there are differences in quality of coaching, one of which is the ability to craft plans for beating other teams and leave it at that. The minute we accept that then there must be arbitrary states we can describe as good, bad or average plans.)

I should clearly have defined the terms better and imposed some limits. This became obvious to me when I read Peter Raymaaker’s comment and despisethesun’s response. Then Ryan V raised similar points. So here is some more of the missing definitions. A bad outcome is when, a) you miss a chance to gain control of the puck, either from an opponent or from the non-control state, b) the puck enters a state of no control or c) is lost to your opponent. A good outcome is when you gain control of the puck or retain control of it or force your opponent to place the puck in the no-control state.

Peter is right that there are quality of opponent issues for some of these states. However, again the environment is the NHL (or any structured league) within which the range of differences in opponent quality is relatively small. Yes, I do know it appear huge to the naked eye at times. However, given the set of all hockey teams in existence at this moment, the NHL is a very homogeneous and tiny subset. In my subsequent work I will try to incorporate opponent effects.

That said, I feel one of the key points I am raising may be being lost in the noise. What your opponent is doing or not doing is not relevant to whether you are better off to a) have no plan, b) have a poorer plan than your opponent, or c) have a better plan than your opponent. I think we can all see that having a better plan (state c) is a good idea and would over time outperform the other two states. That leaves us debating only whether in all conditions you are better off having state a or state b, no plan or bad plan.

Who your opponent is or what they do has no effect on that debate since they can either a) have no plan, b) a worse plan than you, or c) a better plan. If they have no plan then the effect is the same on both states we are considering in that we can’t for either of our states say with confidence how the opponent will respond. If the plan is worse than our state b then we have the situation above where we accepted that state c is the best option. In this scenario our state b is better than their state b and we can’t say whether or not their plan b is better or worse than our state a – no plan since this is the very issue in debate. So essentially we learn nothing. In the third situation the opponent’s plan is superior and we can say our state b the bad plan is worse than their good plan but have agreed above that a good plan beats no plan so both the states we are examing lose. This is why I didn’t incorporate opponent effects in the first place.

Ryan, let me quote what you said, “What I think Renney means by "no strategy" is "each individual player following what they believe to be the optimal strategy". And obviously that might end up really badly, but it could also work out very well, if every player has the hockey sense of a Crosby or Lidstrom”. That was actually exactly what I assumed Renney meant as well. It is certainly what I mean, no plan has been communicated from the coach to the players. That is there is no “team” strategy. It is every man for himself.

Dirk Hoag did a great job of summarizing my argument and enriching it. At the core of my argument is the idea that when a player and a puck meet where the other players are on the ice matters somewhat to the future actions of the player who encounters the puck. Knowing where your team mates are matters even more. Hockey happens so fast that having to identify the locations and tasks of your team mates (and since no player is 100% perfect in their hockey sense the player newly in possession of the puck would still have to take time to identify all his opportunities) puts you at a disadvantage. Having a plan means you know where they should be and what they should be doing. You don’t have to think you can simply act.

One of the things I would love to incorporate into future analysis is hockey sense. The thing is three problems arise immediately when we throw hockey sense into the mix. The first is how on earth do we define hockey sense, we all talk about it, we all know it factors in to team success and game outcomes but how do you define and quantify it? Second, it seems likely the amount of hockey sense on each team in the league is, as in my comments about quality of competition above, roughly equal. Third, if every player has the hockey sense of Crosby or Lidstrom then any advantage from being Crosby or Lidstrom is removed from the analysis.

A team made up of Crosby and Lidstrom clones would be playing another team made up of Crosby and Lidstrom clones by definition. The question remains will they do worse if they have no coordinated team plan than if they have a plan that is inferior to the league average. Coordination removes guess work, players like Crosby and Lidstrom don’ t have perfect knowledge of the environment and thus must occasionally guess. In those moments knowing far out performs guessing and thus my original argument would still stand. All that would change is that the difference between no strategy and the best strategy would be smaller but not non-existent and the ranking of the approaches wouldn’t change.

I’d agree that if we stacked one team with the best players in the NHL and another with players who had never played higher than Junior B and handicapped the inferior team by saying that fthey could only have on hand on their stick while telling the NHL super stars to go out and do their own things that likely the no strategy state would beat the bad strategy state. That is, I freely admit there are states and conditions in which my analysis doesn’t apply. However, none of them occur in the NHL as it exists.

A well written, well thought out, sublime piece of blog posting if there ever was one. While am not a math(stats) guy as far as hockey is concerned, this post superbly explains to me why hockey is such a wonderfully exciting sport to follow. Even at its most basic conceptual level, hockey’s x-factor (non-transitiveness) is the beauty of life itself.

As a reference, I remember that A Theory of Ice has also touched on the subject of randomness before. I think it was in the spring but my mind may have randomly pulled that out.