by bkoron » Tue Aug 15, 2006 2:05 pm
In many cases, the 50/50 model works quite well. However, it can break down in extreme cases.
A board game that uses a batter's card and a pitcher's card typically has some mechanism for deciding whether a given play is resolved on the batter's card or on the pitcher's card, with the two cards coming into play with the same frequency.
If you're designing a batter's card, you have to make assumptions about the results for the 50% of the time the pitcher cards are used. Since that hitter will be facing a wide variety of pitchers over the course of a season, it's reasonable to assume that the results from all of those pitchers cards will average out to something near the league averages.
For example, let's suppose that you're designing a card for a hitter who batted .285. If the league average was .265, you can assume that the plays that are resolved on the pitchers card will produce a .265 batting average. That means you need to design the batter's card to produce a .305 batting average, so the combination of the two will produce an overall average of .285.
That's a case where the board game model works well. Let's look at one where it can break down.
Suppose the league average hitter drew a walk in 10% of his plate appearances. A starting pitcher who faced 800 batters in a season is going to see roughly 400 of those confrontations resolved on the batter's cards, so the pitcher is going to give up 40 walks per season plus whatever number of walks are generated by his own card.
That's not a problem for most pitchers, but what if you have to design a card for one of those seasons when a Greg Maddux, Bob Tewksbury, or Bret Saberhagen walked only 20-25 guys all year Even if you put zero walks on their cards, they're still going to give up 40 walks a year on the results that go to the batters cards.
Any time you have a player who produced a certain event at less than half the league average rate, the 50/50 board game model is going to overshoot the target. In addition to walks, it can happen for homers and some other stats, too.
To overcome this, a game needs to have some mechanism for allowing the two cards to interact. We have lots of computing power at our disposal, so we designed a very different model for DMB that allows the batter and pitcher ratings to interact.
It can be done in a board game, too. In the Strat-O-Matic board game, for example, they have a code that prevents weak hitters from generating homers off the pitcher cards. That's a pretty good solution, but if you don't do something like that for both batters and pitchers and for all types of events, it's not a complete solution.
I don't know how the SOM computer game works, so don't take this as a criticism of that game. I'm just making a general observation that the basic 50/50 model isn't enough to guarantee accuracy for players with very low rates for certain types of events.