Monday, May 14, 2007

Freak Show Stat: Discounted Team Wins

I am in this post going to present what Bill James used to call a “freak show stat”. They are offered in the spirit of fun, not serious research--not that they are incapable of containing any kernels of truth, but they should not be taken too seriously. Freak show stats are a dime a dozen; every kid who has played around with baseball stats has invented one. I used to use BA*1000 + RBI + HR.
Intriguingly, there are some folks out there who take their own freak show stats very seriously, and defend them vigorously, and complain when people point out that they are, well, freak show stats. See the Baseball-Fever board for a few recent examples of this phenomenon.

Anyway, I am offering up my own freak show stat here, and it is offered in that spirit. Quite frankly, I would be surprised if someone out there hasn’t done something nearly identical to what I have done here, and it has just slipped my mind. If so, my apologies.

What sparked this in my head was this post on a non-baseball message board I frequent. A Cubs fan poked fun at a Reds fan, and then a different Reds fan responded with a similarly light-hearted jab, and then some Cubs fan took it a little too seriously:

Subject: I know you make fun of the Cubs, but from a Red's fan? Com'on
Message: Since 1980
Reds have been to the playoffs twice, with only two division titles.
Cubs have been to the playoffs five times, with four division titles.
I'll give you that at least the Red's have a championship in there, but, numbers dont lie. recent history in the last 30 years or so, have the reds just as bad if not worse than the cubs.

First, I should point out that these facts are wrong, before anyone catches it--the Cubs have been to the playoffs four times and won three divisions since 1980, not 5 and 4 as the poster claims.

What drew my attention to this was the arbitrary nature: “since 1980”. What special significance is 1980? 27 years ago, so it’s not a nice round number. Things like “since the turn of the century” may still be arbitrary, but they are commonly used in making criteria for rankings, but 1980 has no particular significance in that regard either. The most likely explanation is that the period is chosen to make the poster’s point. If he had included 1979, after all, the Reds would have another divisional crown to their credit. And God forbid that the 1970, 1972, 1975, and 1976 pennant winners somehow slip in there (not to mention the 1973 division winners).

So the comparison to since 1980 has no particular value in defining a franchise’s fans ability to crow; well, one potentially, but I’ll get to that later. However, it is almost certainly true that fans get more enjoyment from their team’s recent exploits then those of past days. I’m sure that many Tigers fans would have cashed in their 1984 title for last years'.

So how to model this in a way that doesn’t involve drawing arbitrary lines? The obvious answer is a “discount rate” of some sort. Anyone familiar with any kind of interest theory at all can see where this is going, although in this case, past wins are less valuable then current wins, and future wins are irrelevant since they don’t exist yet (imagine the derision the Cubs fan would have received had he said, “Yeah, the Reds won the World Series in 1990, but the Cubs are going to win in 2009.”)

What we can do is take all years into account, but discount the wins by an increasing amount as you go back in time. At this point I should stress that I am not trying to assess the economic value of wins to teams’ bottom lines, which would be a worthwhile question. I am trying to estimate the “fan satisfaction value” of wins.

How to set a rate for fan satisfaction? You could probably draw some clues from people’s actual purchasing behavior on luxury items, like flat screen TVs and the like, or interest rates in general, but remember, this is a freak show stat, and everyone’s personal discount rate will be different. So we’ll just pick a number out of the air to illustrate the concept.

My favorite MLB team, the Indians, conveniently won the pennant exactly ten years ago. So I asked myself how much the satisfaction of the memory of that event, which I still have, would be worth to me in terms of a pennant for the Indians this year. I decided that 75% of a pennant this year would be worth the 1997 pennant. Then you can find the “interest rate” by solving:
.75 = 1/(1+i)^10

i works out, conveniently, to be 2.9%, which I’ll call 3%. So that is our conversion factor between past and present wins. Under this assumption, I would be willing to trade 100 wins last year for 97 wins this year (100/1.03). 100 wins ten years ago are worth 74 wins this year (100/1.03^10), and so on.

Just using wins doesn’t factor in championships at all. One could (again, pulling numbers out of the air) make a playoff appearance worth an additional 10 wins, a pennant worth 20, a World Series worth 40. Or you could just discount the championships themselves. The Cubs’ win in 1908, 99 years ago, would be worth 1/(1.03^99) = .054 2007 world titles. You can think up any number of ways to apply the basic concept.

Before I do a comparison of the Reds and Cubs, I want to go back to something I mentioned further up the page, which is that I can think of one reason why 1980 might be a legitimate starting point for a comparison on these grounds. That is if, in your specific case, wins in 1980 are irrelevant. I was not alive in 1980, so the Indians could have won the World Series and it would mean nothing to me (well, in terms of real experience at least; I could still draw pride as a fan of the team from our great history, but it wouldn’t be a memory that I would have, or a t-shirt that I bought the next day, etc.). I was alive in 1992, but not yet a baseball fan; that would mean nothing to me either. So it would make sense to start my personal comparison from 1994.

Anyway, back to the Cubs and Reds. I will ignore strike-shortened seasons (although you could just discount W%; as I’ve said, there’s any number of ways you can do it, and since it’s just a freak show stat, you can do whatever you want), and just discount all of their wins since 1980.

The Cubs won 2016 games over that period (excluding the current season); the Reds 2117. That’s a ratio of 1.05 to the Reds. The discounted team wins are 1378 for the Cubs and 1435 for the Reds; the ratio is 1.04 to the Reds. So the Cubs come out a little better by discounting wins, but not significantly so, and the Reds have the upper hand either way.

The figure “1378” is garbage; it’s just a number with no inherent meaning on its own. One could play around with the math and express everything in terms of a number that at least had a scale you understand (ala EQA) fairly easily, but it defeats the point of having a freak show stat to some extent.

Let’s do a quick Reds/Cubs championship comparison. First, we’ll look at that period, but count all playoff appearances as a value of 1. The Cubs win this 2.7 to 1.3. But let’s weight the various levels of success differently. 1 for a World Title, .4 for a pennant, .25 for a playoff appearance, and you only get the maximum of the three potential points (i.e. the Cardinals get 1 point for winning it all last year, not 1+.4+.25). Again, you can make up whatever weighting scheme you want.

With this one, the Cubs have 1 point non-discounted, while the Reds have 1.25. The discounted points are .78 to .69 for the Reds, which cuts the ratio from 1.25 to 1.13, but still leaves the Reds on top.

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