Tuesday, April 29, 2008

Math for Winners

One of the most important things that you can do in a Roto league is to figure what you will need to win. Those requirements then help you narrow down what you can reasonably try to do, as you shape your overall strategy.

A quick examination of the 1st and 2nd place scores in previous UPL roto leagues is offered below:


Year Teams Max 1st 2nd Mid Last
Baseball 2003 11 132 114.5 107 70 38.5

2004 14 168 146 128 93 43

2005 12 144 114.5 108 86.5 38

2006 11 132 114 107 73 38

2007 11 132 104.5 104.5 70.5 41.5
Basketball 2004 7 70 58 53 40 19

2005 8 80 55 55 49.25 18

2006 10 100 89.5 71 53.75 30

2007 12 120 87 83 66.5 28.5

Note, I've included scores for the 1st, 2nd, and last place teams, as well as the median score in the league (an average, if there are an even number of teams). Perhaps, a more useful table is this one:


Year Teams Max VMargin 1-Avg 2-Avg 1-%Max 2-%Max
Baseball 2003 11 132 7.5 9.54 8.92 0.867 0.811

2004 14 168 18 12.17 10.67 0.869 0.762

2005 12 144 6.5 9.54 9.00 0.795 0.750

2006 11 132 7 9.50 8.92 0.864 0.811

2007 11 132 0 8.71 8.71 0.792 0.792

Avg 11.8 141.6 7.8 9.89 9.24 0.837 0.785
Basketball 2005 7 70 5 5.80 5.30 0.829 0.757

2006 8 80 0 5.50 5.50 0.688 0.688

2007 10 100 18.5 8.95 7.10 0.895 0.710

2008 12 120 4 8.70 8.30 0.725 0.692

Avg 9.25 92.5 6.88 7.24 6.55 0.784 0.712

What does this table tell us? A couple things.

First, most seasons, the margin of victory isn't that huge. About 8 points for baseball, and about 7 points for basketball. Of course, this is skewed just a bit by two huge seasons (2004 in baseball and 2006 in basketball) where there was a huge difference between the top team (the O.N. Thugs) and the field (aka, Everyone Else). Take out those ridiculous seasons, and the differences become 5 points in baseball and 3 points in basketball. So, assuming that the top teams are close in talent, it's the small differences that will add up.

Next, look at the "Avg" rows. These are just the averages for the values above them. All the way to the right, you see the percentage of points that the 1st and 2nd place teams. The average %Max of the 1st place teams will almost certainly (probably in a 95% confidence interval, if I had to guess) lock up a victory, while the %Max of the 2nd place team may get you there (basically, 50-50).

Remember, we run 12 categories in baseball and 10 in basketball. So, in baseball, 84% of the possible points will probably lock things up, and 80% may still win it. For a 12 team baseball league like we have this year, you figure that 122.5 points will very likely result in victory, while 115 will probably get you there. In basketball, it seems that 79% will most likely get you the victory, while 72% gives you a good shot, so for a 12 team basketball league, like we just had, you're looking at 95 points to be firmly on top, and 86.5 will give you that 50-50 shot at victory. In terms of average placement in each stat category, if you look at the 1-avg and the 2-avg columns, you see that winning teams placed, on average, just under 3rd place in every category in baseball, and right at 3rd place in basketball. This suggests that basketball is a little tighter than baseball, though there isn't anything conclusive as to whether this is the nature of the scoring, the nature of the sport, or the nature of the individuals playing (all could be reasonable assertions).

When you are playing for a championship, I believe that you should project things out as points that you surrender from the max, rather than points that you acquire from scratch. This makes the problem much more constrained, which helps you formulate possible strategies (other than just auto-drafting and hoping for the best). And it sort of assumes winning, which is a good attitude to have. So, for baseball this year, you figure that you can surrender at most 30 points, if you want to have a legit shot at winning. And in the just completed basketball season, you can surrender up to 33.5 points.

Obviously, knowing what you can surrender, and still win, shapes your decisions. Some things become obvious. Let's look at baseball. You can only surrender 30 points. This kills some potential strategies.

You probably can not do the "All Closers, no Starters" pitching strategy. In this case, if things optimally, you will get max points in SV, WHIP, ERA, and L. However, you likely end up with only 1 point in W and K, respectively, since your IP will be much lower than everyone else. And if you try to get back points in W and K, you will likely lose ground in WHIP and ERA. This strategy, optimally executed, will lose you 22 points. You will have to be close to perfect on offense to stand a chance. Similarly, if you overload on speed, you will likely surrender too many points in HR, SLG, and RBI to give yourself a legit chance.

Now, this restriction even comes into play when you look at more reasonable strategies. If you go the dominant pitching route, you run into a problem. Note that high numbers of W will likely result in high number of L's. That's the nature of the beast. Even in an ideal scenario, if you max out on W, you probably won't be able to do much better than 4th place in L. So, even with elite pitching, you going to surrender at least 3 or 4 points. On the other hand batting is possible to max out. This suggests that elite hitting is a better route than elite pitching, all things equal. Of course, all things aren't equal, and you have to weigh out how the best hitters and pitchers are distributed.

So why bother with this post? I think that it's useful to frame how you plan out a season, so that you know have a better idea as to what moves you forward, and what does not. And it also helps you frame more specific strategies, which we'll talk about down the road.

-Chairman (aka O.N. Thugs)

3 comments:

Greg McConnell said...

In hindsight, there are two reasons my fantasy baseball teams struggled mightily from 2002 to 2005.

First, after 2001, I had gotten a bit arrogant. If you'll recall, I drafted Cory Vance in a late round in 2002 just because I could. Seriously, I wasn't putting a premium value on every single roster spot like I do now. Also, I had made no adjustment for the switch to a 6x6 roto format (instead of the straight stat accumulation we did in 2001).

After losing in 2002, my main thought was something along the lines of, "Oh well, you can't win them all." (Although I do think my frustration level was high in August or September because I dropped my entire team and you had to invoke a special commissioner tool to restore league order.)

The 2003 season was much of the same... my team started to struggle and I blamed the players or bad luck, not myself. After all, I had been "smart enough" in 2001 so it was just a matter of getting another hot streak...

I think it was sometime during the 2005 season as you completed a 4-peat and I was suffering through my fourth straight season of mediocrity that I finally decided that this wasn't a matter of bad luck. I had a methodology problem, and my fantasy baseball strategy was in need of a major overhaul.

Sure, I had made a few adjustments from 2002 to 2005, such as noticing how you (and others in the league) maximize the value of your DL slots. At almost all times you would have both of your DL slots stashed with "assets" of some value or potential value down the road, and I began to incorporate that strategy too.

But it was sometime during 2005 (or at least before the 2006 season) that I decided to re-think everything; and this process was a two-pronged approach.

First off, if there was an "epiphany" involved here, it was that I finally realized that the league's scoring had changed in 2002 yet my overall strategy hadn't. What was it about the scoring change that could be affecting my team's performance year in and year out?

I quickly realized (well, if 4 years counts as quickly) that in our old scoring format, it was theoretically possible to beat your opponents into submission (and win) by dominating just a single category. For instance, in theory, under our old scoring rules if one player on your team got a million steals in a season you would win the league no matter what anyone else did (unless they got a million steals too, but come on, what's the likelihood of that happening twice?). Under our new scoring rules, a million steals would just give you a one point advantage in a single category over the nearest player in that category.

In 2001, I had Barry Bonds hitting home runs "for two," and I had Randy Johnson racking up K's "for two." In certain categories my team started to really dominate, and that enabled my stats to essentially overflow and cover for other areas where my team was weaker.

And that's where I came to my first big change. In a roto league, you can't "overflow" any categories into other categories. Instead, each category is a bucket, and while you want to fill that bucket as much as you can, there's no sense in trying to overflow it.

So how to fill the buckets? Well, that brings me to the second prong. I knew there was this guy in the league who kept winning it year after year. Maybe I should pay close attention to how he drafts, how he handles transactions during the season, and what his winning stats look like at season's end?

Yes, Roland, just like the time the American spy plane made the emergency landing in Hainan and fell into the hands of Chinese authorities, I reverse engineered your team.

The first thing I noticed was that having a high OPS seemed to be the cornerstone of your championships; and OPS was an area where my teams tended to struggle. Yeah, I could draft a big bopper or two, but I wasn't doing a good enough job of having the team OPS effort.

So why had my teams lacked in OPS? Well, back in 2001 I viewed fantasy baseball through a "real baseball" perspective. Pitching wins championships. And I had won a championship with that strategy, so why change? In the years that followed, I kept following a philosophy that pitching was at a premium, and I'm going to dominate pitching. Somehow, some way I'll scrape together enough on the hitting side to pull out a championship in the end--at least that's what I thought. But what really was happening was that while I tended to do very well in pitching, my offense was usually below average.

Starting in 2006 I began looking much more closely at OBP and SLG when I drafted, although I still was clinging somewhat to my former "pitching wins championships" approach as I drafted Johan Santana with my first pick.

As it turned out, by scouting for and drafting OPS in 2006, my team got off to its best offensive start in five years--and I knew that I was onto something.

Granted, back in 2001 I did have a great team and it would have translated well scoring-wise in a 6x6 roto (I think). However, it certainly wouldn't have dominated in the same way. And perhaps more importantly, it wouldn't have given me the false sense that I knew what I was doing in fantasy baseball

I keep tinkering with my strategy, and granted, I don't always stick to my game plan when I should. However, at least I've made a bit of progress since 2002. ;-)

Chairman said...

It's interesting, though. At some point, I thought that pitching got to be so undervalued that it was worth loading up on. I think that in 2004 (which I think was the most dominating fantasy team that we've had in the UPL - I was up by something like 35 points on the field by the end of July), I actually went pitcher, pitcher, pitcher in the first three rounds (Unit, Pedro, and Schilling), dug up whatever hitting I could, and then picked up a bunch of so-so closers.

A part of this may be more related to scarcity at different positions. I think that I tend to weigh positional considerations more than others (as evidenced by my trend of picking I-Rod way too early, in years past, and my current infatuation with Chase Utley), which I've got on my list of "boring nuts and bolts fantasy analysis that I'll spend way too much time on that won't be understood by anyone, and only read by C-Lauff."

Greg McConnell said...

A part of this may be more related to scarcity at different positions.

Yeah, 2B and C are two positions where you can really separate yourself from the pack. Last year when I drafted Posada in the 14th round, I commented that it was my best "value pick." (I think Rupert then said, "No, Wang in the 11th...") As it turned out, Posada was far more of a value pick than I could have imagined--and catcher was a position where I dominated most of the field (although CLauff got great numbers from Martin as well).