## Wednesday, February 17, 2010

### Fun with math

I've been re-reading Baseball Between the Numbers, a collection of intriguing and challenging essays on our favorite game by a group of Baseball Prospectus writers (ed. Jonah Keri). In "Is Alex Rodriguez Overpaid?", Nate Silver discusses the probability of a team making the playoffs based on its number of wins. Looking at the 1996-2005 seasons, Silver found that winning exactly 80 games gave a team only a 0.8% chance to make the playoffs. Exactly 85 wins bumped it to 9.3%, but exactly 90 wins jumped that to 56.5%. Winning exactly 95 games was a sure bet (94.3%), and winning exactly 100 was a near-certainty (99.5%). Mr. Silver calls the range between 86-93 wins "the sweet spot," as a graph of the playoff probabilities shows a sharply-increasing slope in that region. He points out that "winning 90 games rather than 89, for example, improves a team's chances of making the playoffs by about 13 percent."

If winning 90 games gives us a greater than 50-50 shot at reaching the post-season, what are the chances that we will win 90 games? I figure we have about a 1-in-10 probability of winning 90, and if I multiply 0.1 times 0.5 or 0.6, I get only a 5-6% chance of an October opportunity. I do give us a 50% chance of landing in Mr. Silver's "sweet spot," which is encouraging if you think the West will be wide open and no one club will run away with it (which I believe to be the case). If I stretch my limited optimism to 2-in-10 or 20%, that doubles the result to 10-12% which still seems reasonable when I imagine Aubrey Huff and Bengie Molina chugging down the line. If you think we have a 50-50 chance of winning 90 (like JCP) that improves the chances to (0.5 x 0.5 and 0.5 x 0.6) about 25-30%. Again, this is just based on the idea that 90 wins gives you a 50-60% (actually 56.5%) chance of making the playoffs. Winning more than 90, of course, improves your chances dramatically.

Here's your homework assignment: think about the 2010 Giants chances to win 90 games and multiply that by .565 (or just cheat like me and use a range from 0.5 to 0.6). What do you think about those odds?

Zo said...

Past performance is no guarantee of future results. These are not, strictly speaking, probabilities, which would take into account all potential permutations. They are outcomes based based on history, which is usually pretty good for baseball because there is enough history to at least mostly factor out any outcomes that might skew the results, like for example a team being the third best in the National League but missing the playoffs because #1 and #2 were in the same division.

So, basically, 89-90 wins gives about an even shot at the playoffs. 90 wins is only 9 wins over .500 ball. That is 1.5 per month, or winning one game more than you lose in a span of six series. Why is that not an achievable goal? This explains why I become so upset when I hear the phrase, "It's early yet" after the Giants tank in May. Teams go on streaks but if you can keep up with a modest goal, you can find yourself within reach at the end of the season.

I don't see the Giants as a dominant team. I do see them as having the pitching rotation to keep them in enough games to achieve 90 wins. The biggest downsides I see are these: 1) reliability of the bullpen, including Brian Wilson, and 2) Bochy's ability to put together a line-up that maximizes the mediocre offensive potential. We do have positional flexibility, that's good, but he has to be able to be nimble enough to not stick with a sure out in rbi situations based on veteran savvy (see: 2009 lineup) and also not chase hitting streaks just when they are cease to be trends (see: Felipe Alou). Not necessarily an easy task.

M.C. O'Connor said...

Another way to think about it is 15 wins per month, assuming a 6 month season and 27 games per month (it goes, Apr-Oct this season, 25, 28, 27, 28, 28, 26, 3).

So we have to go 15-12, on average, each month. That's 5 wins in every 9 games.

Doesn't seem like much, does it? But last year only 4 teams in the NL pulled it off, and only 3 in the AL. The fact is that MOST TEAMS don't win 90 games. What, besides Tim, separates us from the pack?

Ron said...

As I regularly do, I must chime in now with the biggest variable of all, unaccounted for in these probability projections, which is injuries. Our biggest strength is our Starting Pitching. Unfortunately, it is the position most prone to season-changing or career-changing injuries.

God forbid we have one of those seasons when Players are going down on a regular basis. The Trailblazers are having one right now. After last season's great leap forward, & with so many young up-and-coming Players on the roster, everyone, including statisticians, were predicting lots & lots of victories. Then, people started going down so quickly that it got to the point that they could only field 8 Players for practice. They had Head Coach Nate McMillan & Assistant Coach Monty Williams playing in practice - and Nate went down with a torn Achilles Tendon. They plugged holes in the dam & pulled rabbits out of their asses in miraculous fashion until the biggest Blazer of all, Brandon Roy, went down for what is now almost 20 games now. Now, they are teetering on an edge, with a chance that they won't make the playoffs.

Obviously, injuries could affect the other teams in the Division, too. It's just that I've gotten excited so many times about the Giants or another team, just to have a big injury (whether to Noah Lowry of the Giants or Jason Schmidt of the Dodgers, to name a couple recently) change the equation substantially.

Net result: I try to force myself to look at it more game-to-game, series-to-series, month-to-month ... a bit like Zo is suggesting.

Anonymous said...

I've looked at the projections, read articles, blogs, watched people talk about it, etc. and that's really all that you can do before the season starts. The only thing that I think that I know is that the offense will be better. I'd like to think that the pitching would improve as well to even out the almost certain drop in defense, but you never know for sure. All that you can do is wait and see how things will turn out. Now, we often talk about how the Giants got better or worse this offseason, but we should put into account how the other teams have fared as well. The Cardinals lost Joel Piniero and gained a Brad Penny, the Braves lost Javier Vazquez and gained a Melky Cabrera, the Phillies lost a Cliff Lee but gained a Roy Halladay, the Dodgers lost a Randy Wolf yet retained Vicente Padilla, etc. I myself am not too scared about our pitching or even our defense, I'm just scared that I won't be able to enjoy the games as much since I live so far away. I could get an MLB.TV subscription but I won't be home enough to enjoy it. I could listen to the online radio (which I probably will do) but I'd like to actually see the games and go outside. From what I can see, this season will prove to be an exciting one, not just because it will be my first, but because there is so much that can and probably will happen with this group of guys. Who knows, maybe Zito will overcome whatever is stopping him which I'm sure is mental, and pitch like he used to. I remember hearing that he felt too much pressure from being the ace of the staff but then came Tim. Tim's the ace now but he did have a bit of a slow start last season (as did Zito), however, Matty really shined going 10 - 1 at one point. Then Zito seemed to find a groove as did JSanchez (who got chunkier according to SFG.com). So now Zito is about a #3 starter which is more or less what he was with Oakland. Will he revert back to being bad or continue to move forward? I don't know, but I can't wait to see and/or hear.

M.C. O'Connor said...

Yeah, I suppose I've beat the "probability" horse to death. Of course there are variables, like Travis Ishikawa getting hurt at home. But accounting for all that, can you put a number (albeit a rough one) on the "odds" the Giants will achieve the goal of reaching the playoffs? Do they have a better or worse chance than the Dodgers? Or the D-backs?

If I were a GM or an owner, I would be doing everything in my power to increase the odds in the team's favor. As a fan, I have to sit idly by and watch the FO do its thing, and I can't help but ask myself with every move or non-move, "does this increase our playoff chances?"

You all know by now I think the answer is "we have not done enough" because we are relying on fantastic probabilities like FSanchez playing effectively for a full season, Mark DeRosa being a slugger, and Aaron Rowand being better than Aaron Rowand. Or we are assuming that our pitching will be so dominant compared to all other pitching staffs in the league that our hitting and fielding will matter little. Possible? Sure. Probable? Less than sure, for me.

Anonymous said...

Okay, okay, fair enough. I suppose that a 50 - 50 chance is about right. Oh and the sketch is coming along.