Andre Ethier vs. Raul Ibanez

There are two spectacular hitting streaks going on in baseball right now. One has Andre Ethier playing strong with hits in 27 straight games. The other has Raul Ibanez going 0 for his last 34 at bats. PTI just asked which one is more impressive, and with a little help from probability I aim to answer that here.

This season the league-wide MLB batting average is .250. That's interestingly considerably below the usual league total which got as high as .269 in 2006. However since we're looking at which is more impressive (less likely) in the MLB this year, I think .250 is a good number to use.

For Ibanez, it's simple to just take .750^34 to get his odds. The chances of going 0 for 34 over any given set of 34 at bats is just 5.65*10^-5, a very small number. On the other had, with well over 5000 at bats in any given year, there are many chances, so it should happen every 3 or 4 years.

For Ethier we have to make some assumptions about his at-bats per game. He has 111 at bats over his 29 games this season (slightly less than 4 per game). While average doesn't work perfectly because it's especially hard to get a hit with just 2 or 3 at bats, some games he may have been taken out only because he already had a hit. The two cancel out, so we'll go with 111/29 at bats per game. He then has about a 2/3 chance of getting a hit in any given game, and a 1.82*10^-5 chance over any 27 game stretch. Even without compensating for few chances, that's less probable than Ibanez's streak. Overall, Ethier 27 game hit streak is less likely for an average player, and therefor more impressive.

How often does the best team win?

A couple months ago I asked how often the best team wins the world series. It turned out to be a surprisingly low percentage, and with the wacky final four I started asking the same questions about college basketball. Using the random chance in sports method to determine how often the best team won I calculated the probability of the best team being champion. Naturally it extrapolated itself to all sports:

NBA: 81%

This is by far the highest, and also the most wrong. Single teams don't distance themselves as often in the NBA, and some research I did in high school suggests that better teams win 60% of finals games, not 80%. Adjusting for that in the last two rounds puts the odds at around 48%.

College Football: 57%

People rag on the BCS, but I showed during BCS week that small playoffs are often better at selecting champions. Again, adjusting for using only the top teams and not the general random chance lowers the odds to 47%, which is still pretty high.

NFL: 55%

Even though this is the pro sport where the best team wins most often, single elimination hurts it. Byes help though (these odds assume the best team gets a bye). Assuming that the best team only wins .7 of the time (better for the playoffs) lowers the odds to 42%

You may be laughing now because I've corrected the random chance odds for each sport so far. It's much more accurate for the remaining sports though, either because top teams distance themselves farther (MLB and NHL) or because there is a full range of opponents in tourney play (MCBB and WCBB).

Women's College Basketball: 36%

We're probably a little thrown off because of UConn's recent success, but actually with 6 rounds of play even the women's tourney is ripe with upsets.

MLB: 33%

Series' are a necessity in a sport where even the worst teams win almost 40% of their games. The first round should probably become a best of 7 to help that out (it'd boost odds about 5%).

Men's College Basketball: 28%

We've seen this on full display in the tournament, as the clear best three (Ohio St, Kansas, Duke) have all fallen to lesser opponents. 6 rounds is fun though, so it's worth diluting it, but a 7th in the future would be a stretch.

NHL: 28%

This may seem weird with many former dynasties like the Canadiens, but in reality the modern day NHL is as full of parity as baseball, and with an extra round the best team's chances are the worst of any major U.S. sport.

Ron Santo

On December 2nd Chicago Cubs great Ron Santo passed away at the age of 70. Possibly the greatest player ever not to be in the Hall of Fame, Santo played in 9 all-star games at 3rd base during the 60's and early 70's. Statistically, a quick look at http://www.baseball-reference.com/players/s/santoro01.shtml shows that he matches up pretty evenly with the average hall of famer, and fairs even better in advanced statistics like Win Probability Added. As he showed in his broadcasting career though, Ronnie was never about just numbers, he was about love of the game, and love of the Chicago Cubs. And Cubs fans in return loved Ronnie:

And some great radio highlights of Ron Santo:

RIP Ron Santo 1940-2010

Random Chance in Sports

This post is a followup to Random Chance in the NFL which highlighted the lowered competition in the NFL this year. It showed that the best teams win 62% of the time this year, far less than previous years. How often the better team won in previous years and in other sports were still left unknown though. Until now. Here, using the same methodology focusing on variance, here are the data on the last three full seasons in the four major american sports:

	2008	2009	2010
MLB	0.59	0.6	0.59
NBA	0.77	0.77	0.75
NHL	0.56	0.61	0.61
NFL	0.8	0.8	0.78

On average the better team wins 60% of the time in MLB, 77% in the NBA, 60% in the NHL, and 79% in the NFL. But how about this year? How often does the best team win in the NFL this year? It's gotten better since the last look, so far this year in the NFL the better team wins 70% of the time. While this is still an unprecedented increase in parity, it is also slowly getting closer to the norm we'd expect, thanks largely to big losers like the Bills and Panthers. So while this NFL season may have some crazy outcomes, it's still less random than sports like Hockey.

This article originally ran with a bug in the program used to calculate variance. While the effect on previous season results was minimal, it messed with the current season results a lot. The NFL is not actually just random chance this year, although going with just home field advantage would still be pretty good.

Does the best team win the World Series?

Congratulations to the World Champion San Francisco Giants! Here at Kobe, Tell Me How My Stats Taste we've been following the Giants all year, and while we're disappointed that our game 7 tickets now have no value (joining game 5 against the Braves) we're still excited by the outcome.

Some people though (Philllies fans) have expressed doubt that the Giants really were the best team. How often does the best team in baseball win the world series? Let's check it out.

Let's assume that the best team gets to the playoffs (a pretty good assumption).

Next let's assume that there's no home field advantage, because it'd be a pretty even chance that the best team would have the advantage (world series determined by all star game).

As a result, I've created a table, based off the likelihood that the better team wins (calculated similar to the Random Chance in the NFL article).

Chance of Better Winning	Best as Champs
0.55	0.212
0.57	0.257
0.59	0.306
0.61	0.359
0.63	0.415
0.65	0.473

Just a small change makes a big difference, but from the past we've learned that the better team usually wins 60% of the time. That means that the best team wins the world series about 1/3 of the time. So are the Giants really the best team in baseball? Maybe not, but they are World Champions.

Can someone also explain why Renteria and not Lincecum was World Series MVP?

Cubs Futility

A couple of buffoons trying to insult the great city of Chicago today got into an argument. Which is more amazing, the Cubs not winning a championship since 1908, or the Cubs not winning a pennant since 1945? I felt like the Ghostbusters running into Nearly Headless Nick.

What made the comparison tricky is that the number of MLB teams has changed over time. Sure, 65 > 102/2, but it's not that simple because all the years between 1908 and 1945 there were only 16 teams! How could the Cubs not win then?! Looking at all the changing teams, here are the odds (data on teams from FlipFlopFlyBall a great website for baseball fans).

Chances of not winning since last win:

World Series: .00466 or about 1 in 200

Pennant: .00203 or about 1 in 500

Expected wins since last win:

World Series: 5.22 since 1908

Pennant: 5.89 since 1945

So it turns out that not winning a pennant since 1945 is more amazing, even if only by a little bit. But what I really get out of this is that the Cubs are incredibly unlucky. And that despite basic probability laws, the Cubs are due for at least 5 World Series titles.

500 Home Runs

ESPN the Magazine ran an article recently on players shooting for certain milestones, and the ability to tell statistically. They covered 300 wins, and 12,000 yards (this is a milestone?) but they missed the biggest milestone in all of sports: 500 Home Runs.

Can it be shown statistically that MLB players hang on to get 500 home runs? Lets look at the breakdown for retired players home run totals, grouped by hundreds:

Reached	Actual	Expected
700	3	2.1
600	3	4.9
500	16	11.3
400	16	26.3
300	69	61.1
200	168	141.9

While 500 has more than expected (Calculated with exponential trend lines), and 400 in noticeably less, assuming Poisson distribution neither is statistically significant.

Breaking it down into bins of 25 though gets interesting:

Reached	Actual	Expected
600	1	1.42
575	2	1.76
550	3	2.19
525	3	2.72
500	8	3.37
475	4	4.18
450	3	5.19
425	7	6.44
400	2	8

500 home runs is much higher than expected, and strangely 400 home runs in much lower. Both are now statistically significant at the 95% level. What does this mean? It appears that some players do purposefully try to reach 500 home runs (You think Eddie Murray plays to 41 without that?). Oddly, it also appears that there's a barrier at 400, nobody wants to just barely make 400 home runs. I suppose we may get a few more years than expected out of Carlos Delgado (473) and Vlad Guerrero (434).

Giants in the Playoffs?

For weeks now I've been waiting for the Giants to overtake the fluke Padres and to give me a chance to watch the MLB Playoffs in person. But as the season goes on, it's still not happening. Why? Turns out they've actually been a little unlucky, their run differential indicates they should have 76 not 75 wins. What are the chances that the Giants can overtake them?

Assuming pythagorean winning percentages (RS^2/(RA^2+RS^2) estimates winning percentage well, and predicts future success) play out for the rest of the season, it turns out that the Padres will probably win 7 games more than the Giants, and the Giants only have a 3.8% chance of winning the NL West.

Can I take Solace in the Wild Card? The Giants are tied for first place there, but the Cardinals who are a couple games back have been very unlucky this year. Doing a three team simulation between the Cardinals, Giants and Phillies the following Wild Card odds appear:

SFG: .337

PHI: .323

STL: .341

Turns out first place is only a slight advantage, it's actually a tight three way race. Which unfortunately means that I have at best a 37% chance of watching the Giants in the playoffs. At least it's better than the Cubs.

Self Lineup Runs

Who's the best mlb hitter this season? We looked already at Ken Griffey Jr.'s best years using a lineup full of Griffeys. Now, through yesterday, I've looked at the same statistic (which I've decided to call "Self Lineup Runs" or SLR. Please suggest better names.) for the best hitters in baseball. Here's a look at how those with the top 10 OPS fare in SLR:

	Player	Team	SLR
1	MORNEAU	MIN	11.016
2	YOUKILIS, K	BOS	9.819
3	CABRERA, M	DET	9.352
4	ETHIER, A	LAD	8.962
4	CANO, R	NYY	8.959
4	PUJOLS	STL	8.952
7	RASMUS, C	STL	8.296
8	ZIMMERMAN, R	WAS	7.923
9	KONERKO, P	CHW	7.893
10	ROLEN, S	CIN	7.421

Interestingly, for those who know the stats above, this is very closely related to OPS (On Base Percentage plus Slugging), but even closer to 2*OBP + SLG. This correlation was suggested in Wayne Winston's book Mathletics, and will be looked into more later.

Note: Although Ethier, Cano and Pujols don't have the same SLR, it's effectively a tie because of variance in the simulation. Running it again once actually put Pujols ahead of the other two, so it's too close to call.

Ken Griffey Jr.

With the retirement of Ken Griffey Jr. last week baseball lost one of it's best and most liked players, one who even made it through the steroid era unscathed. But just how good was he, and when was he best? Sounds like a perfect time to debut my new baseball simulator program! The program plays a full nine innings with up to 9 batters using singles, doubles, triples, and home runs (it has yet to include speed things like stolen bases and advancing an extra base, and it counts walks as singles). Putting in a player's stats for a year then having them bat over and over repeatedly for a game gives a good indication of how good a player is at swinging away. So, how good was Griffey? Here's the results by year ("runs" being the program calculated category):

	YEAR	TEAM	OPS	RUNS
GRIFFEY JR	1989	Sea	0.74896	3.862
GRIFFEY JR	1990	Sea	0.84987	5.274
GRIFFEY JR	1991	Sea	0.93168	6.8
GRIFFEY JR	1992	Sea	0.89248	5.661
GRIFFEY JR	1993	Sea	1.02355	8.356
GRIFFEY JR	1994	Sea	1.07558	8.828
GRIFFEY JR	1995	Sea	0.85999	6.146
GRIFFEY JR	1996	Sea	1.01857	8.006
GRIFFEY JR	1997	Sea	1.02992	8.006
GRIFFEY JR	1998	Sea	0.97242	7.037
GRIFFEY JR	1999	Sea	0.95552	7.117
GRIFFEY JR	2000	Cin	0.93908	7.081
GRIFFEY JR	2001	Cin	0.89663	6.045
GRIFFEY JR	2002	Cin	0.78522	4.621
GRIFFEY JR	2003	Cin	0.91595	6.458
GRIFFEY JR	2004	Cin	0.86276	5.713
GRIFFEY JR	2005	Cin	0.95036	6.746
GRIFFEY JR	2006	Cin	0.8019	4.682
GRIFFEY JR	2007	Cin	0.8741	6.029
GRIFFEY JR	2008	Cin/CWS	0.7761	4.583
GRIFFEY JR	2009	Sea	0.7333	4.183
GRIFFEY JR	2010	Sea	0.45506	0.712
GRIFFEY JR	Total	--	0.90428	6.264

It turns out that Griffey's strike shortened 1994 season was his best, even better than his 56 home run performances in 97 and 98. How does this compare to other players? The average for the MLB so far this year is 3.68 runs (meaning this program is about half a run too low, most runners go second to home on a single) so even Griffey's worst years were better than average. Amongst other Seattle greats Griffey's '94 (8.83) is better than both A-Roid's '96 (8.41) and Ichiro's '04 (5.39). Still, Junior's not quite on Pujols's level (10.93 in 2008) and a long was behind former greats like the Babe (a whopping 17.63 in 1920). Nevertheless, with his 10 Gold Gloves, 184 stolen bases, and 630 home runs I'd take Ken Griffey Jr. on my team anyways.

Good suggestion Woozle.

Perfect Games

Poor Armando Galarraga. Today should've been a perfect game. However it'll still go down as one of the closest calls ever (Hey MLB, can we just fix the call and make it a perfect game?). Had Jim Joyce made the right call we would've had the third perfect game this season, and we're not even halfway done. What're the chances of that?! Funny I asked...

The key is on-base-percentage (we're not gonna count errors, dropped third strikes, etc.). There has to be 27 consecutive outs. Also useful is that there are 3,240, and about 345,000 all time. For the stats savvy I'm also assuming that perfect games follow poisson statistics, which can be a dubious assumption for low end odds.

The following stats are against MLB average, Yankees (best team), Houston (worst), Justin Morneau (best batter), Aramis Ramirez(worst, of course), and with each of the three "perfect" game pitchers.

Who	OBP		Expected		3+		All-time
MLB	0.33		0.065247621		4.40885E-05		6.966794621
Yankees	0.366		0.01468774		5.22314E-07		1.568278894
Houston	0.286		0.363409878		0.006106128		38.80297759
Morneau	0.487		4.82741E-05		1.86517E-14		0.005154448
A-Ram	0.227		3.100211665		0.598882668		331.0241437
Galarraga	0.218		4.237672039		0.794695585		452.476124
Halladay	0.258		1.02671629		0.08528064		109.627315
Braden	0.277		0.509658225		0.015130549		54.41859965

Because you get to have good pitchers against bad teams every once in a while, I'd suspect the odds of the number of perfect games are roughly equivalent to Houston (there are 18 perfect games in the modern era, plus a couple others that might've qualified in these stats), so we should have three perfect games in a year once every 200 seasons (actually as low as every 100 because poisson stats are kinda inaccurate here). That's more often than you think? Remember, there's now 30 teams in the league, many more than earlier, so more games. Also, this year's league average OBP is the lowest since 1992 (although roughly average overall. Can you say steroids?).

And in good news for Galarraga, let's suppose he pitches 30 starts a year for 15 year (a solid career). If he continues his opponent OBP of .218 (the lowest among league starters), he has a 44.5% chance of pitching another perfect game. Of course, with an OOBP like that, he'll also be the best pitcher of all time.

Good suggestion Greg.