Ichiro 200 hits, probabilistic model Options

[Pirata Morado]

I had some spare time today, so I decided to update my probabilistic model for Ichiro reaching 200 hits yet again. I think that the fact that he missed 8 games is a serious issue that can alter his chances, but he has started off nicely this 2009 with 10 hits on 33 AB, for a .303, of course the sample size is very small yet, but we all know how he heats up in May.

Anyway, here's what my model does:

For each of the remaining games (Remaining Games = 162 - IchiroGames - 8), which right now stands at 146, I simulate the number of possible at bats Ichiro might have. For this I'm using a discrete distribution based upon last year's distribution of AB per game, which is the following:

AB, Frequency
2, 3
3, 24
4, 71
5, 54
6, 9

Where 4 AB is the most frequent, but it allows for different number of AB per game (from 2 to 6)

As a second step, I simulate the number of hits he might have on each game. For this I used a binomial distribution. The binomial distribution counts the number of "success events" out of n trials. In this case, a hit is a successful event while an at-bat is trial. The binomial distribution has 2 parameters which are n=number of trials, and p=probability of a successful event. So all we need is to determine p. I will update this model frequently with 2 options for p. The first scenario for p will be to use his actual 2009 batting average as an estimate of p. The second approach will be to use his career batting average.

Then I will run 5,000 iterations (like if I had 5,000 different "whole seasons") in which for each one of those I will have a different and random amount of total hits. We can estimate the probability of him reaching 200 hits, simply by counting on how many of the iterations he actually exceeded 200 hits. Simple, right?

Results will follow, I'll update this thread frequently as the season progresses.

This post has been edited by Pirata Morado: Apr 24 2009, 12:53 PM

[Pirata Morado]

OK, on to the results. This is a histogram of the iterations, on red you'll see the "career" model, which uses a parameter for p=.330, i.e. his career batting averge. The purple histogram is the "actual" model, which uses a parameter for p=.303, his actual batting average (2009).



You'll notice that under the "actual" model, his probability of reaching at least 200 hits = 43% (the right hand tail), you can't see the right tail for the red distribution, but the probability for the "career" model = 89%.

The histogram also shows the high variability in the total hits, under both models, due to the fact that the season is very young (from 185 to 260 in the RED model). But the expected number of hits for the purple model = 198 hits (just below 200), and for the red model = 215.

[SABR Matt]

Interesting, but the probability of Ichiro hitting .303 is very small IMHO. I think he'll hit at least .315 which has implications for his probability of reaching 200 hits.

[Pirata Morado]

Well, at least you know now the odds of that happening in case you want to bet on it.

I wonder is ther such a bet in Las Vegas?

By the way you can also follow this on my blog: Pirata Morado's blog

This post has been edited by Pirata Morado: Apr 24 2009, 05:13 PM

[SABR Matt]

You might be able to make money betting on Ichiro getting 200 hits this year. Missing 8 games makes it "interesting" for the first time ever. LOL

[DrNaka]

Well, at least you know now the odds of that happening in case you want to bet on it.

I wonder is ther such a bet in Las Vegas?

By the way you can also follow this on my blog: Pirata Morado's blog

Interesting that the standing now for AL West is about the reverse of all the projection in your blog.

As for Ichiro what would be the projection for 100 Runs and 30 SB?

[BatGrrl66]

I would check your site out Pirata, but I understand about every tenth word you say! I am thinking I may be a bit average. (Damn Math head geek, it would be horrible if you did not speak English better than myself).

I would be willing to bet $50.00 US no matter the odds.

This post has been edited by BatGrrl66: Apr 24 2009, 11:47 PM

[Pirata Morado]

Interesting that the standing now for AL West is about the reverse of all the projection in your blog.

As for Ichiro what would be the projection for 100 Runs and 30 SB?

Well, everything seems upside down, right now, have you notice that the Pirates are playing good baseball?

I don't have a model for Runs and SB, but when I have some spare time, I'll do a model for those.

[Pirata Morado]

An update on Ichiro's probabilities after the games of the weekend.

After 11 games, Ichiro can only play in 143 remaining games. His BA right now = .333, which is a little bit higher than his career BA (.33), so the probability is higher now for the 2009 Model.

Probabilities:
2009 Model: 93.88%, expected hits = 219
Career Model: 90.88%, excpected hits = 217.

It changed a lot during the weekend since Ichiro hit .400 (6/15) in those 3 games at Disneyland.

This post has been edited by Pirata Morado: Apr 27 2009, 05:39 PM

[SticksWa]

Thanks PM! I always enjoy you doing stats like these.

[Pirata Morado]

Thanks PM! I always enjoy you doing stats like these.

Thank you very much! I always appreciate kind words like these!

[kevin_ess]

Great stuff, my friend. You're a valuable part of this site.









Wish I was!

[Pirata Morado]

Great stuff, my friend. You're a valuable part of this site.









Wish I was!

Thank you Kevin, I appreciate your words!

Hey, you too are valuable, your jokes are hilarious, I enjoy them pretty much. Everbody gives something valuable to this great site!!!

[Pirata Morado]

An update:

Ichiro has played in 17 games so far, so he has a potential of 137 more games. So far he has 24 hits on 79 AB, for a .304 average.

Under the current 2009 model his probability of reaching at least 200 hits = 53.5%; expected total hits = 201.
Under the career model the probability is stable = 91.24%; expected total hits = 217.

[Pirata Morado]

Another update, as things get very volatile this early in the season.

Parameters: 19 GP, 135 Games Remaining. p = 0.291 (25/86), Probability = 22.7%. Expected Total Hits = 192

[Bandwagon Fan]

My early take on Ichiro 2009:

Running speed is clearly improved over 2008, which was down even before the hamstring injury that forced him to miss a start in July. His speed may be at the level of 2007 at its best. A tremendous positive development.

Ichiro's ability to hit a fastball continues to erode to the point where he is only an average fastball hitter overall and a poor fastball hitter when he is in a slump. Instead of pitching inside, you will see the book on Ichiro will be to throw him high fastballs. Very occasionally he will hit one out but vastly more often he will hit weak popups and fly balls.

His walk rate was horrible in April. I'm surprised the haters haven't charged him with giving up on walks in order to catch up on his 200-hit goal. Certainly suspicious.

As has been noted, much reduced Isolated Slugging, an inability to hit .400 for four weeks or longer (he did not accomplish this in 2008), surviving on infield hits. Continued poor pitch selection and approach with 2-strike or 3-ball counts. His ground ball/fly ball approach, however, has been strong so he is making the most of his reduced physical abilities.

Overall this is the picture of Ichiro in decline. We are not seeing the switch to hit for power. We are not seeing the improved pitch selectivity. We are not seeing innovations in swing, training or equipment. Overall, he remains a contributor but, Geoff Baker's hopes notwithstanding, he is no longer a prime catalyst. What we see is what we get.

One view.

This post has been edited by Bandwagon Fan: May 6 2009, 09:52 AM

[Pirata Morado]

Fun stuff to follow Pirata.

Thank you!

[Pirata Morado]

Let's do another update since Ichiro had a good day yesterday.

21 games played, 133 remaining. 95 AB, 30 hits for a p = 0.316

The following chart is a time series of the probabilities under both models:



As you can see, the probability rose to 76.7% yesterday from a 35% that was the day before, thanks to a 3 for 4 day! We also can notice the high variability of the 2009 model because p is varying a lot from one day to the next one. It will be fun to watch how the spread will tend to reduce in time.

[Sandy - Raleigh]

My early take on Ichiro 2009:

Running speed is clearly improved over 2008, which was down even before the hamstring injury that forced him to miss a start in July. His speed may be at the level of 2007 at its best. A tremendous positive development.

Ichiro's ability to hit a fastball continues to erode to the point where he is only an average fastball hitter overall and a poor fastball hitter when he is in a slump. Instead of pitching inside, you will see the book on Ichiro will be to throw him high fastballs. Very occasionally he will hit one out but vastly more often he will hit weak popups and fly balls.

His walk rate was horrible in April. I'm surprised the haters haven't charged him with giving up on walks in order to catch up on his 200-hit goal. Certainly suspicious.

As has been noted, much reduced Isolated Slugging, an inability to hit .400 for four weeks or longer (he did not accomplish this in 2008), surviving on infield hits. Continued poor pitch selection and approach with 2-strike or 3-ball counts. His ground ball/fly ball approach, however, has been strong so he is making the most of his reduced physical abilities.

Overall this is the picture of Ichiro in decline. We are not seeing the switch to hit for power. We are not seeing the improved pitch selectivity. We are not seeing innovations in swing, training or equipment. Overall, he remains a contributor but, Geoff Baker's hopes notwithstanding, he is no longer a prime catalyst. What we see is what we get.

One view.

Outstanding even-handed analysis. Great job!

[Pirata Morado]

An update after a magnificent weekend by Ichiro:

First off, the parameters: Games = 30, At Bats = 134, Hits = 43 (thus p = .321)

Probability of reaching 200 hits = 85.74%, Expected total hits = 213