Saturday, April 2, 2011

Rhymes vs Sizemore, Issue Officially Beaten to Death

I know what everyone is thinking, “I cannot believe he used his article to rehash an issue that has been discussed literally (not literally) a million times.” And to that I say, fair point. However, this has been arguably the single biggest issue of debate for people following the Detroit Tigers after Sizemore was cut during spring training, and really even before that. For the purpose of this article, I am going to try and avoid offering proof that either Sizemore or Rhymes is the better player “right now” because I do not know the answer to that question. I will disclose right here, that I strongly suspect that Scott Sizemore is the better player right now and would be a superior option to Will Rhymes, but I cannot be sure.

The approach I want this article to take is to look at both players through the prism of expected value to the Detroit Tigers this season. Basically, I want to look at the decision based on the idea that we really do not know what either player will give the Tigers during the season, but we can make some reasonable guesses as to their range of possible production and assign differing probabilities to those ranges to get an expected value.

First let us take a look at Will Rhymes. He is 28 years old, and his triple slash in the majors is .299/.344/.407. In addition, he struck out in 8.4% of his at bats last season and walked in 6.6% of his plate appearances. Rhymes wOBA for the 2010 major league season was .329. His peak triple slash in the last three years in the minors was his 2010 season where he posted .305/.370/.415 line in 364 at bats, during that season he struck out in 9.6% of his at bats and walked in 8.6% of his plate appearances, both minor league highs. His wOBA for that season was .356. His major league equivalent triple slash from that 2010 minor league season would be .268/.325/.350.

Next we have Scott Sizemore. He is 26 years olds, and his triple slash from the majors last season was an ugly .224/.296/.336. He struck out in 28% of his at bats, and walked in 9.2% of his plate appearances. His major league wOBA was .284. Scott Sizemore’s average triple slash over his last three minor league seasons was .300/.378/.464. He struck out in 21.13% of his at bats and walked in 10.12% of his plate appearances. His minor league wOBA is roughly .388. And finally his major league equivalent triple slash from those three minor league seasons would be .269/.336/.417.
The reason I am using Sizemore’s average statistics from the past three seasons and Rhymes most recent minor league season is because I intend to give Rhymes all reasonably positive inferences for the purpose of this discussion. In addition I am using wOBA because, well, I think it is a great stat as it is essentially runs per plate appearance plus a marginal increase to equate the average OBP of the league to wOBA.

So did you catch all that? Anyway moving forward, now we must assign weights to different levels of performance. Just to make this simple, I will only provide three possible levels of performance and only do so using wOBA as the relevant measure. In addition, we assume that the difference in defense between Will Rhymes and Scott Sizemore is negligible (and it probably is).

First, for Scott Sizemore, we can assume it is at least possible he is as bad as he was last season, so the first level for Scott will be a wOBA of .285, which is well below average. Essentially at his lowest ebb, Scott is a replacement level (or slightly worse) player at 2b. Next let us assume it is possible Scott meets his major league equivalent production we garnered from his minor league time, essentially a Michael Cuddyer type hitter playing second base, his wOBA in that scenario is .329. Finally let us assume it is possible Scott Sizemore reaches every bit of his potential and produces just as he did in the minors. Adjusting for the major leagues, his wOBA would be roughly .367 in that scenario.

Next, for Will Rhymes, we can assume it is possible that he is well below average because his minor league equivalent statistics only equate to a slightly better than replacement level wOBA at the major league level, roughly .303. As such, although unlikely, it is possible Will Rhymes is essentially a replacement level player or worse, with a wOBA of .285 just like Scott Sizemore. Next we can assume Will Rhymes might produce as his major league equivalent production from his best season, a wOBA of .303. Finally, we can assume Will Rhymes could be every bit as good as he was in the 2010 minor league season at the major league level, which is slightly better than he was in the majors last season, and can produce a wOBA of .334.

Notice that Will Rhymes’ ceiling is basically his 2010 major league performance because he produced almost equivalently in the majors as he did in the minors during his best minor league season. Also notice that Scott Sizemore’s ceiling is higher at both of the higher levels mostly due to his minor league performance.

If we place heavy emphasis on major league performance and assume it is 45% likely that each player will essentially replicate his major league performance from last season, that means we are giving 45% weight to Sizemore’s lowest level and to Rhymes highest level. If it is then assumed Rhymes and Sizemore both have a slightly lower chance to move to the middle level, say 35%, we can then assign the remaining 20% to the chance Rhymes will be at his lowest level and Sizemore will reach his highest level.

The result looks something like this:

Sizemore EV = .45(.285) + .35(.329) + .2(.367) = .3168 wOBA
Rhymes EV = .45(.334) + .35(.303) + .2(.285) = .31335 wOBA

Therefore, at these levels, Scott Sizemore would be the preferred choice. To make Will Rhymes the correct decision for the Tigers from an expected value standpoint, we would need to raise the percentages of Rhymes likelihood for reaching his peak or intermediate value even more and/or lower Sizemore’s likelihood of reaching his peak or middle values even more.

Now I really did not know what would happen when I gave Rhymes every reasonably good inference and assigned wOBA’s and percentages accordingly, but I cannot say that I’m surprised that Sizemore wins out even at these levels. The point of this article is that when making baseball decisions based on uncertainties, it is probably best to weigh the potential performance of each player at all probable outcomes. Assuming the Tigers did this when they decided Will Rhymes should be the starting second baseman, that would lead me to conclude that they are fairly certain Rhymes can continue to produce as he did last year AND that Sizemore was likely to produce just as he did last year.

My own conclusion based on analyzing a high upside player with low probability of success, Sizemore, and a low upside player with a high probability of success, Rhymes, is that, in most cases, it is probably advantageous to take your chances with the high upside player. This of course is always contingent on the actual values assigned to potential production and probability. However, considering that your worst case scenario is probably only replacement level performance, it seems to be in the team’s best interest to go with a player who has a likely peak performance well above replacement level.

As a result, I find the decision to start Rhymes at second base really hard to justify from a pure expected value standpoint. Obviously I am ignoring some other possible reasons behind the decision. In addition, the percentages I assigned, though a reasonable guess in my opinion, are hardly based on exact science. However, I feel pretty confident, in any case, that the decision was still wrong. Let me know what you think.


  1. I am so sick of Detroit News, Michigan Live and other lame baseball news sources talk about the shallowest aspects of baseball. There was an article about Ajax hanging out with Pauly D from Jersey Shore, but more annoying is their love affair with AVG, RBI, ERA, W and HR. Man I just want to see some straight up sabermetric analysis about a big question that my team is trying to answer, THANK YOU. God knows the Tigers relied too much on inflated BABIPs without really thinking about the implications last year. And we saw those implications after the All-Star Break. 2011 will be doomed if we continue to choose players like Rhymes just because of their spunk and success in limited ABs.

    Anyway, this was a great article thank you! AL Central is a Top 5 Tiger's news source for me, you cut a lot of the stupid fluff out.

  2. Tyler,

    Thank YOU for reading and commenting with your nice words about the article.

    I actually thought I might be cutting out too much fluff and that the article might be a little dense. So I am definitely glad that is exactly what you wanted!

    Enjoy the games!